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Hom(Module,Matrix) -- induced map on Hom

Description

Synopsis

  • Usage:
    Hom(f,g)
  • Inputs:
    • f, a matrix,
    • g, a matrix,
    • DegreeLimit => ...
    • MinimalGenerators => ...
    • Strategy => ...
  • Outputs:
    • a matrix, the map on Hom induced by the maps $f$ and $g$

Synopsis

  • Usage:
    Hom(f,M)
    Hom(M,f)
  • Inputs:
    • f, a matrix,
    • M, a module,
    • DegreeLimit => ...
    • MinimalGenerators => ...
    • Strategy => ...
  • Outputs:
    • a matrix, the map on Hom induced by the map $f$
i1 : R = QQ[x]

o1 = R

o1 : PolynomialRing
 
i2 : f = vars R

o2 = | x |

             1      1
o2 : Matrix R  <-- R
 
i3 : M = image f

o3 = image | x |

                             1
o3 : R-module, submodule of R
 
i4 : g = Hom(f,M)

o4 = | x |

o4 : Matrix
 
i5 : target g

o5 = image {-1} | x |

                             1
o5 : R-module, submodule of R
 
i6 : source g

o6 = image | x |

                             1
o6 : R-module, submodule of R
 
i7 : R = QQ[x]

o7 = R

o7 : PolynomialRing
 
i8 : f = vars R

o8 = | x |

             1      1
o8 : Matrix R  <-- R
 
i9 : M = image f

o9 = image | x |

                             1
o9 : R-module, submodule of R
 
i10 : g = Hom(M,f)

o10 = {-1} | x |

              1      1
o10 : Matrix R  <-- R
 
i11 : target g

       1
o11 = R

o11 : R-module, free, degrees {-1}
 
i12 : source g

       1
o12 = R

o12 : R-module, free

See also

Ways to use this method:

The source of this document is in Macaulay2Doc/functions/Hom-doc.m2:127:0.