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Extracting terms of a multivariate polynomial order by order

• To: mathgroup at smc.vnet.net
• Subject: [mg80280] Extracting terms of a multivariate polynomial order by order
• From: Marcus P S <marcus.ps at gmail.com>
• Date: Thu, 16 Aug 2007 04:51:49 -0400 (EDT)

Hello,

  I have a multivariate polynomial (3 variables) from which I would
like to extract terms order by order.  More explicitly, I want all the
lowest order terms, or all terms of the form

c(L,M,N) x^L y^M z^N

  where L+M+N is smallest, and c(LMN) is some coefficient.  If I have
this, I can extract order by order, and taylor to which order I want
to approximate my polynomial.

  I considered "Coefficients", but if I ask for the coefficients of
the form x^2 z^2, it may return something like "1 + y", which is not
what I want.  Moreover, I have to explicitly request each possible
term of a given order, which seems too mechanical/repetitive to be the
"right way"  to do things.  The function for manipulating SeriesData
objects are similarly limited.

  I am assuming that there is function in Mathematica (even 5.2) that
will do this.  Any suggestions would be greatly welcome.

  Thanks in advance.

  Marcus Silva

• Follow-Ups:
  • Re: Extracting terms of a multivariate polynomial order by order
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>