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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
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