Re: [Axiom-math] Groebner bases of a set of equations

[Sureyya Sahin]

Thank you for the help. I tried your suggestion and I am indeed getting
some results. But if we extend the number of variables by defining a few
of the parameters (in this case cb,sb) while keeping the equations
unchanged, would this effect the polynomial equations and therefore the
solutions? Also, is this a standard way to attack this kind of a
problem, i.e. equations with parameters, in axiom? I guess this needs
some experimentation to obtain the solution.

I was initially thinking that if I get [1] as a Groebner bases, then it
means that there is no solution to the system of equations. But given
this example, I guess I was wrong in my interpretation. What does
getting [1] as a Groebner bases in axiom or another computer algebra
system mean?

Best Regards,

On Tue, 2014-02-18 at 18:39 -0500, Bill Page wrote:
> Try a larger set of variables (generators). Other unlisted symbols
> default to being parameters (from FRAC POLY INT). For example
> 
> [ca,cb,sa,sb,x,y]
> 
> gives a basis of 12 polynomials. See
> 
> http://axiom-wiki.newsynthesis.org/address@hidden
> 
> On 18 February 2014 11:23, sahin <address@hidden> wrote:
> > Hello,
> >
> > I am trying to obtain Groebner bases of a system of equations. Below is my
> > code
> >
> > (1) -> m : List DMP([ca,sa,x,y],FRAC POLY INT)
> > (2) -> m :=
> > [x^2+y^2-r1^2,(x+lab*ca)^2+(y+lab*sa)^2-r2^2,(x+lac*(ca*cb-sa*sb))^2+(y+lac*(sa*cb+ca*sb))^2-r3^2,ca^2+sa^2-1]
> >
> > asking for groebner bases is leading to
> > (3) -> groebner(m)
> >
> >    (3)  [1]
> > Type:
> > List(DistributedMultivariatePolynomial([ca,sa,x,y],Fraction(Polynomial(Integer))))
> >
> > which does not make sense to me. The equations are based on a physical
> > system and I can't see any reason that would lead to an inconsistency. Why
> > am I getting [1] as the result? Any help or insight would be
> > well-appreciated.
> >
> > Best Regards,
> >
> >
> >
> > --
> > View this message in context: 
> > http://nongnu.13855.n7.nabble.com/Groebner-bases-of-a-set-of-equations-tp179213.html
> > Sent from the axiom-math mailing list archive at Nabble.com.
> >
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