# minorsMap -- creates a map of labeled free modules whose image is the minors of a map of labeled free modules

## Synopsis

• Usage:
minorsMap(f,E)
minorsMap(M,E)
• Inputs:
• M, ,
• Outputs:

## Description

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

## Ways to use minorsMap :

• "minorsMap(LabeledModuleMap,LabeledModule)"
• "minorsMap(Matrix,LabeledModule)"

## For the programmer

The object minorsMap is .