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SpectralSequences :: pruningMaps(SpectralSequencePage)

pruningMaps(SpectralSequencePage) -- compute the pruning maps on a spectral sequence page

Synopsis

Description

Returns the pruning maps which are cached in the process of pruning the spectral sequence page.

As a specific example consider the filtered complex $K$ below, obtained by multiplying the minimal free resolution of the rational quartic space curve by successive powers of the irrelevant ideal.

i1 : B = QQ[a..d];
i2 : J = ideal vars B;

o2 : Ideal of B
i3 : C = complete res monomialCurveIdeal(B,{1,3,4});
i4 : K = filteredComplex(J,C,4);

We compute an example of a pruning map below.

i5 : E = prune spectralSequence K;
i6 : pruningMaps E^2

o6 = {-7, 6} : subquotient (| 0 a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6 0 |, | a4bc-a5d a4b3-a6c a5c2-a4b2d a4c3-a4bd2 a3b2c-a4bd a3b4-a5bc a4bc2-a3b3d a3bc3-a3b2d2 a3bc2-a4cd a3b3c-a5c2 a4c3-a3b2cd a3c4-a3bcd2 a3bcd-a4d2 a3b3d-a5cd a4c2d-a3b2d2 a3c3d-a3bd3 a2b3c-a3b2d a2b5-a4b2c a3b2c2-a2b4d a2b2c3-a2b3d2 a2b2c2-a3bcd a2b4c-a4bc2 a3bc3-a2b3cd a2bc4-a2b2cd2 a2b2cd-a3bd2 a2b4d-a4bcd a3bc2d-a2b3d2 a2bc3d-a2b2d3 a2bc3-a3c2d a2b3c2-a4c3 a3c4-a2b2c2d a2c5-a2bc2d2 a2bc2d-a3cd2 a2b3cd-a4c2d a3c3d-a2b2cd2 a2c4d-a2bcd3 a2bcd2-a3d3 a2b3d2-a4cd2 a3c2d2-a2b2d3 a2c3d2-a2bd4 ab4c-a2b3d ab6-a3b3c a2b3c2-ab5d ab3c3-ab4d2 ab3c2-a2b2cd ab5c-a3b2c2 a2b2c3-ab4cd ab2c4-ab3cd2 ab3cd-a2b2d2 ab5d-a3b2cd a2b2c2d-ab4d2 ab2c3d-ab3d3 ab2c3-a2bc2d ab4c2-a3bc3 a2bc4-ab3c2d abc5-ab2c2d2 ab2c2d-a2bcd2 ab4cd-a3bc2d a2bc3d-ab3cd2 abc4d-ab2cd3 ab2cd2-a2bd3 ab4d2-a3bcd2 a2bc2d2-ab3d3 abc3d2-ab2d4 abc4-a2c3d ab3c3-a3c4 a2c5-ab2c3d ac6-abc3d2 abc3d-a2c2d2 ab3c2d-a3c3d a2c4d-ab2c2d2 ac5d-abc2d3 abc2d2-a2cd3 ab3cd2-a3c2d2 a2c3d2-ab2cd3 ac4d2-abcd4 abcd3-a2d4 ab3d3-a3cd3 a2c2d3-ab2d4 ac3d3-abd5 b5c-ab4d b7-a2b4c ab4c2-b6d b4c3-b5d2 b4c2-ab3cd b6c-a2b3c2 ab3c3-b5cd b3c4-b4cd2 b4cd-ab3d2 b6d-a2b3cd ab3c2d-b5d2 b3c3d-b4d3 b3c3-ab2c2d b5c2-a2b2c3 ab2c4-b4c2d b2c5-b3c2d2 b3c2d-ab2cd2 b5cd-a2b2c2d ab2c3d-b4cd2 b2c4d-b3cd3 b3cd2-ab2d3 b5d2-a2b2cd2 ab2c2d2-b4d3 b2c3d2-b3d4 b2c4-abc3d b4c3-a2bc4 abc5-b3c3d bc6-b2c3d2 b2c3d-abc2d2 b4c2d-a2bc3d abc4d-b3c2d2 bc5d-b2c2d3 b2c2d2-abcd3 b4cd2-a2bc2d2 abc3d2-b3cd3 bc4d2-b2cd4 b2cd3-abd4 b4d3-a2bcd3 abc2d3-b3d4 bc3d3-b2d5 bc5-ac4d b3c4-a2c5 ac6-b2c4d c7-bc4d2 bc4d-ac3d2 b3c3d-a2c4d ac5d-b2c3d2 c6d-bc3d3 bc3d2-ac2d3 b3c2d2-a2c3d2 ac4d2-b2c2d3 c5d2-bc2d4 bc2d3-acd4 b3cd3-a2c2d3 ac3d3-b2cd4 c4d3-bcd5 bcd4-ad5 b3d4-a2cd4 ac2d4-b2d5 c3d4-bd6 0 |) <----- 0 : {-5, 5}
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     {-7, 7} : subquotient ({2} | 0 0 0 0 -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 |, {2} | -a4b2 -a5c -a4bd -a4c2 -a3b3 -a4bc -a3b2d -a3bc2 -a3b2c -a4c2 -a3bcd -a3c3 -a3b2d -a4cd -a3bd2 -a3c2d -a2b4 -a3b2c -a2b3d -a2b2c2 -a2b3c -a3bc2 -a2b2cd -a2bc3 -a2b3d -a3bcd -a2b2d2 -a2bc2d -a2b2c2 -a3c3 -a2bc2d -a2c4  -a2b2cd -a3c2d -a2bcd2 -a2c3d -a2b2d2 -a3cd2 -a2bd3 -a2c2d2 -ab5 -a2b3c -ab4d -ab3c2 -ab4c -a2b2c2 -ab3cd -ab2c3 -ab4d -a2b2cd -ab3d2 -ab2c2d -ab3c2 -a2bc3 -ab2c2d -abc4  -ab3cd -a2bc2d -ab2cd2 -abc3d -ab3d2 -a2bcd2 -ab2d3 -abc2d2 -ab2c3 -a2c4 -abc3d -ac5  -ab2c2d -a2c3d -abc2d2 -ac4d  -ab2cd2 -a2c2d2 -abcd3 -ac3d2 -ab2d3 -a2cd3 -abd4 -ac2d3 -b6 -ab4c -b5d -b4c2 -b5c -ab3c2 -b4cd -b3c3 -b5d -ab3cd -b4d2 -b3c2d -b4c2 -ab2c3 -b3c2d -b2c4  -b4cd -ab2c2d -b3cd2 -b2c3d -b4d2 -ab2cd2 -b3d3  -b2c2d2 -b3c3 -abc4 -b2c3d -bc5  -b3c2d -abc3d -b2c2d2 -bc4d  -b3cd2 -abc2d2 -b2cd3 -bc3d2 -b3d3 -abcd3 -b2d4 -bc2d3 -b2c4 -ac5 -bc4d -c6  -b2c3d -ac4d -bc3d2 -c5d  -b2c2d2 -ac3d2 -bc2d3 -c4d2 -b2cd3 -ac2d3 -bcd4 -c3d3 -b2d4 -acd4 -bd5 -c2d4 0 0 0 0 |) <----- 0 : {-5, 6}
                            {3} | 0 0 0 0 a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0 0 0 0 |  {3} | a4c   a4d  0     0     a3bc  a3bd  0      0      a3c2   a3cd  0      0     a3cd   a3d2  0      0      a2b2c a2b2d  0      0       a2bc2  a2bcd  0       0      a2bcd  a2bd2  0       0       a2c3    a2c2d 0       0      a2c2d   a2cd2  0       0      a2cd2   a2d3   0      0       ab3c ab3d   0     0      ab2c2 ab2cd   0      0      ab2cd ab2d2   0      0       abc3   abc2d  0       0      abc2d  abcd2   0       0      abcd2  abd3    0      0       ac4    ac3d  0      0     ac3d    ac2d2  0       0      ac2d2   acd3    0      0      acd3   ad4    0     0      b4c b4d   0    0     b3c2 b3cd   0     0     b3cd b3d2   0     0      b2c3  b2c2d  0      0      b2c2d b2cd2   0      0      b2cd2 b2d3    0      0       bc4   bc3d  0      0     bc3d   bc2d2  0       0      bc2d2  bcd3    0      0      bcd3  bd4    0     0      c5    c4d  0     0    c4d    c3d2  0      0     c3d2    c2d3   0      0     c2d3   cd4    0     0     cd4   d5    0    0     0 0 0 0 |     0
                            {3} | 0 0 0 0 a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 |  {3} | a5    a4b  -a4c  -a4d  a4b   a3b2  -a3bc  -a3bd  a4c    a3bc  -a3c2  -a3cd a4d    a3bd  -a3cd  -a3d2  a3b2  a2b3   -a2b2c -a2b2d  a3bc   a2b2c  -a2bc2  -a2bcd a3bd   a2b2d  -a2bcd  -a2bd2  a3c2    a2bc2 -a2c3   -a2c2d a3cd    a2bcd  -a2c2d  -a2cd2 a3d2    a2bd2  -a2cd2 -a2d3   a2b3 ab4    -ab3c -ab3d  a2b2c ab3c    -ab2c2 -ab2cd a2b2d ab3d    -ab2cd -ab2d2  a2bc2  ab2c2  -abc3   -abc2d a2bcd  ab2cd   -abc2d  -abcd2 a2bd2  ab2d2   -abcd2 -abd3   a2c3   abc3  -ac4   -ac3d a2c2d   abc2d  -ac3d   -ac2d2 a2cd2   abcd2   -ac2d2 -acd3  a2d3   abd3   -acd3 -ad4   ab4 b5    -b4c -b4d  ab3c b4c    -b3c2 -b3cd ab3d b4d    -b3cd -b3d2  ab2c2 b3c2   -b2c3  -b2c2d ab2cd b3cd    -b2c2d -b2cd2 ab2d2 b3d2    -b2cd2 -b2d3   abc3  b2c3  -bc4   -bc3d abc2d  b2c2d  -bc3d   -bc2d2 abcd2  b2cd2   -bc2d2 -bcd3  abd3  b2d3   -bcd3 -bd4   ac4   bc4  -c5   -c4d ac3d   bc3d  -c4d   -c3d2 ac2d2   bc2d2  -c3d2  -c2d3 acd3   bcd3   -c2d3 -cd4  ad4   bd4   -cd4 -d5   0 0 0 0 |
                            {3} | 0 0 0 0 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0 0 0 0 |  {3} | 0     0    a5    a4b   0     0     a4b    a3b2   0      0     a4c    a3bc  0      0     a4d    a3bd   0     0      a3b2   a2b3    0      0      a3bc    a2b2c  0      0      a3bd    a2b2d   0       0     a3c2    a2bc2  0       0      a3cd    a2bcd  0       0      a3d2   a2bd2   0    0      a2b3  ab4    0     0       a2b2c  ab3c   0     0       a2b2d  ab3d    0      0      a2bc2   ab2c2  0      0       a2bcd   ab2cd  0      0       a2bd2  ab2d2   0      0     a2c3   abc3  0       0      a2c2d   abc2d  0       0       a2cd2  abcd2  0      0      a2d3  abd3   0   0     ab4  b5    0    0      ab3c  b4c   0    0      ab3d  b4d    0     0      ab2c2  b3c2   0     0       ab2cd  b3cd   0     0       ab2d2  b3d2    0     0     abc3   b2c3  0      0      abc2d   b2c2d  0      0       abcd2  b2cd2  0     0      abd3  b2d3   0     0    ac4   bc4  0      0     ac3d   bc3d  0       0      ac2d2  bc2d2 0      0      acd3  bcd3  0     0     ad4  bd4   0 0 0 0 |

