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

*To*: mathgroup at smc.vnet.net*Subject*: [mg71373] Re: [mg71318] Re: finding the (v,w) weighted degree of a polynomial*From*: Daniel Lichtblau <danl at wolfram.com>*Date*: Thu, 16 Nov 2006 00:52:59 -0500 (EST)*References*: <200611121148.GAA18658@smc.vnet.net><ejc5b4$6st$1@smc.vnet.net> <200611151143.GAA01169@smc.vnet.net>

xarnaudx at gmail.com wrote: > thanks to all of you! > > adopted solution: > WDeg[Q_, v_, w_] := > {v, w}.Internal`DistributedTermsList[Q, {x, y}, MonomialOrder -> > {{v, w}, {0, 1}}][[1, 1, 1]]; > > The last suggested solution, despite of being very elegant, has an > issue: different monomials of same weighted degree can cancel each > other and vanish. For example: > P(x,y) = x^3 y - x^1 y^2 > For the (1,2)-degree, when replacing {x -> t, y -> t^2}, we get: P(t) = > t^5 - t^5 = 0 > Resulting in a weighted degree of 0 instead of the correct answer which > would be 5. Right. I knew that, once, long ago. The corrected version uses random coefficients to avoid this cancellation pitfall. weightedDegree[poly_, vars_, wts_] := Module[{t}, Exponent[poly /. Thread[vars -> Table[Random[],{Length[wts]}]*t^wts], t]] In[25]:= weightedDegree[x^3*y - x*y^2, {x,y}, {1,2}] Out[25]= 5 I like Internal`DistributedTermsList (I wrote it), but I think it is overkill for this particular problem. Though if you need more information about a polynomial with respect to a particular term order, it's the function of choice (granted, as an "internal" function it is not documented). Daniel Lichtblau Wolfram Research

**References**:**finding the (v,w) weighted degree of a polynomial***From:*"xarnaudx@gmail.com" <xarnaudx@gmail.com>

**Re: finding the (v,w) weighted degree of a polynomial***From:*"xarnaudx@gmail.com" <xarnaudx@gmail.com>