Re: finding the weighted degree of a polynomial

*To*: mathgroup at smc.vnet.net*Subject*: [mg79726] Re: finding the weighted degree of a polynomial*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 2 Aug 2007 04:02:22 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f8pk97$2pg$1@smc.vnet.net>

Arnaud Dagnelies wrote: > Let p(x,y) be a polynomial in x,y expressed in its expanded form, i.e. > as a sum of terms as follows: > > p(x,y) = sum c_ij x^i y^j > > I want to find the (a,b)-weighted degree of this polynomial defined as > > wdeg(p, {a,b}) = max (ai + bj) with c_ij != 0 > > (where a and b are given fixed values) > > help is welcome, > thanks First, we convert the polynomial into a list, then change the values of x and y by provided by the parameters, and finally apply the function *Max* to the resulting list of numeric values. In[1]:= wdeg[poly_, {a_, b_}] := Max[List @@ poly /. {x -> a, y -> b}] p = x^10 + 10*x^9*y + 120*x^7*y^3 + 210*x^6*y^4 + 252*x^5*y^5 + 120*x^3*y^7 + 45*x^2*y^8 + 10*x*y^9 + y^10; wdeg[p, {3, 5}] Out[3]= 253125000 Regards, Jean-Marc