Bug in PolynomialReduce

• To: mathgroup at smc.vnet.net
• Subject: [mg15005] Bug in PolynomialReduce
• From: "Greg Arnold" <Gregory.Arnold at sensors.wpafb.af.mil>
• Date: Sat, 5 Dec 1998 01:30:10 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```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:

In[46]:=
gb=GroebnerBasis[{r1==z/y,r2==x/y},{x,y,z,r1,r2}]; gb // InputForm

Out[46]//InputForm=
{r1*y - z, -r1 + z/y, x - r2*y}

In[48]:=
Length[gb]

Out[48]=
3

In[53]:=
pr=PolynomialReduce[ z/y+x/y,gb,{x,y,z,r1,r2}]; pr // InputForm

Out[53]//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 3.0.0.0 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.