sum ChainComplex -- direct sum of the components of a chain complex

sum ChainComplex -- direct sum of the components of a chain complex

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

The degrees of the components are preserved.

i1 : R = ZZ/101[a..d];

i2 : C = res coker vars R



      1      4      6      4      1

o2 = R  <-- R  <-- R  <-- R  <-- R

                                 

     0      1      2      3      4



o2 : ChainComplex

i3 : sum C



      16

o3 = R



o3 : R - module, free

i4 : degrees oo



o4 = {{0}, {1}, {1}, {1}, {1}, {2}, {2}, {2}, {2}, {2}, {2}, {3}, {3}, {3}, {3}, {4}}



o4 : List

See also:

sum -- compute the sum

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

Synopsis of use:

Operator: sum

Class of argument 1: ChainComplex

Class of typical returned value: Module

Code:

     -- ../m2/chaincomplexes.m2:67
     sum ChainComplex := Module => C -> directSum apply(sort spots C, i -> C_i)