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]; |
i2 : A=labeledModule(S^2); o2 : free S-module with labeled basis |
i3 : B=labeledModule(S^3); o3 : free S-module with labeled basis |
i4 : C=labeledModule(S^3); o4 : free S-module with labeled basis |
i5 : D=labeledModule(S^{2:-1}); o5 : free S-module with labeled basis |
i6 : f=map(A,B,{{1,1,1},{0,3,5}}) o6 = | 1 1 1 | | 0 3 5 | 2 3 o6 : Matrix S <--- S |
i7 : g=map(C,D,{{x,y},{0,z},{y,0}}) o7 = | x y | | 0 z | | y 0 | 3 2 o7 : Matrix S <--- S |
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 |