Minimal set of Generators(basis) for an ideal/module

[VInay Wagh]

I am working in a multi-variable polynomial ring over a field (e.g. QQ
or CC). How do I get the minimal set of generators for an ideal I (or
module M)?

I am here referring to something I can do in Singular with the command
minbase.
(http://www.singular.uni-kl.de/Manual/latest/sing_266.htm)

Thanks in advance

-- VInay

[Volker Braun]

I don't know if this particular function is wrapped in Sage. But this Singular function requires the ideal to be homogeneous or the ring to be local. You don't mention this in your email, so I just wanted to point it out.

[Martin Albrecht]

On 29 September 2011 09:44, Volker Braun <vbrau...@gmail.com> wrote:
> I don't know if this particular function is wrapped in Sage.

Yes it is, as almost any function in Singular, thanks to the Singular function
interface :)

Using the example from

http://www.singular.uni-kl.de/Manual/latest/sing_266.htm

sage: P.<x,y,z> = PolynomialRing(GF(181),order='neglex')
sage: I = Ideal(x^2+x*y*z,y^2-z^3*y,z^3+y^5*x*z)
sage: from sage.libs.singular.function_factory import singular_function
sage: maxideal = singular_function('maxideal')
sage: J = maxideal(3,ring=P)+I
sage: minbase = singular_function('minbase')
sage: minbase(J)
[x^2, x*y*z, x*z^2, y^2, y*z^2, z^3]

Cheers,
Martin

--
name: Martin Albrecht
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_www: http://www.informatik.uni-bremen.de/~malb
_jab: martinr...@jabber.ccc.de

[Vinay Wagh]

@Volker Thanks for pointing that out... I had forgotten to mention
that in my post. BY the way any idea, why such a restriction? Can we
get away with that in sage (of course for that now we cant use
Martin's code...)

@Martin Thanks for the code.
Actually I wanted to do this "without" going back and forth Singular.
(i.e. defining the object as Singular objects.) This is one more
"trick" I have learnt today wherein I can avoid going to Singular and
do almost everything I could have done there :-)

Thanks once again...
-- VInay

On 29 September 2011 14:53, Martin Albrecht

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