If $f: A\to B$ and $g: C\to D$ are maps of labeled modules, then tensor(f,g) is the map of labeled modules $$ f\otimes g: A\otimes C \to B\otimes D. $$
i1 : S=ZZ/101[x,y,z];
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i2 : A=labeledModule(S^2);
o2 : free S-module with labeled basis
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i3 : B=labeledModule(S^3);
o3 : free S-module with labeled basis
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i4 : C=labeledModule(S^3);
o4 : free S-module with labeled basis
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i5 : D=labeledModule(S^{2:-1});
o5 : free S-module with labeled basis
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i6 : f=map(A,B,{{1,1,1},{0,3,5}})
o6 = | 1 1 1 |
| 0 3 5 |
2 3
o6 : Matrix S <--- S
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i7 : g=map(C,D,{{x,y},{0,z},{y,0}})
o7 = | x y |
| 0 z |
| y 0 |
3 2
o7 : Matrix S <--- S
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i8 : tensor(f,g)
o8 = | x y x y x y |
| 0 z 0 z 0 z |
| y 0 y 0 y 0 |
| 0 0 3x 3y 5x 5y |
| 0 0 0 3z 0 5z |
| 0 0 3y 0 5y 0 |
6 6
o8 : Matrix S <--- S
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