Re: Constant term in polynomial?

*To*: mathgroup at smc.vnet.net*Subject*: [mg3349] Re: [mg3326] Constant term in polynomial?*From*: Peder Thusgaard Ruhoff <ptk at imada.ou.dk>*Date*: Thu, 29 Feb 1996 03:24:30 -0500*Sender*: owner-wri-mathgroup at wolfram.com

On Mon, 26 Feb 1996, Ronald Bruck <bruck at mtha.usc.edu> wrote: > > Arrgh, I feel stupid asking this question, but I can't think how to do it: > how do I find the constant term in a polynomial in several variables in > Mathematica? For example, the "7" in 7 + 3 x y + y^2 ? > > I suppose one way would be to use > > Coefficient[Coefficient[7 + 3 x y + y^2,x,0],y,0]. > > But that's incredibly clunky, especially since I may have fifty or more > variables in my real-life problem. > ... many lines deleted ... > > --Ron Bruck > > > > Dear Ron, One way to solve your problem is to define a function PolynomialConstant in the following way (based on an idea in Bahder, Mathematica for Scientists and Engineers, page 345) =========================================================================== In[1]:= PolynomialConstant[expr_, vars_List] /; PolynomialQ[expr, vars] := Fold[Coefficient[#1, #2, 0]&, expr, vars] In[2]:= PolynomialConstant[expr_, var_] /; PolynomialQ[expr, var] := Coefficient[expr, var, 0] =========================================================================== Some examples =========================================================================== In[3]:= PolynomialConstant[7 + 3 x y + y^2, {x, y}] Out[3]= 7 In[4]:= PolynomialConstant[(x + y + 1)^10, {x, y}] Out[4]= 1 In[5]:= PolynomialConstant[(x + y + 1)^10, x] 2 3 4 5 6 7 Out[5]= 1 + 10 y + 45 y + 120 y + 210 y + 252 y + 210 y + 120 y + 8 9 10 > 45 y + 10 y + y In[6]:= PolynomialConstant[x y z, {x, y, z}] Out[6]= 0 In[7]:= PolynomialConstant[Sin[x]^3 + y + 5 z, {Sin[x], y}] Out[7]= 5 z =========================================================================== You can also try to solve your problem using the built-in function CoefficientList. Hope this helps, Peder ------------------------------------------------------------------------------ Peder Thusgaard Ruhoff Phone: (+45) 66 15 86 96, ext. 2411 Department of Information Technology Fax: (+45) 65 93 26 91 Odense University, Campusvej 55 Email: ptk at imada.ou.dk DK-5230 Odense M, DENMARK "It is important for him who wants to discover not to confine himself to one chapter of science, but to keep in touch with various others." - Jacques Hadamard ------------------------------------------------------------------------------ ==== [MESSAGE SEPARATOR] ====