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Bug in PolynomialReduce

  • To: mathgroup at
  • Subject: [mg15005] Bug in PolynomialReduce
  • From: "Greg Arnold" <Gregory.Arnold at>
  • Date: Sat, 5 Dec 1998 01:30:10 -0500
  • Sender: owner-wri-mathgroup at

Hello all,

I'm trying to use GroebnerBasis and PolynomialReduce to simplify
equations which I'm trying to integrate.  My general problem is that I
want to be able to substitute for complex functions.  However, I'm not
getting the expected result even for this fairly simple case:

gb=GroebnerBasis[{r1==z/y,r2==x/y},{x,y,z,r1,r2}]; gb // InputForm

{r1*y - z, -r1 + z/y, x - r2*y}



pr=PolynomialReduce[ z/y+x/y,gb,{x,y,z,r1,r2}]; pr // InputForm

{{0, 0, y^(-1), 0}, (r2*y + z)/y}

(1) I expect to have only 3 coefficients (not 4) in the first part, and
(2) the residual (the last part) should reduce to r1+r2

Am I doing something wrong?  I'm running WinNT.  Is there a bug
that has been fixed in 3.0.1?

P.S.  I did notice that if I choose the order {x,z,y,r1,r2}, then I will
get the expected result for both (1) and (2)!.  However, I cannot think
of a way to decide which way(s) will work and which will not.

Thanks in advance!


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