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MathGroup Archive 2006

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finding the (v,w) weighted degree of a polynomial

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71266] finding the (v,w) weighted degree of a polynomial
  • From: "xarnaudx at gmail.com" <xarnaudx at gmail.com>
  • Date: Sun, 12 Nov 2006 06:48:12 -0500 (EST)

Let P(x,y) be a bivariate polynomial in x,y.

for example:
P(x,y) = y^4 + x^5 + x^3 y^2

For any monomial M(x,y) = x^i y^j, the (v,w) weighted degree of M(x,y)
is defined as vi + wj.
And we consider that the (v,w)-degree of P will be the (v,w)-degree of
its highest monomial.

in the example above:
(4,5)-deg (P) = 4*3 + 2*5 = 22

...the question is: how to formulate this in mathematica?!
The aim is to write a function like:
WDeg[P_, v_, w_] := ....

thanks for help!


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