     {-7, 8} : subquotient ({4} | 0 0 0 0 a4d  a3bd  a3cd  a3d2  a2b2d  a2bcd  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd3   ac3d  ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d2  bcd3   bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |, {4} | a4d  a3bd  a3cd  a3d2  a2b2d  a2bcd  a2bd2  a2c2d  a2cd2  a2d3   ab3d  ab2cd  ab2d2  abc2d  abcd2  abd3   ac3d  ac2d2  acd3   ad4   b4d  b3cd  b3d2  b2c2d b2cd2  b2d3   bc3d  bc2d2  bcd3   bd4   c4d  c3d2  c2d3   cd4   d5   0 0 0 0 |) <----- 0 : {-5, 7}
                            {4} | 0 0 0 0 -a4c -a3bc -a3c2 -a3cd -a2b2c -a2bc2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -abcd2 -ac4  -ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3d  -bc2d2 -bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |  {4} | -a4c -a3bc -a3c2 -a3cd -a2b2c -a2bc2 -a2bcd -a2c3  -a2c2d -a2cd2 -ab3c -ab2c2 -ab2cd -abc3  -abc2d -abcd2 -ac4  -ac3d  -ac2d2 -acd3 -b4c -b3c2 -b3cd -b2c3 -b2c2d -b2cd2 -bc4  -bc3d  -bc2d2 -bcd3 -c5  -c4d  -c3d2  -c2d3 -cd4 0 0 0 0 |     0
                            {4} | 0 0 0 0 -a4b -a3b2 -a3bc -a3bd -a2b3  -a2b2c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab2d2 -abc3 -abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c2d -b2cd2 -b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |  {4} | -a4b -a3b2 -a3bc -a3bd -a2b3  -a2b2c -a2b2d -a2bc2 -a2bcd -a2bd2 -ab4  -ab3c  -ab3d  -ab2c2 -ab2cd -ab2d2 -abc3 -abc2d -abcd2 -abd3 -b5  -b4c  -b4d  -b3c2 -b3cd  -b3d2  -b2c3 -b2c2d -b2cd2 -b2d3 -bc4 -bc3d -bc2d2 -bcd3 -bd4 0 0 0 0 |
                            {4} | 0 0 0 0 a5   a4b   a4c   a4d   a3b2   a3bc   a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2bd2  a2c3  a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2d  abcd2  abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |  {4} | a5   a4b   a4c   a4d   a3b2   a3bc   a3bd   a3c2   a3cd   a3d2   a2b3  a2b2c  a2b2d  a2bc2  a2bcd  a2bd2  a2c3  a2c2d  a2cd2  a2d3  ab4  ab3c  ab3d  ab2c2 ab2cd  ab2d2  abc3  abc2d  abcd2  abd3  ac4  ac3d  ac2d2  acd3  ad4  0 0 0 0 |

