PolynomialReduce

• To: mathgroup at smc.vnet.net
• Subject: [mg8803] PolynomialReduce
• From: Gianluca Gorni <gorni at dimi.uniud.it>
• Date: Thu, 25 Sep 1997 12:26:38 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Hello mathgroupers!

I have just found what looks like a shortcoming
of PolynomialReduce. I have got a polynomial "poly"
and a list of three other polynomials "polylist",
and it turns out that poly is a linear combination of
the polynomials from the list:

In[3]:= poly == Expand[{-(1/4), -1, 1/4} . polylist]

Out[3]= True

Still, PolynomialReduce does not seem to notice:

In[4]:= Last[PolynomialReduce[poly, polylist]]===0

Out[4]= False

The documentation says that the last element in PolynomialReduce
is "minimal", but it does not elaborate. Wouldn't it be
reasonable that it checked at least for linear dependence?

Cheers!
Gianluca Gorni

The version and the actual polynomials are as follows:

Mathematica 3.0 Kernel for Power Macintosh
-- Terminal graphics initialized --

In[1]:= poly = Subscript[v, 1]*Subscript[b, 1, 1]*Subscript[b, 1, 2] +
Subscript[v, 3]*Subscript[b, 1, 1]*Subscript[b, 1, 2] +
2*Subscript[v, 3]*Subscript[b, 1, 2]^2 +
2*Subscript[v, 3]*Subscript[b, 1, 1]*Subscript[b, 2, 2] +
Subscript[v, 2]*Subscript[b, 1, 2]*Subscript[b, 2, 2] +
4*Subscript[v, 3]*Subscript[b, 1, 2]*Subscript[b, 2, 2];

In[2]:= polylist = {Subscript[v, 1]*Subscript[b, 1, 1]^2 +
Subscript[v, 2]*Subscript[b, 1, 2]^2 +
Subscript[v, 3]*(Subscript[b, 1, 1] + 2*Subscript[b, 1, 2])^2,
Subscript[v, 1]*Subscript[b, 1, 2]^2 +
Subscript[v, 2]*Subscript[b, 2, 2]^2 +
Subscript[v, 3]*(Subscript[b, 1, 2] + 2*Subscript[b, 2, 2])^2,
Subscript[v, 1]*(Subscript[b, 1, 1] + 2*Subscript[b, 1, 2])^2 +
Subscript[v, 2]*(Subscript[b, 1, 2] + 2*Subscript[b, 2, 2])^2 +
Subscript[v, 3]*(Subscript[b, 1, 1] + 4*Subscript[b, 1, 2] +
4*Subscript[b, 2, 2])^2};

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Gianluca Gorni
Universita` di Udine
Dipartimento di Matematica e Informatica
via delle Scienze 208
I-33100 Udine UD
Italy

Ph.:(39) (432) 558422    Fax:(39) (432) 558499
mailto:gorni at dimi.uniud.it
http://www.dimi.uniud.it

```

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