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 [].
>

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