     {-7, 9} : image 0 <----- 0 : {-5, 8}
                          0

     {-7, 10} : 0 <----- 0 : {-5, 9}
                     0

     {-2, 1} : cokernel | bc-ad b3-a2c ac2-b2d c3-bd2 a b c d | <--------- cokernel | d c b a | : {0, 0}
                                                                   | 1 |

     {-2, 2} : cokernel {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 | <------------------- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | : {0, 1}
                        {3} | c   d   0   0   0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |    {2} | 1 0 0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
                        {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |    {3} | 0 1 0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
                        {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |    {3} | 0 0 1 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
                                                                                   {3} | 0 0 0 1 |

     {-2, 3} : subquotient ({4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {4} | d  a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |) <----- 0 : {0, 2}
                            {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |  {4} | -c 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 |     0
                            {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {4} | -b 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |
                            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {4} | a  0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |

     {-2, 4} : subquotient ({5} | d c b a a b c d |, {5} | a b c d |) <----- 0 : {0, 3}
                                                                         0

     {-2, 5} : 0 <----- 0 : {0, 4}
                    0

     {-3, 2} : subquotient (| a b c d bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a2 ab ac ad b2 bc bd c2 cd d2 |) <------------------- cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 | : {-1, 1}
                                                                                                                                                                     {1} | 1 0 0 0 |            {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
                                                                                                                                                                     {1} | 0 1 0 0 |            {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
                                                                                                                                                                     {1} | 0 0 1 0 |            {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
                                                                                                                                                                     {1} | 0 0 0 1 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {3} | 0 0 0 0 |
                                                                                                                                                                     {3} | 0 0 0 0 |
                                                                                                                                                                     {3} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |
                                                                                                                                                                     {2} | 0 0 0 0 |

     {-3, 3} : subquotient ({2} | a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {2} | -b2 -ac -bd -c2 a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |) <------------------------------------- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-1, 2}
                            {3} | 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {3} | c   d   0   0   0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     {3} | 1 0 0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                            {3} | 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {3} | a   b   -c  -d  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |     {4} | 0 1 0 0 0 0  0 0 0 0  0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                            {3} | 0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {3} | 0   0   a   b   0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |     {4} | 0 0 0 0 0 -1 0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  1 0 0 0  0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {3} | 0 0 1 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 1 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 -1 0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  1 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {3} | 0 0 0 0 1 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 1 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {3} | 0 0 0 0 0 0  0 0 1 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 1 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {4} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                 {5} | 0 0 0 0 0 0  0 0 0 0  0 0 |

     {-3, 4} : subquotient ({4} | d  ad ac ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |, {4} | d  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  |) <----- 0 : {-1, 3}
                            {4} | -c 0  0  0  0  ad ac ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  0  0  0  0  -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |  {4} | -c 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  |     0
                            {4} | -b 0  0  0  0  0  0  0  0  ad ac ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad 0  0  0  0  -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |  {4} | -b 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  |
                            {4} | a  0  0  0  0  0  0  0  0  0  0  0  0  ad ac ab a2 0  0  0  0  0  0  0  0  0  0  0  0  bd bc b2 ab 0  0  0  0  0  0  0  0  0  0  0  0  cd c2 bc ac 0  0  0  0  0  0  0  0  d2 cd bd ad a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |  {4} | a  0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 |

     {-3, 5} : subquotient ({5} | ad ac ab a2 bd bc b2 ab cd c2 bc ac d2 cd bd ad a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |) <----- 0 : {-1, 4}
                                                                                                                                                             0

     {-3, 6} : 0 <----- 0 : {-1, 5}
                    0

     {-4, 3} : subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 abc-a2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | abc-a2d ab3-a3c a2c2-ab2d ac3-abd2 b2c-abd b4-a2bc abc2-b3d bc3-b2d2 bc2-acd b3c-a2c2 ac3-b2cd c4-bcd2 bcd-ad2 b3d-a2cd ac2d-b2d2 c3d-bd3 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <------------------------------- cokernel {2} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 2}
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 1 0 0 0 0 0 0 0 0 0 |            {2} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 1 0 0 0 0 0 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 1 0 0 0 0 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 1 0 0 0 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 1 0 0 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 0 1 0 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 0 0 1 0 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 0 0 0 1 0 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 0 0 0 0 1 0 |            {2} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {2} | 0 0 0 0 0 0 0 0 0 1 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {4} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   {3} | 0 0 0 0 0 0 0 0 0 0 |

     {-4, 4} : subquotient ({2} | a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  0  -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {2} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |) <------------------------------------------------------------------- cokernel {4} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-2, 3}
                            {3} | 0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  0  ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {3} | ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   0    0    0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |     {4} | 1 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                            {3} | 0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0  a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {3} | a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |     {5} | 0 1 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                            {3} | 0  0  0  a2 0  0  0  ab 0  0  0  ac 0  0  0  ad 0  0  0  b2 0  0  0  bc 0  0  0  bd 0  0  0  c2 0  0  0  cd 0  0  0  d2 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {3} | 0    0    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |     {5} | 0 0 0 0 0 -1 0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 -1 0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {4} | 0 0 1 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 1 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 -1 0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 -1 0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {4} | 0 0 0 0 1 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  1 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {4} | 0 0 0 0 0 0  1 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |            {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {5} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     {6} | 0 0 0 0 0 0  0 0 0 0 0  0 0  0 0  0 0 0 0  0 0 0 0  0 0 |

