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. Thanks in advance! Greg