MaplePrimes - comments on Post, Bug in PolynomialIdeals

MaplePrimes - comments on Post, Bug in PolynomialIdeals http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 10:08:28 GMT Tue, 09 Jun 2026 10:08:28 GMT The latest comments added to the Post, Bug in PolynomialIdeals http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, Bug in PolynomialIdeals http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals Regression http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135895 I find it rather a question than a post. It is OK in Maple 13: > with(PolynomialIdeals): >J := ``(t*(a+A), A*(b+B+t), b*(a+A), B*a-A*(b+t), variables = {A, B, a, b, t}): >J2 := ``(t*(a+A), A*(b+B+t), b*(a+A), B*(a+A), variables = {A, B, a, b, t}): >R := Radical(J): >R2 := Radical(J2): >IdealContainment(J2, J, J2); >IdealContainment(R, J); >IdealContainment(R2, J2);                                     true                                     true                                     true > p := b*A*(b+B): >IdealMembership(p, R); >IdealMembership(p, R2);                                     false                                     false The latest comments added to the Post, Bug in PolynomialIdeals 135895 Mon, 16 Jul 2012 18:14:16 Z Markiyan Hirnyk Markiyan Hirnyk Version related http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135898 Hello again, I am sure this problem is specific to version 16 of Maple, as clearly such a severe bug would have long been recognised and fixed in earlier versions. In particular note <blockquote> The PolynomialIdeals[IsRadical], PolynomialIdeals[Radical] and PolynomialIdeals[RadicalMembership] commands were updated in Maple 16. </blockquote> from the help page <a href="http://www.maplesoft.com/support/help/view.aspx?path=PolynomialIdeals/IsRadical">?PolynomialIdeals/IsRadical</a>. Cheers, Erik The latest comments added to the Post, Bug in PolynomialIdeals 135898 Mon, 16 Jul 2012 19:29:42 Z ErikP ErikP It looks like a bug in the heuristic splitting http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135899 It looks like a bug in the heuristic splitting routine.  This means there is also a problem in PrimeDecomposition.  Here is a workaround: <pre>restart: kernelopts(opaquemodules=false): unprotect(PolynomialIdeals:-Radical): PolynomialIdeals:-Radical := proc(J::PolynomialIdeal, $) local vars, char, R, i; option cache; vars := PolynomialIdeals:-IdealInfo:-Variables(J); char := PolynomialIdeals:-IdealInfo:-Characteristic(J); if char <> 0 and 0 < nops(PolynomialIdeals:-IdealInfo:-Parameters(J)) then error "non-perfect coefficient fields are not supported" end if; if PolynomialIdeals:-IsZeroDimensional(J) then R := PolynomialIdeals:-ideal_algorithms:-zradical(J) elif char = 0 then R := {J}; # R := {PolynomialIdeals:-ideal_algorithms:-heusplit(J)}; R := map(PolynomialIdeals:-ideal_algorithms:-gsplit, R); R := map(PolynomialIdeals:-ZeroDimensionalDecomposition, R, ':-split' = true); R := map(PolynomialIdeals:-ideal_algorithms:-zradical, R); R := PolynomialIdeals:-ideal_algorithms:-reduce(R); R := select(PolynomialIdeals:-IsProper, R); R := map(PolynomialIdeals:-Contract, R, vars); R := PolynomialIdeals:-Intersect(op(R)) else error "positive-dimensional ideals in positive characteristic are not supported" end if; R end proc: with(PolynomialIdeals); J := : J2 := : R := Radical(J): R2 := Radical(J2): IdealContainment(J2, J, J2); IdealContainment(R, J); IdealContainment(R2, J2); p := b*A*(b+B): IdealMembership(p, R); IdealMembership(p, R2);</pre> <pre> </pre> <pre>You can also revert to the algorithm of Maple 15.</pre> <pre>restart: kernelopts(opaquemodules=false): unprotect(PolynomialIdeals:-Radical): PolynomialIdeals:-Radical := proc(J::PolynomialIdeal, $) local vars, char, R, i; option remember, system; vars := PolynomialIdeals:-IdealInfo:-Variables(J); char := PolynomialIdeals:-IdealInfo:-Characteristic(J); if char <> 0 and 0 < nops(PolynomialIdeals:-IdealInfo:-Parameters(J)) then error "non-perfect coefficient fields are not supported" end if; if PolynomialIdeals:-IsZeroDimensional(J) then PolynomialIdeals:-ideal_algorithms:-zradical(J) elif char = 0 then R := {PolynomialIdeals:-ZeroDimensionalDecomposition(J)}; R := map(PolynomialIdeals:-ideal_algorithms:-zradical, R); PolynomialIdeals:-Intersect(seq(PolynomialIdeals:-Contract(i, vars), i = R)) else error "positive-dimensional ideals in positive characteristic are not supported" end if end proc: with(PolynomialIdeals); J := : J2 := : R := Radical(J): R2 := Radical(J2): IdealContainment(J2, J, J2); IdealContainment(R, J); IdealContainment(R2, J2); p := b*A*(b+B): IdealMembership(p, R); IdealMembership(p, R2);</pre> The latest comments added to the Post, Bug in PolynomialIdeals 135899 Mon, 16 Jul 2012 19:38:08 Z roman_pearce roman_pearce Bug recorded http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135900 @ErikP Thanks for reporting.  This bug has been recorded in the bug database at Maplesoft. The latest comments added to the Post, Bug in PolynomialIdeals 135900 Mon, 16 Jul 2012 19:54:18 Z Clare So Clare So little question: "$" http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135909 <a href="http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals#comment135899">@roman_pearce</a>  What does the "$" mean in the definition of the proc? The latest comments added to the Post, Bug in PolynomialIdeals 135909 Mon, 16 Jul 2012 22:28:38 Z Axel Vogt Axel Vogt @Axel Vogt  "$" is a marker that indicates http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals?ref=Feed:MaplePrimes:Bug in PolynomialIdeals:Comments#comment135912 <a href="http://www.mapleprimes.com/posts/135889-Bug-In-PolynomialIdeals#comment135909">@Axel Vogt</a>  "$" is a marker that indicates no more arguments can be matched: <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=parameter_classes#endofparams">http://www.maplesoft.com/support/help/Maple/view.aspx?path=parameter_classes#endofparams</a> The latest comments added to the Post, Bug in PolynomialIdeals 135912 Mon, 16 Jul 2012 22:50:04 Z Clare So Clare So