     {-4, 5} : subquotient ({4} | ad  bd  cd  d2  a2d a2c a2b a3 0   0   0   0  0   0   0   0  0   0   0   0  abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   b2d b2c b3 ab2 0   0   0  0   0   0   0  0   0   0   0  0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   c2d c3 bc2 ac2 0   0  0   0   0   0  0   0   0   0  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0  0   0   0   0  0   0   0   ad  bd  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |, {4} | ad  bd  cd  d2  a3 0  0  0  a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0   b3 0  0  0  b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0   c3 0  0  0  c2d 0   0   0   cd2 0   0   0   d3 0  0  0  |) <----- 0 : {-2, 4}
                            {4} | -ac -bc -c2 -cd 0   0   0   0  a2d a2c a2b a3 0   0   0   0  0   0   0   0  0   0   0   0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0   0   0   0   0   0   0   0   0  0   b2d b2c b3 ab2 0   0   0  0   0   0   0  0   0   0   0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   0   0   0   0   0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0  0   0   cd2 c2d bcd acd 0   0   0   0   0   0   0   0   d3 cd2 bd2 ad2 0  0   0   0   0  0   0   0   -ac -bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |  {4} | -ac -bc -c2 -cd 0  a3 0  0  0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0   0  b3 0  0  0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0   0  c3 0  0  0   c2d 0   0   0   cd2 0   0   0  d3 0  0  |     0
                            {4} | -ab -b2 -bc -bd 0   0   0   0  0   0   0   0  a2d a2c a2b a3 0   0   0   0  0   0   0   0   0   0   0   0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0   0   0   0   0  0   0   0   0  0   b2d b2c b3 ab2 0   0   0  0   0   0   0   0   0   0   0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0   0   0   0   0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0  0   0   0   0   0   0   cd2 c2d bcd acd 0   0   0   0   0  0   0   0   d3 cd2 bd2 ad2 0  0   0   0   -ab -b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |  {4} | -ab -b2 -bc -bd 0  0  a3 0  0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0   0  0  b3 0  0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0   0  0  c3 0  0   0   c2d 0   0   0   cd2 0   0  0  d3 0  |
                            {4} | a2  ab  ac  ad  0   0   0   0  0   0   0   0  0   0   0   0  a2d a2c a2b a3 0   0   0   0   0   0   0   0   0   0   0   0   abd abc ab2 a2b 0   0   0   0   0   0   0   0   0   0   0   0   acd ac2 abc a2c 0   0   0   0   0   0   0   0   ad2 acd abd a2d 0   0   0  0   0   0   0  0   0   0   0  0   b2d b2c b3 ab2 0   0   0   0   0   0   0   0   0   0   0   0   bcd bc2 b2c abc 0   0   0   0   0   0   0   0   bd2 bcd b2d abd 0   0  0   0   0   0  0   0   0   0  0   0   c2d c3 bc2 ac2 0   0   0   0   0   0   0   0   cd2 c2d bcd acd 0  0   0   0   0  0   0   0   d3 cd2 bd2 ad2 a2  ab  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |  {4} | a2  ab  ac  ad  0  0  0  a3 0   0   0   a2b 0   0   0   a2c 0   0   0   a2d 0   0   0   ab2 0   0   0   abc 0   0   0   abd 0   0   0   ac2 0   0   0   acd 0   0   0   ad2 0  0  0  b3 0   0   0   b2c 0   0   0   b2d 0   0   0   bc2 0   0   0   bcd 0   0   0   bd2 0  0  0  c3 0   0   0   c2d 0   0   0   cd2 0  0  0  d3 |

     {-4, 6} : subquotient ({5} | a2d a2c a2b a3 abd abc ab2 a2b acd ac2 abc a2c ad2 acd abd a2d b2d b2c b3 ab2 bcd bc2 b2c abc bd2 bcd b2d abd c2d c3 bc2 ac2 cd2 c2d bcd acd d3 cd2 bd2 ad2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, {5} | a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |) <----- 0 : {-2, 5}
                                                                                                                                                                                                                                                                                                                                                                     0

     {-4, 7} : 0 <----- 0 : {-2, 6}
                    0

     {-5, 4} : subquotient (| a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, | a2bc-a3d a2b3-a4c a3c2-a2b2d a2c3-a2bd2 ab2c-a2bd ab4-a3bc a2bc2-ab3d abc3-ab2d2 abc2-a2cd ab3c-a3c2 a2c3-ab2cd ac4-abcd2 abcd-a2d2 ab3d-a3cd a2c2d-ab2d2 ac3d-abd3 b3c-ab2d b5-a2b2c ab2c2-b4d b2c3-b3d2 b2c2-abcd b4c-a2bc2 abc3-b3cd bc4-b2cd2 b2cd-abd2 b4d-a2bcd abc2d-b3d2 bc3d-b2d3 bc3-ac2d b3c2-a2c3 ac4-b2c2d c5-bc2d2 bc2d-acd2 b3cd-a2c2d ac3d-b2cd2 c4d-bcd3 bcd2-ad3 b3d2-a2cd2 ac2d2-b2d3 c3d2-bd4 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <--------------------------------------------------- cokernel {3} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | : {-3, 3}
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {3} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 |            {3} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

