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relabelCellComplex -- relabels a cell complex

Synopsis

• Usage:
relabelCellComplex(C,H)
• Inputs:
• C, ,
• H, , whose keys are cells of C and whose corresponding value is the cell's new label
• Optional inputs:
• InferLabels => , default value true
• Outputs:
• , whose cells are relabeled by the values in the hashtable H

Description

Given a cell complex C and a hashtable, whose key-value pairs are a cell from C and a new label for that cell, this command relabels C accordingly. Labels for cells not provided in the hashtable are inferred to be the least common multiple of the labels of their boundary cells, unless the option InferLabels is set to false.

 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