On special polynomials decomposition
- To: mathgroup at smc.vnet.net
- Subject: [mg126612] On special polynomials decomposition
- From: Konstantin Nosov <nodus0 at gmail.com>
- Date: Thu, 24 May 2012 03:33:24 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
Dear friends
I'm seeking for standard Mathematica means for solving the following problem. Say, there is a polynomial in multiple variables. I try to present this polynomial in the form of polynomial in new variables, which are in turn polynomials in initial variables.
For example, the polynomial
a^2+2*a*b+a^2*b+b^2+a*c+a*b*c+c^2
can be presented as
(a*b+c)*(a+c)+(a+b)^2,
i.e. as a polynomial in the new variables {v1=a*b+c, v2=a+c, v3=a+b}.
Solution is complete, if for a given polynomial and new polynomials-variables at least one such presentation could be obtained or impossibility of the presentation is confirmed.
I'll be appreciate for any suggestion.