# ChainComplex ^ ZZ -- access member, cohomological degree

## Synopsis

• Operator: ^
• Usage:
C^n
• Inputs:
• Outputs:
• , The (-n)-th component C_(-n) of C

## Description

Subscripts refer to homological degree, and superscripts refer to cohomological degree. It is only a matter of notation: C_(-n) is always the same as C^n.
 i1 : R = QQ[x,y,z]; i2 : C = res coker vars R 1 3 3 1 o2 = R <-- R <-- R <-- R <-- 0 0 1 2 3 4 o2 : ChainComplex i3 : C = dual C 1 3 3 1 o3 = 0 <-- R <-- R <-- R <-- R -4 -3 -2 -1 0 o3 : ChainComplex i4 : C^2 3 o4 = R o4 : R-module, free, degrees {3:-2} i5 : C^2 == C_(-2) o5 = true