     {-5, 5} : subquotient ({2} | 0 a2b2 a2bd a2bd 0 a3c  a3c  a2c2 a2b2 ab3  ab2d ab2d a2bd a2bc a2bc a2bc abc2 abc2 a2c2 ab2c ab2c abcd abcd abcd 0       abd2 ac3  abd2 0 a2cd a2cd a2cd ac2d ac2d ab3  ab2c b4   b3d  b3d  ab2d 0        b2c2 b2c2 abc2 b3c  b3c  b2cd b2cd b2cd abcd 0       b2d2 bc3  b2d2 abd2 0       bc2d bc2d bc3  ac3  0       0        bc2d ac2d 0       bcd2 bcd2 c4   bcd2 0       bd3  c3d  c3d  0 bd3  0 acd2 acd2 acd2 c2d2 c2d2 0 0 0         0         0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 0          0          0 0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0         0          0         0              0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {2} | -a2b2 -a3c -a2bd -a2c2 -ab3 -a2bc -ab2d -abc2 -ab2c -a2c2 -abcd -ac3 -ab2d -a2cd -abd2 -ac2d -b4 -ab2c -b3d -b2c2 -b3c -abc2 -b2cd -bc3 -b3d -abcd -b2d2 -bc2d -b2c2 -ac3 -bc2d -c4  -b2cd -ac2d -bcd2 -c3d -b2d2 -acd2 -bd3 -c2d2 a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |) <----- 0 : {-3, 4}
                            {3} | 0 -a2c 0    0    0 -a2d -a2d 0    -a2c -abc 0    0    0    -abd -abd -abd 0    0    0    -ac2 -ac2 0    0    0    acd     0    0    0    0 -ad2 -ad2 -ad2 0    0    -abc -ac2 -b2c 0    0    0    -ac2+b2d 0    0    0    -bc2 -bc2 0    0    0    0    bcd     0    0    0    0    bd2     0    0    0    0    c3      0        0    0    c2d     0    0    0    0    cd2     0    0    0    0 0    0 -d3  -d3  -d3  0    0    0 0 -a2cd     -a2cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2+ab2d 0 -abcd      -abcd      0 0 0 0 0 0 -ac3+abd2 0 0 0 0 0 0 0 0 0 -abc2+b3d -a2c2+ab2d -ac3+abd2 -ac3+b2cd+abd2 0 0 0 0 0 -bc3+ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c   a2d  0     0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {3} | a2c   a2d  0     0     abc  abd   0     0     ac2   acd   0     0    acd   ad2   0     0     b2c b2d   0    0     bc2  bcd   0     0    bcd  bd2   0     0     c3    c2d  0     0    c2d   cd2   0     0    cd2   d3    0    0     0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |     0
                            {3} | 0 -a3  a2c  a2c  0 -a2b -a2b a2d  -a3  -a2b abc  abc  a2c  -ab2 -ab2 -ab2 abd  abd  a2d  -a2c -a2c ac2  ac2  ac2  abc+a2d acd  acd  acd  0 -abd -abd -abd ad2  ad2  -a2b -a2c -ab2 b2c  b2c  abc  b3-a2c   b2d  b2d  abd  -abc -abc bc2  bc2  bc2  ac2  b2c+abd bcd  bcd  bcd  acd  ac2+b2d bd2  bd2  bcd  acd  ac2+b2d c3-bd2   bd2  ad2  bc2+acd c2d  c2d  c2d  c2d  bcd+ad2 cd2  cd2  cd2  0 cd2  0 -bd2 -bd2 -bd2 d3   d3   0 0 -a2bc-a3d -a2bc-a3d 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3-a3c    0 -ab2c-a2bd -ab2c-a2bd 0 0 0 0 0 0 0         0 0 0 0 0 0 0 0 0 b4-a2bc   ab3-a3c    0         b3c+ab2d       0 0 0 0 0 -b3d+a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {3} | a3    a2b  -a2c  -a2d  a2b  ab2   -abc  -abd  a2c   abc   -ac2  -acd a2d   abd   -acd  -ad2  ab2 b3    -b2c -b2d  abc  b2c   -bc2  -bcd abd  b2d   -bcd  -bd2  ac2   bc2  -c3   -c2d acd   bcd   -c2d  -cd2 ad2   bd2   -cd2 -d3   0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |
                            {3} | 0 0    -a3  -a3  0 0    0    -a2b 0    0    -a2b -a2b -a3  0    0    0    -ab2 -ab2 -a2b 0    0    -a2c -a2c -a2c -a2b    -a2d -abc -a2d 0 0    0    0    -abd -abd 0    0    0    -ab2 -ab2 -a2b 0        -b3  -b3  -ab2 0    0    -abc -abc -abc -a2c -ab2    -abd -b2c -abd -a2d -a2c    -b2d -b2d -b2c -abc -b3     -ac2+b2d -b2d -abd -abc    -acd -acd -bc2 -acd -abd    -ad2 -bcd -bcd 0 -ad2 0 0    0    0    -bd2 -bd2 0 0 a3b       a3b       0 0 0 0 0 0 0 0 0 0 0 0 0 0          0 a2b2       a2b2       0 0 0 0 0 0 ab3-a3c   0 0 0 0 0 0 0 0 0 0         0          ab3-a3c   -a3c           0 0 0 0 0 b4-a2bc   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a3    a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {3} | 0     0    a3    a2b   0    0     a2b   ab2   0     0     a2c   abc  0     0     a2d   abd   0   0     ab2  b3    0    0     abc   b2c  0    0     abd   b2d   0     0    ac2   bc2  0     0     acd   bcd  0     0     ad2  bd2   0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |

     {-5, 6} : subquotient ({4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a3d  0 0 -a2bd 0 0 0 0 -a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2d -a2bd 0 0 0 -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2d -abcd -a2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b3d -ab2d 0 0 0 -b2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -bc2d -b2cd -abcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c3d -bc2d -ac2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |, {4} | a2d  abd  acd  ad2  b2d  bcd  bd2  c2d  cd2  d3   a4 0  0  0  a3b 0   0   0   a3c 0   0   0   a3d 0   0   0   a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0    ab3 0   0   0   ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0    ac3 0   0   0   ac2d 0    0    0    acd2 0    0    0    ad3 0   0   0   b4 0  0  0  b3c 0   0   0   b3d 0   0   0   b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0    bc3 0   0   0   bc2d 0    0    0    bcd2 0    0    0    bd3 0   0   0   c4 0  0  0  c3d 0   0   0   c2d2 0    0    0    cd3 0   0   0   d4 0  0  0  |) <----- 0 : {-3, 5}
                            {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 -a3c 0 0 a2bc  0 0 0 0 a2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab2c  a2bc  0 0 0 abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac3   abc2  a2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c  ab2c  0 0 0 b2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc3   b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c4   bc3   ac3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |  {4} | -a2c -abc -ac2 -acd -b2c -bc2 -bcd -c3  -c2d -cd2 0  a4 0  0  0   a3b 0   0   0   a3c 0   0   0   a3d 0   0   0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0    0   ab3 0   0   0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0    0   ac3 0   0   0    ac2d 0    0    0    acd2 0    0    0   ad3 0   0   0  b4 0  0  0   b3c 0   0   0   b3d 0   0   0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0    0   bc3 0   0   0    bc2d 0    0    0    bcd2 0    0    0   bd3 0   0   0  c4 0  0  0   c3d 0   0   0    c2d2 0    0    0   cd3 0   0   0  d4 0  0  |     0
                            {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 -a3b 0 0 a2b2  0 0 0 0 a2bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3   a2b2  0 0 0 ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc2  ab2c  a2bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b4   ab3   0 0 0 b3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c2  b3c   ab2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc3  b2c2  abc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |  {4} | -a2b -ab2 -abc -abd -b3  -b2c -b2d -bc2 -bcd -bd2 0  0  a4 0  0   0   a3b 0   0   0   a3c 0   0   0   a3d 0   0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0    0   0   ab3 0   0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0    0   0   ac3 0   0    0    ac2d 0    0    0    acd2 0    0   0   ad3 0   0  0  b4 0  0   0   b3c 0   0   0   b3d 0   0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0    0   0   bc3 0   0    0    bc2d 0    0    0    bcd2 0    0   0   bd3 0   0  0  c4 0  0   0   c3d 0   0    0    c2d2 0    0   0   cd3 0   0  0  d4 0  |
                            {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  a4   0 0 -a3b  0 0 0 0 -a3c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2 -a3b  0 0 0 -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2 -a2bc -a3c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3 -a2b2 0 0 0 -ab2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc2 -ab2c -a2bc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac3 -abc2 -a2c2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |  {4} | a3   a2b  a2c  a2d  ab2  abc  abd  ac2  acd  ad2  0  0  0  a4 0   0   0   a3b 0   0   0   a3c 0   0   0   a3d 0    0    0    a2b2 0    0    0    a2bc 0    0    0    a2bd 0    0    0    a2c2 0    0    0    a2cd 0    0    0    a2d2 0   0   0   ab3 0    0    0    ab2c 0    0    0    ab2d 0    0    0    abc2 0    0    0    abcd 0    0    0    abd2 0   0   0   ac3 0    0    0    ac2d 0    0    0    acd2 0   0   0   ad3 0  0  0  b4 0   0   0   b3c 0   0   0   b3d 0    0    0    b2c2 0    0    0    b2cd 0    0    0    b2d2 0   0   0   bc3 0    0    0    bc2d 0    0    0    bcd2 0   0   0   bd3 0  0  0  c4 0   0   0   c3d 0    0    0    c2d2 0   0   0   cd3 0  0  0  d4 |

     {-5, 7} : subquotient ({5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |, {5} | a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 |) <----- 0 : {-3, 6}
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 0

     {-5, 8} : 0 <----- 0 : {-3, 7}
                    0

     {-6, 5} : subquotient (| a4 a3b a3c a3d a2b2 a2bc a2bd a2c2 a2cd a2d2 ab3 ab2c ab2d abc2 abcd abd2 ac3 ac2d acd2 ad3 b4 b3c b3d b2c2 b2cd b2d2 bc3 bc2d bcd2 bd3 c4 c3d c2d2 cd3 d4 a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0 |, | a3bc-a4d a3b3-a5c a4c2-a3b2d a3c3-a3bd2 a2b2c-a3bd a2b4-a4bc a3bc2-a2b3d a2bc3-a2b2d2 a2bc2-a3cd a2b3c-a4c2 a3c3-a2b2cd a2c4-a2bcd2 a2bcd-a3d2 a2b3d-a4cd a3c2d-a2b2d2 a2c3d-a2bd3 ab3c-a2b2d ab5-a3b2c a2b2c2-ab4d ab2c3-ab3d2 ab2c2-a2bcd ab4c-a3bc2 a2bc3-ab3cd abc4-ab2cd2 ab2cd-a2bd2 ab4d-a3bcd a2bc2d-ab3d2 abc3d-ab2d3 abc3-a2c2d ab3c2-a3c3 a2c4-ab2c2d ac5-abc2d2 abc2d-a2cd2 ab3cd-a3c2d a2c3d-ab2cd2 ac4d-abcd3 abcd2-a2d3 ab3d2-a3cd2 a2c2d2-ab2d3 ac3d2-abd4 b4c-ab3d b6-a2b3c ab3c2-b5d b3c3-b4d2 b3c2-ab2cd b5c-a2b2c2 ab2c3-b4cd b2c4-b3cd2 b3cd-ab2d2 b5d-a2b2cd ab2c2d-b4d2 b2c3d-b3d3 b2c3-abc2d b4c2-a2bc3 abc4-b3c2d bc5-b2c2d2 b2c2d-abcd2 b4cd-a2bc2d abc3d-b3cd2 bc4d-b2cd3 b2cd2-abd3 b4d2-a2bcd2 abc2d2-b3d3 bc3d2-b2d4 bc4-ac3d b3c3-a2c4 ac5-b2c3d c6-bc3d2 bc3d-ac2d2 b3c2d-a2c3d ac4d-b2c2d2 c5d-bc2d3 bc2d2-acd3 b3cd2-a2c2d2 ac3d2-b2cd3 c4d2-bcd4 bcd3-ad4 b3d3-a2cd3 ac2d3-b2d4 c3d3-bd5 0 |) <--------------------------------------------------------------------------------- cokernel {4} | -d -b -d -c 0  0  -d 0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c2  -ac 0   0   -cd -ad 0   0   0   -d2 -bd 0   0   0   0   0   0   0   0   0   0   0   0   0   | : {-4, 4}
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | c  a  0  0  0  -d 0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -bd b2  -d2 0   0   0   0   0   0   0   0   0   0   0   0   0   -d2 -bd 0   0   0   0   0   0   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  b  a  -d 0  0  0  0  0  -d 0  0  0  0  0  -d -c 0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   c2  cd  0   0   0   0   -d2 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  c  b  a  0  0  -d 0  0  0  -d 0  0  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   -d2 0   0   0   0   0   0   0   -d2 0   0   0   0   0   0   0   0   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  c  a  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  -d -b 0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   -d2 bd  b2  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   0   0   0   -d2 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  c  b  a  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  -d 0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  -d 0  0  0  0  -d 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0   -d2 0   0   0   -d2 0   0   0   0   0   |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {4} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |            {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d  c  b  a  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   |
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {5} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                {0} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |

