The output is also as you report with Sage-6.0. Generally speaking it is a good idea to check with a recent version, preferebaly the lastest, before reporting a problem. Version 5.12 is prehistoric!
Of course your point is still valid. In th Sage function , all the work is done by Singular. My guess is that within Singular there is a special case which catches when 1 is a generator and returns [] in that case, but it is only a guess, and I hope that someone more familiar with Singular will speak up. I do agree with you that the primiary decomposition of the unit ideal should be empty. John On 19 December 2013 09:59, Matthias Goerner <[email protected]> wrote: > Version: > 'Sage Version 5.2, Release Date: 2012-07-25' > OS: > Darwin Kernel Version 11.4.2: Thu Aug 23 16:25:48 PDT 2012; > root:xnu-1699.32.7~1/RELEASE_X86_64 x86_64 > > > On Wednesday, December 18, 2013 10:58:31 PM UTC-8, Matthias Goerner wrote: >> >> >> Ideal(PolynomialRing(RationalField(),['x','y']),-1).primary_decomposition() >> returns [] as expected but >> Ideal(PolynomialRing(RationalField(),['x','y']),1).primary_decomposition() >> returns [Ideal (1) of Multivariate Polynomial Ring in x, y over Rational >> Field]. >> >> Clearly the ideals are identical, so they should have the same primary >> decomposition (independent of the unit it is generated by). Either, both >> should return [] or [Ideal(1)]. >> One would also expect the output of primary decomposition to not include >> (1) similarly to the prime factorization of a natural number not including >> 1, e.g., list(factor(1)) returns []. > > -- > You received this message because you are subscribed to the Google Groups > "sage-support" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sage-support. > For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
