i1 : A = QQ[x,y,z];
|
i2 : M = image matrix{{x*y,x},{x*z,x}}
o2 = image | xy x |
| xz x |
2
o2 : A-module, submodule of A
|
i3 : N = image matrix{{y^2,x},{z^2,x}}
o3 = image | y2 x |
| z2 x |
2
o3 : A-module, submodule of A
|
i4 : M + N
o4 = image | xy x y2 x |
| xz x z2 x |
2
o4 : A-module, submodule of A
|
Notice that, in Macaulay2, each module comes equipped with a list of generators, and operations such as sum do not try to simplify the list of generators.
Intersection, quotients, annihilators are found using standard notation:
i5 : intersect(M,N)
o5 = image | x xy2-xz2 |
| x 0 |
2
o5 : A-module, submodule of A
|
i6 : M : N
o6 = ideal x
o6 : Ideal of A
|
i7 : N : M
o7 = ideal(y + z)
o7 : Ideal of A
|
i8 : Q = A/x^5;
|
i9 : M = substitute(M,Q)
o9 = image | xy x |
| xz x |
2
o9 : Q-module, submodule of Q
|
i10 : ann M
4
o10 = ideal x
o10 : Ideal of Q
|
i11 : M : x
o11 = image | 1 y-z x4 |
| 1 0 0 |
2
o11 : Q-module, submodule of Q
|