[168] in mathematical software users group
Re: grobner basis question
daemon@ATHENA.MIT.EDU (Reid M. Pinchback)
Wed May 31 12:11:02 1995
To: msug@MIT.EDU
Cc: sywong@MIT.EDU
Reply-To: msug@MIT.EDU
In-Reply-To: Your message of Sun, 28 May 1995 14:35:36 -0400.
<9505281835.AA22938@alfredo.MIT.EDU>
Date: Wed, 31 May 1995 12:09:47 EDT
From: "Reid M. Pinchback" <reidmp@MIT.EDU>
>Dear MSUGers,
>I've been trying to perform some grobner basis calculation with Maple V.3
>and I got some strange error message. I have an ideal generated by two
>polynomials G1, G2, with variables t,x,a,b. With I type
> gbasis([G1,G2], [t,x,a,b], plex);
>Maple keeps complaining that
> Error, (in grobner/iplex/reduce) cannot evaluate boolean
>On the other hand, if I compute just
> gbasis([G1], [t,x,a,b], plex);
>(or with [G2]) then I get no error message (and the expected answer).
>What is going on?
I get the same results as you. One interesting thing I spotted.
If I replace the complex value "I" with some other name, eg:
H1:=subs(I=k,G1): H2:=diff(H1,t):
then gbasis is willing to work with these polynomials. I don't know
what the final result is; I aborted the computation after a couple of
minutes. My point is that the complexity of the polynomials probably
isn't an issue.
My next test was to take G1 and eliminate every term that contained "I"
in it. Again, gbasis was willing to then work with the resulting
[G1,G2] and even came up with an answer relatively quickly.
From these two tests I'm led to suspect that the algorithms implemented
for the grobner package assume polynomials with coefficients over
the rationals (and, obviously, thus also the integers). If it doesn't
also augmented this by allowing the obvious algebraic extensions like
roots of rationals (which "I" could be - and by Maple is - viewed as),
then you may have tripped over a limitation in the grobner package.
I'm also inclined to think that grobner doesn't have a concept of
'side relations', which would be the other approach to dealing with
reducing "I".
If my suspicions are correct, then your alternative would probably be
to use the Gauss package so that you could specify the coefficient
domain. I haven't done this myself, but there is an article about it
in MapleTech Issue 9. I don't know a great deal about grobner basis
methods, but I've heard that the algorithm implemented in the Gauss
version of grobner is the "weak" version of the typical algorithm
(Buchberger's), not the strong version. Whether or not that would be
relevant to your situation or not, I don't know.
===============================================================
= Reid M. Pinchback =
= Senior Faculty Liaison =
= Academic Computing Services, MIT =
= =
= Email: reidmp@mit.edu =
= URL: http://web.mit.edu/user/r/e/reidmp/www/home.html =
===============================================================
