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Macaulay2Doc :: Hom(Module,Module)

Hom(Module,Module) -- module of homomorphisms

Synopsis

Description

If M or N is an ideal or ring, it is regarded as a module in the evident way.

i1 : R = QQ[x,y]/(y^2-x^3);
i2 : M = image matrix{{x,y}}

o2 = image | x y |

                             1
o2 : R-module, submodule of R
i3 : H = Hom(M,M)

o3 = image {-1} | x y  |
           {-1} | y x2 |

                             2
o3 : R-module, submodule of R
Specific homomorphisms may be obtained using homomorphism.
i4 : f0 = homomorphism H_{0}

o4 = {1} | 1 0 |
     {1} | 0 1 |

o4 : Matrix
i5 : f1 = homomorphism H_{1}

o5 = {1} | 0 x |
     {1} | 1 0 |

o5 : Matrix
In this example, f0 is the identity map, and f1 maps x to y and y to x^2.

See also