-- -*- M2-comint -*- {* hash: -708321331 *} i1 : R = QQ[x,y,z]; i2 : I = ideal(x*y,x*z,y*z) o2 = ideal (x*y, x*z, y*z) o2 : Ideal of R i3 : M = I/I^2 o3 = subquotient (| xy xz yz |, | x2y2 x2yz xy2z x2z2 xyz2 y2z2 |) 1 o3 : R-module, subquotient of R i4 : f = matrix{{x,y}} o4 = | x y | 1 2 o4 : Matrix R <--- R i5 : g = matrix{{x^2,x*y,y^2,z^4}} o5 = | x2 xy y2 z4 | 1 4 o5 : Matrix R <--- R i6 : M = subquotient(f,g) o6 = subquotient (| x y |, | x2 xy y2 z4 |) 1 o6 : R-module, subquotient of R i7 : N = (image f)/(image g) o7 = subquotient (| x y |, | x2 xy y2 z4 |) 1 o7 : R-module, subquotient of R i8 : N1 = (image f + image g)/(image g) o8 = subquotient (| x y x2 xy y2 z4 |, | x2 xy y2 z4 |) 1 o8 : R-module, subquotient of R i9 : M === N o9 = true i10 : generators M o10 = | x y | 1 2 o10 : Matrix R <--- R i11 : relations M o11 = | x2 xy y2 z4 | 1 4 o11 : Matrix R <--- R i12 : N2 = R*M_0 + I*M o12 = subquotient (| x x2y xy2 x2z xyz xyz y2z |, | x2 xy y2 z4 |) 1 o12 : R-module, subquotient of R i13 : M/N2 o13 = subquotient (| x y |, | x x2y xy2 x2z xyz xyz y2z x2 xy y2 z4 |) 1 o13 : R-module, subquotient of R i14 : prune(M/N2) o14 = cokernel {1} | y x z4 | 1 o14 : R-module, quotient of R i15 : ambient M 1 o15 = R o15 : R-module, free i16 : ambient M === target relations M o16 = true i17 : ambient M === target generators M o17 = true i18 : super M o18 = cokernel | x2 xy y2 z4 | 1 o18 : R-module, quotient of R i19 : super M === cokernel relations M o19 = true i20 : M + M o20 = subquotient (| x y x y |, | x2 xy y2 z4 |) 1 o20 : R-module, subquotient of R i21 : trim (M+M) o21 = subquotient (| y x |, | y2 xy x2 z4 |) 1 o21 : R-module, subquotient of R i22 : minimalPresentation M o22 = cokernel {1} | y x 0 0 z4 0 | {1} | 0 0 y x 0 z4 | 2 o22 : R-module, quotient of R i23 : prune M o23 = cokernel {1} | y x 0 0 z4 0 | {1} | 0 0 y x 0 z4 | 2 o23 : R-module, quotient of R i24 :