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Re: Constant term in polynomial?
*To*: mathgroup at smc.vnet.net
*Subject*: [mg3333] Re: Constant term in polynomial?
*From*: bruck at pacificnet.net (Ronald Bruck)
*Date*: Wed, 28 Feb 1996 03:35:12 -0500
*Organization*: University of Southern California
*Sender*: owner-wri-mathgroup at wolfram.com
In article <4gmhdc$gmv at dragonfly.wolfram.com>, bruck at mtha.usc.edu (Ronald
Bruck) 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 ?
...
:First[7 + 3 x y + y^2] will work for this one, since the 7 is present and
:appears first in the FullForm representation. But it won't work in
:First[3 x y + y^2], which returns 3 x y.
:
:OK, so I can build a command which computes Variables[First[expr]], and
:if that's empty, returns 0; otherwise returns First[expr]. Also clunky
:IMHO, but it seems the most workable--unless there's some trap I'm missing?
Yep, there's a trap -- First[3 x y] returns 3! So I ended up implementing
it as follows:
ConstantCoefficient[poly_] := Module[{c},
If[Head[poly] === Plus,
c = First[poly];
If[Variables[c] == {}, Return[c], Return[0]],
(* else head != plus *)
If[Variables[poly] == {}, Return[poly], Return[0]]
]
]
This won't recognize E + x as having constant term E, but fortunately my
polynomials all have rational coefficients.
It does seem there ought to be a built-in function to do this.
Someone e-mailed me a suggestion to use poly /. x_^e_ -> 0. This almost
works (it doesn't recognize the x in 7 + x as a power of x); it does
seem rather dangerous to apply the rule x_ -> 0!
The suggestion reminds me of another problem: suppose I want to work with
multivariable polynomials up through a certain degree p. So when, e.g., I
multiply two such polys, I need to get rid of terms like x^p y. This can
be done by applying rules like
(x^m_ y^n_ /; Positive[m+n-p]) -> 0
(although on one machine I have to use
(q__ x^m_ y^n_ /; Positive[m+n-p]) -> 0,
don't ask me why), with the annoyance that we also have to build rules for
x^m_ y -> 0 and x y^m_ -> 0 and x^m_ -> 0 and y^n_ -> 0! Is there some
more elegant way to do this--as well as faster--preferably one which works
for general variables, not just x and y? This came up when I was solving
an integral equation for a function of two variables, and used
undetermined coefficients.
--Ron Bruck
Now 100% ISDN from this address
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