# fromOrdinal -- outputs the label of a basis element of a labeled module

## Synopsis

• Usage:
fromOrdinal(i,F)
• Inputs:
• Outputs:
• ,

## Description

This function allows one to access the labels of the basis elements of a labeled free module. For instance, if $F$ is a labeled free module of $r$, then its basis is labeled by a list $L$. This function takes an integer $i$ between $0$ and outputs the $i$'th element of $L$.

This function is particularly useful when defining maps between labeled free modules.

 i1 : S=ZZ/101[x_{0,0,0}..x_{2,1,1}]; i2 : A=labeledModule(S^3); o2 : free S-module with labeled basis i3 : fromOrdinal(0,A) o3 = 0 i4 : B=labeledModule(S^2); o4 : free S-module with labeled basis i5 : C=symmetricPower(2,B) 3 o5 = S o5 : free S-module with labeled basis i6 : fromOrdinal(0,C) o6 = {0, 0} o6 : List i7 : f=map(A,C,(i,j)->x_(flatten {fromOrdinal(j,A)}|fromOrdinal(i,C))) o7 = | x_{0, 0, 0} x_{1, 0, 0} x_{2, 0, 0} | | x_{0, 0, 1} x_{1, 0, 1} x_{2, 0, 1} | | x_{0, 1, 1} x_{1, 1, 1} x_{2, 1, 1} | 3 3 o7 : Matrix S <--- S