lacking features that is clearly used in grobner basis

Librairie C++ de calcul formel/ C++ symbolic computation library

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jocaps
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Inscription : lun. avr. 17, 2017 4:32 pm

lacking features that is clearly used in grobner basis

Message par jocaps » mar. janv. 02, 2018 10:30 am

Hi,

I was wondering if there is really no way to get leading term monomial list from a list of (multivariate) polynomials such as? Or apply monomial ordering (of certain ordering type, e.g. plex, tdeg etc.) to a certain polynomial

I am sure these features (maybe hidden internally) exists in giac but can they not be called in say XCaS or giacpy? For instance a function that gives me the dimension of a complex variety does not exist, but I could write an algorithm (using grobner basis and Hilbert function) that could do this for me. Though, monomial orderings and extraction of monomial ideals should all be manually programmed by me which I am sure is already available in giac's C code (otherwise gbasis would not have worked).

Jose

parisse
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Inscription : mar. déc. 20, 2005 4:02 pm
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Re: lacking features that is clearly used in grobner basis

Message par parisse » mar. janv. 02, 2018 12:13 pm

lcoeff accepts a third argument for ordering, e.g. lcoeff(x*y^2+x^2,[x,y]) and lcoeff(x*y^2+x^2,[x,y],tdeg)
There are many other C++ commands, but they do not take symbolic polynomials as arguments, they work with internal multivariate polynomials. There are various formats for multivariate polynomials, one of them is exposed in Xcas or giacpy (you can convert to and from it with symb2poly), but it lacks user commands (mainly because nobody asked before), other formats are too specialized for gb computation efficiency and are not exposed at all in Xcas/giacpy.

jocaps
Messages : 118
Inscription : lun. avr. 17, 2017 4:32 pm

Re: lacking features that is clearly used in grobner basis

Message par jocaps » mar. janv. 02, 2018 12:59 pm

Oh nice. So if I put in the ordering as a third parameter I actually get the leading term (not only the leading coefficient) with respect to the that ordering. I couldn't have guessed (I don't think it was also in the manual, but I have an older pdf version of the manual). Thanks and sorry for the disturbance, for now this is sufficient for my purposes

Jose

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