ChainComplex _ ZZ -- component

Synopsis

• Operator: _
• Usage:
C_i
• Inputs:
• Outputs:
• , the i-th component of C

Description

 i1 : R = QQ[x,y,z]/(x^3,y^3,z^3,x*y*z); i2 : C = res(coker vars R, LengthLimit=>8) 1 3 7 16 37 86 200 465 1081 o2 = R <-- R <-- R <-- R <-- R <-- R <-- R <-- R <-- R 0 1 2 3 4 5 6 7 8 o2 : ChainComplex i3 : rank C_7 o3 = 465 i4 : C.dd_3 o4 = {2} | x 0 -z2 0 0 -xy 0 y2 0 0 0 0 0 xz2 xy2 0 | {2} | -y 0 0 -z2 yz y2 0 0 0 0 x2 0 0 0 0 x2y | {2} | z 0 0 0 0 0 0 0 0 -y2 0 x2 0 0 0 0 | {3} | 0 z y x 0 0 0 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 z y x 0 0 0 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 z y x 0 0 0 0 0 0 | {3} | 0 0 0 0 0 0 0 0 0 0 z y x 0 0 0 | 7 16 o4 : Matrix R <--- R

Programming hint

The chain complex C is implemented as a hash table, but since the computation of a projective resolution can be stopped prematurely, Macaulay2 doesn't bother populating the hash table with the relevant free modules until explicitly requested by the user, for example, in response to the command C_i described above. The hash table C can be examined directly with code like C#i, but in order to populate the hash table completely, use complete(ChainComplex).