ChainComplex ^ ZZ -- access member, cohomological degree

Synopsis

• Operator: ^

• Usage:

  C^n

• Inputs:
  • C, a chain complex
  • n, an integer
• Outputs:
  • a module, The (-n)-th component C_(-n) of C

Description

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

See also

• ChainComplex -- the class of all chain complexes
• ChainComplex ^ Array -- projection onto summand