relabelCellComplex -- relabels a cell complex

Synopsis

• Usage:

  relabelCellComplex(C,H)

• Inputs:
  • C, a cell complex,
  • H, a hash table, whose keys are cells of C and whose corresponding value is the cell's new label
• Optional inputs:
  • InferLabels => a Boolean value, default value true
• Outputs:
  • a cell complex, whose cells are relabeled by the values in the hashtable H

Description

i1 : R = QQ[a,b,c];

i2 : P1 = convexHull matrix {{0,1,0},{0,0,1}};

i3 : P2 = convexHull matrix {{1,0,1},{0,1,1}};

i4 : P = polyhedralComplex {P1,P2};

i5 : C = cellComplex(R,P);

i6 : verts = cells(0,C);

i7 : v0 = verts#0;

i8 : v1 = verts#1;

i9 : v2 = verts#2;

i10 : v3 = verts#3;

i11 : T = new HashTable from {v0 => a^2*b, v1 => b*c^2, v2 => b^2, v3 => a*c};

i12 : relabeledC = relabelCellComplex(C,T);

i13 : for c in cells(0,relabeledC) list cellLabel(c)

        2        2      2
o13 = {b , a*c, a b, b*c }

o13 : List

i14 : for c in cells(1,relabeledC) list cellLabel(c)

        2 2       2     2    2   2   2 2
o14 = {b c , a*b*c , a*b c, a b*c , a b }

o14 : List

See also

• cellLabel -- return the label of a cell
• RingMap ** CellComplex -- tensors labels via a ring map