     {-6, 6} : subquotient ({2} | 0 a3b2 a3bd a3bd 0 a4c  a4c  a3c2 a3b2 a2b3  a2b2d a2b2d a3bd a3bc  a3bc  a3bc  a2bc2 a2bc2 a3c2 a2b2c a2b2c a2bcd a2bcd a2bcd 0        a2bd2 a2c3  a2bd2 0 a3cd  a3cd  a3cd  a2c2d a2c2d a2b3  a2b2c ab4   ab3d  ab3d  a2b2d 0          ab2c2 ab2c2 a2bc2 ab3c  ab3c  ab2cd ab2cd ab2cd a2bcd 0         ab2d2 abc3  ab2d2 a2bd2 0         abc2d abc2d abc3  a2c3  0         0          abc2d a2c2d 0         abcd2 abcd2 ac4   abcd2 0         abd3  ac3d  ac3d  abd3  0 a2cd2 a2cd2 a2cd2 ac2d2 ac2d2 ab4   ab3c  b5   b4d  b4d  ab3d  0         b3c2 b3c2 ab2c2 b4c   b4c   b3cd  b3cd  b3cd  ab2cd 0        b3d2  b2c3 b3d2  ab2d2 0        b2c2d b2c2d b2c3 abc3  0        0         b2c2d abc2d 0         b2cd2 b2cd2 bc4   b2cd2 abcd2 0         b2d3  bc3d  bc3d  b2d3  abd3  0         bc2d2 bc2d2 c5             bc4   ac4   0              0         bc3d  ac3d  0         0          bc2d2 ac2d2 0         bcd3  bcd3  c4d   c4d   bcd3  0        bd4  c3d2  c3d2  0 bd4  0 acd3 acd3 acd3 c2d3 c2d3 0 0 0         0         0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 0           0           0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0           0           0           0                 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0          0           0           0                0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 0 0 0 0 |, {2} | -a3b2 -a4c -a3bd -a3c2 -a2b3 -a3bc -a2b2d -a2bc2 -a2b2c -a3c2 -a2bcd -a2c3 -a2b2d -a3cd -a2bd2 -a2c2d -ab4 -a2b2c -ab3d -ab2c2 -ab3c -a2bc2 -ab2cd -abc3 -ab3d -a2bcd -ab2d2 -abc2d -ab2c2 -a2c3 -abc2d -ac4  -ab2cd -a2c2d -abcd2 -ac3d -ab2d2 -a2cd2 -abd3 -ac2d2 -b5 -ab3c -b4d -b3c2 -b4c -ab2c2 -b3cd -b2c3 -b4d -ab2cd -b3d2 -b2c2d -b3c2 -abc3 -b2c2d -bc4  -b3cd -abc2d -b2cd2 -bc3d -b3d2 -abcd2 -b2d3 -bc2d2 -b2c3 -ac4 -bc3d -c5  -b2c2d -ac3d -bc2d2 -c4d  -b2cd2 -ac2d2 -bcd3 -c3d2 -b2d3 -acd3 -bd4 -c2d3 0 0 0 0 |) <----- 0 : {-4, 5}
                            {3} | 0 -a3c 0    0    0 -a3d -a3d 0    -a3c -a2bc 0     0     0    -a2bd -a2bd -a2bd 0     0     0    -a2c2 -a2c2 0     0     0     a2cd     0     0     0     0 -a2d2 -a2d2 -a2d2 0     0     -a2bc -a2c2 -ab2c 0     0     0     -a2c2+ab2d 0     0     0     -abc2 -abc2 0     0     0     0     abcd      0     0     0     0     abd2      0     0     0     0     ac3       0          0     0     ac2d      0     0     0     0     acd2      0     0     0     0     0 -ad3  -ad3  -ad3  0     0     -ab2c -abc2 -b3c 0    0    0     -abc2+b3d 0    0    0     -b2c2 -b2c2 0     0     0     0     b2cd     0     0    0     0     b2d2     0     0     0    0     bc3      0         0     0     bc2d      0     0     0     0     0     bcd2      0     0     0     0     0     bd3       0     0     0              0     0     c4             0         0     0     c3d       0          0     0     c2d2      0     0     0     0     0     cd3      0    0     0     0 0    0 -d4  -d4  -d4  0    0    0 0 -a3cd     -a3cd     0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2+a2b2d 0 -a2bcd      -a2bcd      0 0 0 0 0 0 -a2c3+a2bd2 0 0 0 0 0 0 0 0 0 -a2bc2+ab3d -a3c2+a2b2d -a2c3+a2bd2 -a2c3+ab2cd+a2bd2 0 0 0 0 0 -abc3+a2c2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2c2+b4d -a2bc2+ab3d -abc3+a2c2d -abc3+b3cd+a2c2d 0 0 0 0 0 -b2c3+abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   d4    0    0     0 0 0 0 |  {3} | a3c   a3d  0     0     a2bc  a2bd  0      0      a2c2   a2cd  0      0     a2cd   a2d2  0      0      ab2c ab2d   0     0      abc2  abcd   0      0     abcd  abd2   0      0      ac3    ac2d  0      0     ac2d   acd2   0      0     acd2   ad3    0     0      b3c b3d   0    0     b2c2 b2cd   0     0     b2cd b2d2   0     0      bc3   bc2d  0      0     bc2d  bcd2   0      0     bcd2  bd3    0     0      c4    c3d  0     0    c3d    c2d2  0      0     c2d2   cd3    0     0     cd3   d4    0    0     0 0 0 0 |     0
                            {3} | 0 -a4  a3c  a3c  0 -a3b -a3b a3d  -a4  -a3b  a2bc  a2bc  a3c  -a2b2 -a2b2 -a2b2 a2bd  a2bd  a3d  -a3c  -a3c  a2c2  a2c2  a2c2  a2bc+a3d a2cd  a2cd  a2cd  0 -a2bd -a2bd -a2bd a2d2  a2d2  -a3b  -a3c  -a2b2 ab2c  ab2c  a2bc  ab3-a3c    ab2d  ab2d  a2bd  -a2bc -a2bc abc2  abc2  abc2  a2c2  ab2c+a2bd abcd  abcd  abcd  a2cd  a2c2+ab2d abd2  abd2  abcd  a2cd  a2c2+ab2d ac3-abd2   abd2  a2d2  abc2+a2cd ac2d  ac2d  ac2d  ac2d  abcd+a2d2 acd2  acd2  acd2  acd2  0 -abd2 -abd2 -abd2 ad3   ad3   -a2b2 -a2bc -ab3 b3c  b3c  ab2c  b4-a2bc   b3d  b3d  ab2d  -ab2c -ab2c b2c2  b2c2  b2c2  abc2  b3c+ab2d b2cd  b2cd b2cd  abcd  abc2+b3d b2d2  b2d2  b2cd abcd  abc2+b3d bc3-b2d2  b2d2  abd2  b2c2+abcd bc2d  bc2d  bc2d  bc2d  ac2d  b2cd+abd2 bcd2  bcd2  bcd2  bcd2  acd2  ac2d+b2d2 bd3   bd3   bd3            bc2d  ac2d  b2cd+abd2      c4-bcd2   bcd2  acd2  ac2d+b2d2 c3d-bd3    bd3   ad3   bc2d+acd2 c2d2  c2d2  c2d2  c2d2  c2d2  bcd2+ad3 cd3  cd3   cd3   0 cd3  0 -bd3 -bd3 -bd3 d4   d4   0 0 -a3bc-a4d -a3bc-a4d 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3-a4c    0 -a2b2c-a3bd -a2b2c-a3bd 0 0 0 0 0 0 0           0 0 0 0 0 0 0 0 0 ab4-a3bc    a2b3-a4c    0           ab3c+a2b2d        0 0 0 0 0 -ab3d+a3cd  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b5-a2b2c   ab4-a3bc    -ab3d+a3cd  b4c+a3cd         0 0 0 0 0 -b4d+a2bcd  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0 0 0 0 |  {3} | a4    a3b  -a3c  -a3d  a3b   a2b2  -a2bc  -a2bd  a3c    a2bc  -a2c2  -a2cd a3d    a2bd  -a2cd  -a2d2  a2b2 ab3    -ab2c -ab2d  a2bc  ab2c   -abc2  -abcd a2bd  ab2d   -abcd  -abd2  a2c2   abc2  -ac3   -ac2d a2cd   abcd   -ac2d  -acd2 a2d2   abd2   -acd2 -ad3   ab3 b4    -b3c -b3d  ab2c b3c    -b2c2 -b2cd ab2d b3d    -b2cd -b2d2  abc2  b2c2  -bc3   -bc2d abcd  b2cd   -bc2d  -bcd2 abd2  b2d2   -bcd2 -bd3   ac3   bc3  -c4   -c3d ac2d   bc2d  -c3d   -c2d2 acd2   bcd2   -c2d2 -cd3  ad3   bd3   -cd3 -d4   0 0 0 0 |
                            {3} | 0 0    -a4  -a4  0 0    0    -a3b 0    0     -a3b  -a3b  -a4  0     0     0     -a2b2 -a2b2 -a3b 0     0     -a3c  -a3c  -a3c  -a3b     -a3d  -a2bc -a3d  0 0     0     0     -a2bd -a2bd 0     0     0     -a2b2 -a2b2 -a3b  0          -ab3  -ab3  -a2b2 0     0     -a2bc -a2bc -a2bc -a3c  -a2b2     -a2bd -ab2c -a2bd -a3d  -a3c      -ab2d -ab2d -ab2c -a2bc -ab3      -a2c2+ab2d -ab2d -a2bd -a2bc     -a2cd -a2cd -abc2 -a2cd -a2bd     -a2d2 -abcd -abcd -a2d2 0 0     0     0     -abd2 -abd2 0     0     0    -ab3 -ab3 -a2b2 0         -b4  -b4  -ab3  0     0     -ab2c -ab2c -ab2c -a2bc -ab3     -ab2d -b3c -ab2d -a2bd -a2bc    -b3d  -b3d  -b3c -ab2c -b4      -abc2+b3d -b3d  -ab2d -ab2c     -abcd -abcd -b2c2 -abcd -a2cd -ab2d     -abd2 -b2cd -b2cd -abd2 -a2d2 -a2cd     -b2d2 -b2d2 -bc3+ac2d-b2d2 -b2c2 -abc2 -b3c+a2c2-ab2d -ac3+b2cd -b2cd -abcd -b3d      -ac2d+b2d2 -b2d2 -abd2 -abcd     -acd2 -acd2 -bc2d -bc2d -acd2 -abd2    -ad3 -bcd2 -bcd2 0 -ad3 0 0    0    0    -bd3 -bd3 0 0 a4b       a4b       0 0 0 0 0 0 0 0 0 0 0 0 0 0           0 a3b2        a3b2        0 0 0 0 0 0 a2b3-a4c    0 0 0 0 0 0 0 0 0 0           0           a2b3-a4c    -a4c              0 0 0 0 0 ab4-a3bc    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0          0           ab4-a3bc    -a3bc            0 0 0 0 0 b5-a2b2c    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     0     ad3  bd3   0 0 0 0 |  {3} | 0     0    a4    a3b   0     0     a3b    a2b2   0      0     a3c    a2bc  0      0     a3d    a2bd   0    0      a2b2  ab3    0     0      a2bc   ab2c  0     0      a2bd   ab2d   0      0     a2c2   abc2  0      0      a2cd   abcd  0      0      a2d2  abd2   0   0     ab3  b4    0    0      ab2c  b3c   0    0      ab2d  b3d    0     0     abc2   b2c2  0     0      abcd   b2cd  0     0      abd2  b2d2   0     0    ac3   bc3  0      0     ac2d   bc2d  0      0      acd2  bcd2  0     0     ad3  bd3   0 0 0 0 |

     {-6, 7} : subquotient ({4} | a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   a4d  0 0 -a3bd 0 0 0 0 -a3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b2d -a3bd 0 0 0 -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c2d -a2bcd -a3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab3d -a2b2d 0 0 0 -ab2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc2d -ab2cd -a2bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac3d -abc2d -a2c2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b4d -ab3d 0 0 0 -b3cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2c2d -b3cd -ab2cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -bc3d -b2c2d -abc2d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c4d -bc3d -ac3d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |, {4} | a3d  a2bd  a2cd  a2d2  ab2d  abcd  abd2  ac2d  acd2  ad3   b3d  b2cd  b2d2  bc2d  bcd2  bd3   c3d  c2d2  cd3   d4   0 0 0 0 |) <----- 0 : {-4, 6}
                            {4} | -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 -a4c 0 0 a3bc  0 0 0 0 a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b2c  a3bc  0 0 0 a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2c3   a2bc2  a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab3c  a2b2c  0 0 0 ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc3   ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ac4   abc3   a2c3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b4c  ab3c  0 0 0 b3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c3   b3c2  ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4   b2c3   abc3   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c5   bc4   ac4   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |  {4} | -a3c -a2bc -a2c2 -a2cd -ab2c -abc2 -abcd -ac3  -ac2d -acd2 -b3c -b2c2 -b2cd -bc3  -bc2d -bcd2 -c4  -c3d  -c2d2 -cd3 0 0 0 0 |     0
                            {4} | -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 -a4b 0 0 a3b2  0 0 0 0 a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2b3   a3b2  0 0 0 a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a2bc2  a2b2c  a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab4   a2b3   0 0 0 ab3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ab2c2  ab3c   a2b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 abc3  ab2c2  a2bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b5   ab4   0 0 0 b4c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3c2   b4c   ab3c   0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c3  b3c2   ab2c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bc4  b2c3  abc3  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |  {4} | -a3b -a2b2 -a2bc -a2bd -ab3  -ab2c -ab2d -abc2 -abcd -abd2 -b4  -b3c  -b3d  -b2c2 -b2cd -b2d2 -bc3 -bc2d -bcd2 -bd3 0 0 0 0 |
                            {4} | a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  a5   0 0 -a4b  0 0 0 0 -a4c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3b2  -a4b  0 0 0 -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a3c2  -a3bc  -a4c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2b3 -a3b2  0 0 0 -a2b2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2bc2 -a2b2c -a3bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2c3 -a2bc2 -a3c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab4 -a2b3 0 0 0 -ab3c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2c2 -ab3c -a2b2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -abc3 -ab2c2 -a2bc2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ac4 -abc3 -a2c3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |  {4} | a4   a3b   a3c   a3d   a2b2  a2bc  a2bd  a2c2  a2cd  a2d2  ab3  ab2c  ab2d  abc2  abcd  abd2  ac3  ac2d  acd2  ad3  0 0 0 0 |

     {-6, 8} : image 0 <----- 0 : {-4, 7}
                          0

     {-6, 9} : 0 <----- 0 : {-4, 8}
                    0

o6 : PageMap

See also