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SpectralSequences :: minimalPresentation(SpectralSequencePage)

minimalPresentation(SpectralSequencePage) -- a minimal presentation of a spectral sequence page

Synopsis

Description

Returns a minimal presentation of the spectral sequence page.

If we fail to prune a spectral sequence then the out-put can be highly unintelligable.

As a specific example consider the filtered complex K below, obtained by multiplying the minimal free resolution of the rational quartic space curve by sucessive 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);

Compare some pruned and non-prunded pages the spectral sequence E below.

i5 : E = spectralSequence K;
i6 : E^3

     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
o6 = |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 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 0 |, | 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 0 |)|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 -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d 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} | -ab2 -a2c -abd -ac2 -b3 -abc -b2d -bc2 -b2c -ac2 -bcd -c3 -b2d -acd -bd2 -c2d 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  |)|subquotient ({4} | ad  bd  cd  d2  a2d  0 0 -abd 0 0 0 0 -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -b2d -abd 0 0 0 -bcd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -c2d -bcd -acd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d  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} | d  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  |)                                                                                  |subquotient ({5} | 0 0 0 0 0 0 ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 bd2 bcd b2d bc2 b2c b3 cd2 c2d c3 d3 a2 ab ac ad b2 bc bd c2 cd d2 |, {5} | a2 ab ac ad b2 bc bd c2 cd d2 |)                                                                                                                                                                                                                                                                                                                                                                                                                                       |0                                                                                                                                                                                                                  |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |             {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 ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   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} | ac   ad   0    0    bc  bd   0    0    c2   cd   0    0   cd   d2   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  | |             {4} | -ac -bc -c2 -cd -a2c 0 0 abc  0 0 0 0 ac2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b2c  abc  0 0 0 bc2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -c 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} | -c 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, 4}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |             {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 a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  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} | a2   ab   -ac  -ad  ab  b2   -bc  -bd  ac   bc   -c2  -cd ad   bd   -cd  -d2  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} | -ab -b2 -bc -bd -a2b 0 0 ab2  0 0 0 0 abc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3   ab2  0 0 0 b2c  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -b 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} | -b 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  |                                                                                   |{-1, 4}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{0, 4}                                                                                                                                                                                                             |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |             {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    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   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    a2   ab   0   0    ab   b2   0    0    ac   bc  0    0    ad   bd   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} | a2  ab  ac  ad  a3   0 0 -a2b 0 0 0 0 -a2c 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -ab2 -a2b 0 0 0 -abc 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -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 a  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} | a  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, 4}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |{-2, 4}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                   |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
     |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |subquotient (| 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 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 |, | 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 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 |)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |subquotient ({2} | 0 ab2 abd abd 0 a2c a2c ac2 ab2 b3  b2d b2d abd abc abc abc bc2 bc2 ac2 b2c b2c bcd bcd bcd 0     bd2 c3  0 bd2 0 acd acd acd c2d c2d 0 0 0        0        0 0 0 0 0 0 0 0 0 0 0 0 0 0        0 0        0        0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 -b2 -ac -bd -c2 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} | -b2 -ac -bd -c2 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  |)|subquotient ({4} | d  ad  0 0 -bd 0 0 0 0 -cd 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0   0   0   0  0   0   0   0   0   0   0   0   0  cd2 c2d c3 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  |)|subquotient ({5} | d2 cd bd ad c2 bc ac b2 ab a2 a b c d |, {5} | a b c d |)                                                                                                                                       |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |             {3} | 0 -ac 0   0   0 -ad -ad 0   -ac -bc 0   0   0   -bd -bd -bd 0   0   0   -c2 -c2 0   0   0   cd    0   0   0 0   0 -d2 -d2 -d2 0   0   0 0 -acd     -acd     0 0 0 0 0 0 0 0 0 0 0 0 0 -ac2+b2d 0 -bcd     -bcd     0 0 0 0 0 0 -c3+bd2 0 0 0 0 0 0 0 0 c   d   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} | c   d   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} | -c -ac 0 0 bc  0 0 0 0 c2  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0   0  ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0   0   0  bd2 bcd b2d bc2 b2c b3 0   0   0   0   0   0   0   0   0  0   0   0  cd2 0   0   0  0   0   0  d3 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  | |                                                                                                                                                                                                                   |
     |{-4, 3}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{-3, 3}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |             {3} | 0 -a2 ac  ac  0 -ab -ab ad  -a2 -ab bc  bc  ac  -b2 -b2 -b2 bd  bd  ad  -ac -ac c2  c2  c2  bc+ad cd  cd  0 cd  0 -bd -bd -bd d2  d2  0 0 -abc-a2d -abc-a2d 0 0 0 0 0 0 0 0 0 0 0 0 0 b3-a2c   0 -b2c-abd -b2c-abd 0 0 0 0 0 0 0       0 0 0 0 0 0 0 0 a   b   -c  -d  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} | a   b   -c  -d  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} | -b -ab 0 0 b2  0 0 0 0 bc  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0  ad2 acd abd a2d ac2 abc a2c ab2 a2b a3 0   0   0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0  bd2 bcd bc2 0   0   0   0   0   0  0   0   0  0   cd2 c2d c3 0   0   0  0  d3 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  | |{0, 3}                                                                                                                                                                                                             |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |             {3} | 0 0   -a2 -a2 0 0   0   -ab 0   0   -ab -ab -a2 0   0   0   -b2 -b2 -ab 0   0   -ac -ac -ac -ab   -ad -bc 0 -ad 0 0   0   0   -bd -bd 0 0 a2b      a2b      0 0 0 0 0 0 0 0 0 0 0 0 0 0        0 ab2      ab2      0 0 0 0 0 0 b3-a2c  0 0 0 0 0 0 0 0 0   0   a   b   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   a   b   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} | a  a2  0 0 -ab 0 0 0 0 -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   0  0   0   0   0   0   0   0   0   0   0  0   0   0   0   0   0   0   0   0   0  ad2 acd abd ac2 abc ab2 0   0   0   0   0   0  0   0   0   0   0   0  0   0   0   bd2 bcd b2d bc2 b2c b3 0   0   0  0   0   0   0  cd2 c2d c3 0  0  d3 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 | |                                                                                                                                                                                                                   |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                   |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |{-2, 3}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |{-1, 3}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |                                                                                                                                                                                                                   |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
     |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |subquotient (| a2 ab ac ad b2 bc bd c2 cd d2 bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |, | bc-ad b3-a2c ac2-b2d c3-bd2 a3 a2b a2c a2d ab2 abc abd ac2 acd ad2 b3 b2c b2d bc2 bcd bd2 c3 c2d cd2 d3 |)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |subquotient ({2} | ad ac ab a2 0 0 0 bd bc b2 ab 0 0 0 cd c2 bc ac 0 0 0 d2 cd bd ad 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  |)                                                                                                                                                                                                                                   |subquotient ({4} | d  d2 cd bd ad c2 bc ac b2 ab a2 0  0  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  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 |)|
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |             {3} | 0  0  0  0  a 0 0 0  0  0  0  b 0 0 0  0  0  0  c 0 0 0  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  |                                                                                                                                                                                                                                    |             {4} | -c 0  0  0  0  0  0  0  0  0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  0  0  0  0  0  0  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 | |
     |{-4, 2}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{-3, 2}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |{-2, 2}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |             {3} | 0  0  0  0  0 a 0 0  0  0  0  0 b 0 0  0  0  0  0 c 0 0  0  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} | -b 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  d2 cd bd ad c2 bc ac b2 ab a2 0  0  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 | |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |             {3} | 0  0  0  0  0 0 a 0  0  0  0  0 0 b 0  0  0  0  0 0 c 0  0  0  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} | 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  d2 cd bd c2 bc b2 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 | |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                   |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |{-1, 2}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{0, 2}                                                                                                                                                                                                             |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
     |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |0                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |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 |)                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |subquotient ({2} | d c b a 0 0 0 -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |, {2} | -b2 -ac -bd -c2 a 0 0 0 b 0 0 0 c 0 0 0 d 0 0 0 |)                                                                       |
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     |{-4, 1}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{-3, 1}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |{-2, 1}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |{-1, 1}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |             {3} | 0 0 0 0 0 1 0 a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |  {3} | a   b   -c  -d  0 0 a 0 0 0 b 0 0 0 c 0 0 0 d 0 |                                                                        |
     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |             {3} | 0 0 0 0 0 0 1 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |  {3} | 0   0   a   b   0 0 0 a 0 0 0 b 0 0 0 c 0 0 0 d |                                                                        |
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     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                                                                                                                                                                                                                   |
     |{-4, 0}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{-3, 0}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      |{-2, 0}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              |{-1, 0}                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |{0, 0}                                                                                                                                                                                                             |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

o6 : SpectralSequencePage
i7 : prune E^3

     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
o7 = |cokernel {4} | -d -b -d -c 0  0  -c 0  0  0  -d 0  0  0  0  -d -c 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                                       |
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     |{-4, 4}                                                                                                                                                                                                                                                      |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |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 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 ||                                                                                        |                                                                                |                                        |
     |{-4, 3}                                                                                                                                                                                                                                                      |         {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 ||{-2, 3}                                                                                 |{-1, 3}                                                                         |{0, 3}                                  |
     |                                                                                                                                                                                                                                                             |         {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 ||                                                                                        |                                                                                |                                        |
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     |                                                                                                                                                                                                                                                             |         {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 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 0 0 0 0 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |         {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 0 0 0 0 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 ||                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |{-3, 3}                                                                                                                                         |                                                                                        |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |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 ||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                                       |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |{-4, 2}                                                                                                                                                                                                                                                      |{-3, 2}                                                                                                                                         |         {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 ||         {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, 2}                                  |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||         {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 ||                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |         {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 ||                                                                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |{-1, 2}                                                                         |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |{-2, 2}                                                                                 |                                                                                |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |0                                                                                       |cokernel {1} | d c b a 0 0 0 0 0 0 0 0 0 0 0 0 |                                |cokernel {3} | d c b a 0 0 0 0 0 0 0 0 ||
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |         {1} | 0 0 0 0 d c b a 0 0 0 0 0 0 0 0 |                                |         {3} | 0 0 0 0 d c b a 0 0 0 0 ||
     |{-4, 1}                                                                                                                                                                                                                                                      |{-3, 1}                                                                                                                                         |{-2, 1}                                                                                 |         {1} | 0 0 0 0 0 0 0 0 d c b a 0 0 0 0 |                                |         {3} | 0 0 0 0 0 0 0 0 d c b a ||
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |         {1} | 0 0 0 0 0 0 0 0 0 0 0 0 d c b a |                                |                                        |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |{0, 1}                                  |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |{-1, 1}                                                                         |                                        |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+
     |0                                                                                                                                                                                                                                                            |0                                                                                                                                               |0                                                                                       |0                                                                               |cokernel | d c b a |                    |
     |                                                                                                                                                                                                                                                             |                                                                                                                                                |                                                                                        |                                                                                |                                        |
     |{-4, 0}                                                                                                                                                                                                                                                      |{-3, 0}                                                                                                                                         |{-2, 0}                                                                                 |{-1, 0}                                                                         |{0, 0}                                  |
     +-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+------------------------------------------------------------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------+--------------------------------------------------------------------------------+----------------------------------------+

o7 : SpectralSequencePage

See also