i1 : A = QQ[x,y,z]; |
i2 : M = cokernel matrix(A, {{1,2,3},{4,5,6},{7,8,9}}) o2 = cokernel | 1 2 3 | | 4 5 6 | | 7 8 9 | 3 o2 : A-module, quotient of A |
i3 : N = cokernel matrix{{x,y},{z,0}} o3 = cokernel | x y | | z 0 | 2 o3 : A-module, quotient of A |
i4 : H = Hom(M,N) o4 = subquotient (| 1 0 |, | x 0 0 y 0 0 |) | 0 1 | | z 0 0 0 0 0 | | -2 0 | | 0 x 0 0 y 0 | | 0 -2 | | 0 z 0 0 0 0 | | 1 0 | | 0 0 x 0 0 y | | 0 1 | | 0 0 z 0 0 0 | 6 o4 : A-module, subquotient of A |
i5 : f = homomorphism H_{0} o5 = | 1 -2 1 | | 0 0 0 | o5 : Matrix |
i6 : target f === N o6 = true |
i7 : source f === M o7 = true |
i8 : matrix f o8 = | 1 -2 1 | | 0 0 0 | 2 3 o8 : Matrix A <--- A |