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TensorComplexes :: minorsMap

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

Synopsis

Description

This function assumes that E has the form E=∧b B ⊗∧b A where A and B are labeled free S-modules and where f: A*→B (or where M is matrix representing such a map). The output is the map

E→S

sending each basis element to the corresponding b×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 :