-- -*- M2-comint -*- {* hash: -1943954118 *} i1 : M = ZZ^2 ++ ZZ^3 5 o1 = ZZ o1 : ZZ-module, free i2 : M_[0] o2 = | 1 0 | | 0 1 | | 0 0 | | 0 0 | | 0 0 | 5 2 o2 : Matrix ZZ <--- ZZ i3 : M_[1] o3 = | 0 0 0 | | 0 0 0 | | 1 0 0 | | 0 1 0 | | 0 0 1 | 5 3 o3 : Matrix ZZ <--- ZZ i4 : M_[1,0] o4 = | 0 0 0 1 0 | | 0 0 0 0 1 | | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | 5 5 o4 : Matrix ZZ <--- ZZ i5 : R = QQ[a..d]; i6 : M = (a => image vars R) ++ (b => coker vars R) o6 = subquotient (| a b c d 0 |, | 0 0 0 0 |) | 0 0 0 0 1 | | a b c d | 2 o6 : R-module, subquotient of R i7 : M_[a] o7 = {1} | 1 0 0 0 | {1} | 0 1 0 0 | {1} | 0 0 1 0 | {1} | 0 0 0 1 | {0} | 0 0 0 0 | o7 : Matrix i8 : isWellDefined oo o8 = true i9 : M_[b] o9 = {1} | 0 | {1} | 0 | {1} | 0 | {1} | 0 | {0} | 1 | o9 : Matrix i10 : isWellDefined oo o10 = true i11 : C = res coker vars R 1 4 6 4 1 o11 = R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 o11 : ChainComplex i12 : D = (a=>C) ++ (b=>C) 2 8 12 8 2 o12 = R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 o12 : ChainComplex i13 : D_[a] 2 1 o13 = 0 : R <--------- R : 0 | 1 | | 0 | 8 4 1 : R <------------------- R : 1 {1} | 1 0 0 0 | {1} | 0 1 0 0 | {1} | 0 0 1 0 | {1} | 0 0 0 1 | {1} | 0 0 0 0 | {1} | 0 0 0 0 | {1} | 0 0 0 0 | {1} | 0 0 0 0 | 12 6 2 : R <----------------------- R : 2 {2} | 1 0 0 0 0 0 | {2} | 0 1 0 0 0 0 | {2} | 0 0 1 0 0 0 | {2} | 0 0 0 1 0 0 | {2} | 0 0 0 0 1 0 | {2} | 0 0 0 0 0 1 | {2} | 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 | {2} | 0 0 0 0 0 0 | 8 4 3 : R <------------------- R : 3 {3} | 1 0 0 0 | {3} | 0 1 0 0 | {3} | 0 0 1 0 | {3} | 0 0 0 1 | {3} | 0 0 0 0 | {3} | 0 0 0 0 | {3} | 0 0 0 0 | {3} | 0 0 0 0 | 2 1 4 : R <------------- R : 4 {4} | 1 | {4} | 0 | 5 : 0 <----- 0 : 5 0 o13 : ChainComplexMap i14 :