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R = QQ[x] S = QQ[y] f = map(S,R,{0}) assert( ker f === ideal vars R) h = map(S^1,R^1,f,{{1}}) ker h assert( ker h === image vars R) debug Core R=ZZ/101[a,b,c] S=ZZ/101[t] f = map(S,R,{t^4,t^5,t^6}) assert not isHomogeneous f assert( ker f == ideal matrix {{b^2-a*c, a^3-c^2}} ) h = map(S^1,R^1,f,{{1}}) assert( ker h == image matrix{{b^2-a*c, a^3-c^2}}) R=ZZ/101[a,b,c,Degrees=>{4,5,6}] S=ZZ/101[t] f = map(S,R,{t^4,t^5,t^6}) assert isHomogeneous f assert( ker f == ideal matrix {{b^2-a*c, a^3-c^2}} ) assert checkHilbertHint generators graphIdeal f h = map(S^1,R^1,f,{{1}}) assert( ker h == image matrix{{b^2-a*c, a^3-c^2}}) R=ZZ/101[a,b,c,DegreeRank=>3] S=ZZ/101[t] f = map(S,R,{t^4,t^5,t^6},DegreeMap => d -> {4*d#0 + 5*d#1 + 6*d#2}) assert isHomogeneous f assert( ker f == ideal matrix {{b^2-a*c, a^3-c^2}} ) assert checkHilbertHint generators graphIdeal f h = map(S^1,R^1,f,{{1}}) -- assert( ker h == image matrix{{b^2-a*c, a^3-c^2}}) R=ZZ/101[c][b][a] assert( degreeLength R == 3 ) S=ZZ/101[t] f = map(S,R,{t^4,t^5,t^6},DegreeMap => d -> {4*d#0 + 5*d#1 + 6*d#2}) assert isHomogeneous f assert( ker f == ideal matrix {{b^2-a*c, a^3-c^2}} ) -- assert checkHilbertHint generators graphIdeal f end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test ker.out" -- End: