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-- test kernel for module maps over ring maps S = QQ[y] R = QQ[x,Degrees=>{2}] f = map(S,R,{y^2}) m = matrix {{1,y^2}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) m = matrix {{1,y}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y^2+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x+1}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x+1}, {-1}}) ) S = QQ[y] R = QQ[x] f = map(S,R,{y^2}) m = matrix {{1,y^2}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) m = matrix {{1,y}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y^2+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x+1}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x+1}, {-1}}) ) S = QQ[y] R = QQ[x] f = map(S,R,{y^2+1}) m = matrix {{1,y^2}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x-1}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x-1}, {-1}}) ) m = matrix {{1,y}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == 0 ) assert( coimage n == R^{{0}, {-1}} ) m = matrix {{1,y^2+1}} n = map(S^1,R^(-degrees source m),f,m) assert( n * gens ker n == 0 ) assert( ker n == image map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) assert( coimage n == cokernel map(R^{{0}, {-2}}, R^{{-2}}, {{x}, {-1}}) ) -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test ker8.out" -- End: