i1 : kk = QQ o1 = QQ o1 : Ring |
i2 : R = kk[a,b] o2 = R o2 : PolynomialRing |
i3 : S = kk[z,t] o3 = S o3 : PolynomialRing |
i4 : f = map(S,R,{z^2,t^2}) 2 2 o4 = map(S,R,{z , t }) o4 : RingMap S <--- R |
i5 : M = S^1/ideal(z^3,t^3) o5 = cokernel | z3 t3 | 1 o5 : S-module, quotient of S |
i6 : g = map(M,M,matrix{{z*t}}) o6 = | zt | o6 : Matrix |
i7 : p = pushFwd(f,g) o7 = {0} | 0 0 ab 0 | {1} | 0 0 0 b | {2} | 1 0 0 0 | {1} | 0 a 0 0 | o7 : Matrix |
i8 : kerg = pushFwd(f,ker g) o8 = cokernel {2} | b a 0 0 0 0 0 | {2} | 0 -b a 0 0 0 0 | {3} | 0 0 0 b a 0 0 | {3} | 0 0 0 0 0 b a | 4 o8 : R-module, quotient of R |
i9 : kerp = prune ker p o9 = cokernel {1} | b a 0 0 0 0 0 | {1} | 0 -b a 0 0 0 0 | {2} | 0 0 0 b a 0 0 | {2} | 0 0 0 0 0 b a | 4 o9 : R-module, quotient of R |