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extmap.m2
R = ZZ/101[a..f,MonomialOrder => Lex] I = ideal(a,b,c) J = ideal(b,c,d,e) J' = ideal(b,c^2,d^2+e*f,e) K = cokernel generators intersect(I,J) K' = cokernel generators intersect(I,J') f = inducedMap(K,K') g = Ext^3(f,R) assert(ann source g == I) assert(ann target g == I) assert(g == 1) h = Ext^3(K,matrix {{d}}) assert(h == d) R = ZZ/101[a..d] I = ideal (a*b,c*d) M = R^1/I J = ideal (a^2*b^2,c^2*d^2) N = R^1/J f = inducedMap(M,N) g = Ext^2(f,R) assert( g - a*b*c*d == 0 ) I = intersect(ideal(a,b), ideal(c,d)) J = ideal apply(first entries gens I, r -> r^2) M = R^1/I N = R^1/J f = inducedMap(M,N) g = Ext^2(f,R) so = m -> m_(sortColumns m) print presentation target g h = matrix{{a^2,b^2,0,0},{0,0,c^2,d^2}} assert( so presentation target g - so h == 0 or so presentation target g - so h^{1,0} == 0 ) print presentation source g h2 = matrix {{a, b, 0, 0}, {0, 0, c, d}} assert( so presentation source g - so h2 == 0 or so presentation source g - so h2^{1,0} == 0 ) h3 = matrix {{a*b, 0}, {0, c*d}} assert( so matrix g - so h3 == 0 or so matrix g - so h3^{1,0} == 0 ) end -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test extmap.out" -- End: