# Groebner bases of a set of equations Classic List Threaded 5 messages Open this post in threaded view
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## Groebner bases of a set of equations

 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)   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  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.htmlSent from the axiom-math mailing list archive at Nabble.com. _______________________________________________ Axiom-math mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-math
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## Re: Groebner bases of a set of equations

 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/SandBoxGroebnerBasis#msg20140219000533+0000@...On 18 February 2014 11:23, sahin <[hidden email]> 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)   > 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  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. > > _______________________________________________ > Axiom-math mailing list > [hidden email] > https://lists.nongnu.org/mailman/listinfo/axiom-math_______________________________________________ Axiom-math mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-math
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## Re: Groebner bases of a set of equations

 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  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  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/SandBoxGroebnerBasis#msg20140219000533+0000@...> > On 18 February 2014 11:23, sahin <[hidden email]> 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)   > > 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  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. > > > > _______________________________________________ > > Axiom-math mailing list > > [hidden email] > > https://lists.nongnu.org/mailman/listinfo/axiom-math_______________________________________________ Axiom-math mailing list [hidden email] https://lists.nongnu.org/mailman/listinfo/axiom-math