-- -*- M2-comint -*- {* hash: -262633672 *} i1 : A = ZZ/101[x,y]; i2 : M = cokernel random(A^3, A^{-2,-2}) o2 = cokernel | -42x2+22xy-12y2 -11x2+17xy-31y2 | | -3x2+33xy-20y2 16x2-16xy+19y2 | | 47x2-18xy+35y2 -8x2+24xy-41y2 | 3 o2 : A-module, quotient of A i3 : R = cokernel matrix {{x^3,y^4}} o3 = cokernel | x3 y4 | 1 o3 : A-module, quotient of A i4 : N = prune (M**R) o4 = cokernel | -31x2+32xy+3y2 -48x2+24xy-28y2 x3 x2y-2xy2-7y3 47xy2-7y3 y4 0 0 | | x2-4xy-18y2 -6xy+50y2 0 -9xy2+40y3 38xy2-17y3 0 y4 0 | | 18xy+37y2 x2+33xy+16y2 0 -26y3 xy2+27y3 0 0 y4 | 3 o4 : A-module, quotient of A i5 : C = resolution N 3 8 5 o5 = A <-- A <-- A <-- 0 0 1 2 3 o5 : ChainComplex i6 : d = C.dd 3 8 o6 = 0 : A <-------------------------------------------------------------------------- A : 1 | -31x2+32xy+3y2 -48x2+24xy-28y2 x3 x2y-2xy2-7y3 47xy2-7y3 y4 0 0 | | x2-4xy-18y2 -6xy+50y2 0 -9xy2+40y3 38xy2-17y3 0 y4 0 | | 18xy+37y2 x2+33xy+16y2 0 -26y3 xy2+27y3 0 0 y4 | 8 5 1 : A <-------------------------------------------------------------------------- A : 2 {2} | 14xy2-29y3 47xy2+46y3 -14y3 36y3 -3y3 | {2} | 26xy2+44y3 -30y3 -26y3 -19y3 25y3 | {3} | -4xy-13y2 6xy+14y2 4y2 28y2 -40y2 | {3} | 4x2-4xy-27y2 -6x2+17xy+21y2 -4xy+17y2 -28xy-38y2 40xy+39y2 | {3} | -26x2-45xy-46y2 38xy-40y2 26xy+y2 19xy-50y2 -25xy+34y2 | {4} | 0 0 x+46y -44y 8y | {4} | 0 0 -19y x+46y 37y | {4} | 0 0 36y 41y x+9y | 5 2 : A <----- 0 : 3 0 o6 : ChainComplexMap i7 : s = nullhomotopy (x^3 * id_C) 8 3 o7 = 1 : A <------------------------ A : 0 {2} | 0 x+4y 6y | {2} | 0 -18y x-33y | {3} | 1 31 48 | {3} | 0 36 -8 | {3} | 0 -20 -45 | {4} | 0 0 0 | {4} | 0 0 0 | {4} | 0 0 0 | 5 8 2 : A <--------------------------------------------------------------------------- A : 1 {5} | 7 41 0 14y -35x+20y xy+28y2 -42xy-45y2 34xy+47y2 | {5} | -23 26 0 -17x-22y 44x-7y 9y2 xy-43y2 -38xy-25y2 | {5} | 0 0 0 0 0 x2-46xy+8y2 44xy+17y2 -8xy+24y2 | {5} | 0 0 0 0 0 19xy-12y2 x2-46xy+25y2 -37xy-36y2 | {5} | 0 0 0 0 0 -36xy-11y2 -41xy-36y2 x2-9xy-33y2 | 5 3 : 0 <----- A : 2 0 o7 : ChainComplexMap i8 : s*d + d*s 3 3 o8 = 0 : A <---------------- A : 0 | x3 0 0 | | 0 x3 0 | | 0 0 x3 | 8 8 1 : A <----------------------------------- A : 1 {2} | x3 0 0 0 0 0 0 0 | {2} | 0 x3 0 0 0 0 0 0 | {3} | 0 0 x3 0 0 0 0 0 | {3} | 0 0 0 x3 0 0 0 0 | {3} | 0 0 0 0 x3 0 0 0 | {4} | 0 0 0 0 0 x3 0 0 | {4} | 0 0 0 0 0 0 x3 0 | {4} | 0 0 0 0 0 0 0 x3 | 5 5 2 : A <-------------------------- A : 2 {5} | x3 0 0 0 0 | {5} | 0 x3 0 0 0 | {5} | 0 0 x3 0 0 | {5} | 0 0 0 x3 0 | {5} | 0 0 0 0 x3 | 3 : 0 <----- 0 : 3 0 o8 : ChainComplexMap i9 : s^2 5 3 o9 = 2 : A <----- A : 0 0 8 3 : 0 <----- A : 1 0 o9 : ChainComplexMap i10 :