# chainComplex(SimplicialComplex) -- The chain complex of boundary maps.

## Synopsis

• Function: chainComplex
• Usage:
chainComplex C
• Inputs:
• C, ,
• Outputs:

## Description

The ChainComplex of boundary maps from i-faces to (i-1)-faces.

 i1 : R = QQ[a..f]; i2 : D = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f,b*c*d,b*d*e,b*e*f,c*d*f,c*e*f); i3 : R' = ZZ/2[a..f]; i4 : D' = simplicialComplex monomialIdeal(a*b*c,a*b*f,a*c*e,a*d*e,a*d*f,b*c*d,b*d*e,b*e*f,c*d*f,c*e*f); i5 : c = chainComplex D 1 6 15 10 o5 = QQ <-- QQ <-- QQ <-- QQ -1 0 1 2 o5 : ChainComplex i6 : c' = chainComplex D' ZZ 1 ZZ 6 ZZ 15 ZZ 10 o6 = (--) <-- (--) <-- (--) <-- (--) 2 2 2 2 -1 0 1 2 o6 : ChainComplex i7 : c.dd_1 o7 = | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | | -1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 | | 0 -1 0 0 0 -1 0 0 0 1 1 1 0 0 0 | | 0 0 -1 0 0 0 -1 0 0 -1 0 0 1 1 0 | | 0 0 0 -1 0 0 0 -1 0 0 -1 0 -1 0 1 | | 0 0 0 0 -1 0 0 0 -1 0 0 -1 0 -1 -1 | 6 15 o7 : Matrix QQ <--- QQ i8 : c'.dd_1 o8 = | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 | | 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 | | 0 1 0 0 0 1 0 0 0 1 1 1 0 0 0 | | 0 0 1 0 0 0 1 0 0 1 0 0 1 1 0 | | 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 | | 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 | ZZ 6 ZZ 15 o8 : Matrix (--) <--- (--) 2 2