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## [Axiom-developer] [AxiomProblems] Problem with coefficients

 From: Bill Page Subject: [Axiom-developer] [AxiomProblems] Problem with coefficients Date: Mon, 07 Mar 2005 21:24:10 -0600

Changes http://page.axiom-developer.org/zope/mathaction/AxiomProblems/diff
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According to the Axiom book function 'coefficients' does not
include zeros in the list. Furthermore it does not say explicitly
in what order the coefficients themselves are listed. Remember
that there are also terms of degree higher than 1. In fact the
two multivariate polynomials that you used above are formally
identical
\begin{axiom}
Dg :=  [p3 - 3*p2 + 3*p1 - p0,3*p2 - 6*p1 + 3*p0,3*p1 - 3*p0,p0]
(Dg::List MPOLY([p0,p1,p2,p3],?)=Dg::List MPOLY([p3,p2,p1,p0],?))::Boolean
\end{axiom}

For you example problem, to produce a list of coefficients of
the terms of degree 1, including the zeros and in a specific
order, use the function 'coefficient' like this:
\begin{axiom}
[[coefficient(p,x,1) for x in [p0,p1,p2,p3]] for p in Dg]
\end{axiom}

And of course you can use this to produce a matrix.
\begin{axiom}
matrix %
\end{axiom}
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