[Axiom-math] Groebner bases of a system of polynomial equations

[sahin]

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,




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