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 = subquotient (| 1 x 0 |, | -y 0 x2 0 |)
| 0 0 1 | | x 0 -y 0 |
| 0 y x | | 0 -y 0 x2 |
| 1 0 0 | | 0 x 0 -y |
4
o3 : R-module, subquotient of R
|
i4 : H1 = prune H
o4 = cokernel {0} | 0 -y |
{1} | -y x |
2
o4 : R-module, quotient of R
|
Specific homomorphisms may be obtained using
homomorphism.
i5 : f1 = homomorphism H_{0}
o5 = {1} | 1 0 |
{1} | 0 1 |
o5 : Matrix
|
i6 : f2 = homomorphism H_{1}
o6 = {1} | x y |
{1} | 0 0 |
o6 : Matrix
|
i7 : f3 = homomorphism H_{2}
o7 = {1} | 0 x |
{1} | 1 0 |
o7 : Matrix
|
In this example, f1 is the identity map, f2 is multiplication by x, and f3 maps x to y and y to x^2.