ChainComplex ^ ZZ -- access member, cohomological degree

Synopsis

Usage:
C^n
Operator: ^
Inputs:
- C, a chain complex
- n, an integer
Outputs:
- a module, 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 = R  <-- R  <-- R  <-- R
                           
     -3     -2     -1     0

o3 : ChainComplex

i4 : C^2

      3
o4 = R

o4 : R-module, free, degrees {-2, -2, -2}

i5 : C^2 == C_(-2)

o5 = true

ChainComplex ^ ZZ -- access member, cohomological degree

Synopsis

Description

See also