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

Synopsis

• Function: sum

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