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

Synopsis

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

See also

Ways to use fromOrdinal :

For the programmer

The object fromOrdinal is a method function.