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 |