RingMap ** CellComplex -- tensors labels via a ring map

Operator: **
Usage:

f ** C
Inputs:
- f, a ring map,
- C, a cell complex,
Outputs:
- a cell complex, whose cells labels are given by taking the tensor product by the ring map f

Description

Given a ring map f and a cell complex C, then for each label, viewed as a module M, this function constructs a cell complex whose new labels are f ** M

i1 : S = QQ[x,y,z];

i2 : R = QQ[a,b,c];

i3 : f = map(R,S,matrix{{a,b,c^2}});

o3 : RingMap R <-- S

i4 : v1 = newCell({},x);

i5 : v2 = newCell({},y);

i6 : v3 = newCell({},z);

i7 : e12 = newCell({v1,v2});

i8 : e23 = newCell({v2,v3});

i9 : C = cellComplex(S,{e12,e23});

i10 : cells(1,C)/cellLabel

o10 = {y*z, x*y}

o10 : List

i11 : D = f ** C;

i12 : cells(1,D)/cellLabel

               2
o12 = {a*b, b*c }

o12 : List

Ways to use this method:

RingMap ** CellComplex -- tensors labels via a ring map

The source of this document is in CellularResolutions/doc.m2:1111:0.

RingMap ** CellComplex -- tensors labels via a ring map

Description

See also

Ways to use this method: