toOrdinal -- turns the label of a basis element of a labeled module into a corresponding ordinal

This function allows one to move from the labels of the basis elements of a labeled free module of rank r to the the integers {0,1, …, r-1}. More specifically, if F is a labeled free module where we have labeled the basis with the list L, then this function an element l∈L to the ordinal j such that l is the j’th element of L.

i1 : S=ZZ/101[x_{0,0,0}..x_{2,1,1}];

i2 : C=symmetricPower(2,labeledModule(S^3))

      6
o2 = S

o2 : free S-module with labeled basis

i3 : basisList C

o3 = {{0, 0}, {0, 1}, {1, 1}, {0, 2}, {1, 2}, {2, 2}}

o3 : List

i4 : toOrdinal({0,0},C)

o4 = 0

i5 : toOrdinal({1,2},C)

o5 = 4