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}];
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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
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i6 : fromOrdinal(0,C)
o6 = {0, 0}
o6 : List
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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
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The object fromOrdinal is a method function.