This function assumes that $E$ has the form $E=\wedge^b B \otimes \wedge^b A$ where $A$ and $B$ are labeled free $S$-modules and where $f: A^*\to B$ (or where $M$ is matrix representing such a map). The output is the map $$ E\to S $$ sending each basis element to the corresponding $b\times b$ minor of $f$ (or $M$).
i1 : S=ZZ/101[x,y,z]; |
i2 : A=labeledModule(S^2); o2 : free S-module with labeled basis |
i3 : B=labeledModule(S^{3:-2});
o3 : free S-module with labeled basis
|
i4 : M=matrix{{x^2,x*y,y^2},{y^2,y*z,z^2}}
o4 = | x2 xy y2 |
| y2 yz z2 |
2 3
o4 : Matrix S <--- S
|
i5 : f=map(A,B,M);
2 3
o5 : Matrix S <--- S
|
i6 : E=(exteriorPower(2,B))**(exteriorPower(2,A))
3
o6 = S
o6 : free S-module with labeled basis
|
i7 : minorsMap(f,E)
o7 = | -xy3+x2yz -y4+x2z2 -y3z+xyz2 |
1 3
o7 : Matrix S <--- S
|
i8 : minorsMap(M,E)
o8 = | -xy3+x2yz -y4+x2z2 -y3z+xyz2 |
1 3
o8 : Matrix S <--- S
|
The object minorsMap is a method function.