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View File Name :
modules.m2
-- equality of modules S = QQ[x,y,z]/z^2 assert(S^{-1,1} != S^{1,-1}) assert(0 * S^1 == 0 * S^{2}) assert(0 * S^1 == 0 * S^{1,1}) assert(0 * S^1 != subquotient(matrix"x", matrix"x")) assert(0 * S^1 != subquotient(matrix{{0_S}}, matrix"x")) assert(image id_(S^1) == S^1) assert(image matrix"x" != S^{-1}) assert(image matrix"x,y" != image matrix"x") assert(image matrix"x,y" == image matrix"y,x") assert(coker matrix"x,y" != coker matrix"x") assert(coker matrix"x,y" == coker matrix"y,x") assert(subquotient(matrix"x,y", matrix"x2,y") != subquotient(matrix"x", matrix"x2")) assert(subquotient(matrix"x,y", matrix"x2,y") == subquotient(matrix"x", matrix"x2,y")) assert(subquotient(matrix"x,y", matrix"x2,y") != subquotient(matrix"z2", matrix"x2,y")) assert(subquotient(matrix"x,y", matrix"z2") == image matrix"x,y") assert(subquotient(id_(S^1), matrix"x,y") == coker matrix"x,y")