Hom(Module,Module) -- module of homomorphisms

Synopsis

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

To recover the modules used to create a Hom-module, use the function formation.

Specific homomorphisms may be obtained using homomorphism, as follows.

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 the example above, f0 is the identity map, and f1 maps x to y and y to x^2.