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monideal.m2
-- Copyright 1995 by Michael Stillman R = ZZ/101[symbol a..symbol f] T = (degreesRing R)_0 mi = monomialIdeal matrix {{a^3, a*b*d^4, a*c*e, b*d*f^2, c^2*d^3, c^5}} mi2 = monomialIdeal matrix {{a^2, c^7, b*d*e*f}} F = monomialIdeal matrix {{d^4}} assert(mi : F == monomialIdeal matrix {{a^3, a*b, a*c*e, b*f^2, c^2}}) assert(mi : F == saturate(mi, monomialIdeal matrix {{d}})) assert(radical mi == monomialIdeal matrix {{a, c, b*d*f}}) assert(mi*mi == monomialIdeal (generators mi ** generators mi)) assert(intersect(mi, mi2) == monomialIdeal matrix {{ a^3, a^2*c^5, c^7, a^2*c^2*d^3, a^2*b*d^4, a^2*c*e, a*b*c*d*e*f, b*c^5*d*e*f, b*c^2*d^3*e*f, a*b*d^4*e*f, a^2*b*d*f^2, b*d*e*f^2}}) assert(mi + mi2 == monomialIdeal (generators mi | generators mi2)) borel1 = borel monomialIdeal matrix {{b*c*d}} assert(borel1 == monomialIdeal matrix {{a^3, a^2*b, a*b^2, b^3, a^2*c, a*b*c, b^2*c, a*c^2, b*c^2, a^2*d, a*b*d, b^2*d, a*c*d, b*c*d}}) mi3 = borel monomialIdeal matrix {{d*e*f^2}} assert isBorel mi3 assert(saturate(mi3, monomialIdeal matrix {{a,b,c,d,e}}) == monomialIdeal matrix {{a,b,c,d}}) assert(monomialIdeal independentSets mi2 == monomialIdeal matrix {{b*d*e, b*d*f, b*e*f, d*e*f}}) assert( independentSets ideal vars R === {1_R} ) assert(codim mi2 == 3) assert(poincare mi2 == 1 - T^2 - T^4 + T^6 - T^7 + T^9 + T^11 - T^13) assert(poincare mi2 == poincare resolution cokernel generators mi2) -- primary decomposition of a monomial ideal. -- routines: -- topComponents I -- assprimes I -- primaryDecomposition I -- I1 = monomialIdeal matrix{{a,b^3,c^4, b^2*c, b*c^3}} I2 = monomialIdeal matrix{{c^2,b^3,d^4, b*c*d}} I3 = monomialIdeal matrix{{a,b}} I4 = monomialIdeal matrix{{a^3,b^3,c^3,d^3}} I = intersect(intersect(I1,I2),intersect(I3,I4)) -- Bug in newly added code 29 Dec 2022), fixed today. R = ZZ/101[a,b,c,d] I1 = monomialIdeal(a^2*b*c,b^3*c,b*d^3) I2 = monomialIdeal(a*b*c^2,b*c^2*d,c^3*d) assert(hash I1 == hash I2) assert(I1 =!= I2) assert(# unique{I1, I2} == 2) end-- -- Local Variables: -- compile-command: "make -C $M2BUILDDIR/Macaulay2/packages/Macaulay2Doc/test monideal.out" -- End:
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