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Macaulay2Doc :: sum(ChainComplexMap)

sum(ChainComplexMap) -- direct sum of the components of a chain map

Synopsis

Description

sum C -- yields the sum of the modules in a chain complex map.

The degrees of the components are preserved.

i1 : R = ZZ/101[a..c];
i2 : C = res coker vars R

      1      3      3      1
o2 = R  <-- R  <-- R  <-- R  <-- 0
                                  
     0      1      2      3      4

o2 : ChainComplex
i3 : sum C.dd

o3 = {0} | 0 a b c 0  0  0  0  |
     {1} | 0 0 0 0 -b -c 0  0  |
     {1} | 0 0 0 0 a  0  -c 0  |
     {1} | 0 0 0 0 0  a  b  0  |
     {2} | 0 0 0 0 0  0  0  c  |
     {2} | 0 0 0 0 0  0  0  -b |
     {2} | 0 0 0 0 0  0  0  a  |
     {3} | 0 0 0 0 0  0  0  0  |

             8       8
o3 : Matrix R  <--- R
i4 : betti oo

            0 1
o4 = total: 8 8
        -1: . 1
         0: 1 3
         1: 3 3
         2: 3 1
         3: 1 .

o4 : BettiTally

See also