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Re: Multiplying large polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg14719] Re: [mg14685] Multiplying large polynomials
• From: Carl Woll <carlw at fermi.phys.washington.edu>
• Date: Tue, 10 Nov 1998 01:21:09 -0500
• Sender: owner-wri-mathgroup at wolfram.com

Hi Thomas,

This looks like a good application for Series.

poly1 = a h^2 + b;
poly2 = d h + e;
N = 2;

s1 = poly1 + O[h]^3;
s2 = poly2 + O[h]^3;

s1 s2

should return something like

b e + b d h + a e h^2 + O[h]^3

Carl Woll
Dept of Physics
U of Washington

On Sun, 8 Nov 1998, Thomas Bell wrote:

> I'm trying to multiply two huge polynomials, and memory is a major
> concern.  I want to truncate the resulting polynomial to a specified
> power (N) in one of the variables (h), and I was wondering if it was
> possible to tell Mathematica to not bother multiplying two terms if the
> resulting power of h was greater than N.  This is, of course, in the
> hope that this "automatic truncation" would save time and memory.  For
> example, if
> 
> poly1 = a h^2 + b;
> poly2 = d h + e;
> N = 2;
> 
> then I would like to result to be
> 
> result = a e h^2 + b d h + b e
> 
> Instead, I have to write
> 
> result = Expand[poly1 poly2]/.h^3 -> 0;
> 
> which forces Mathematica to create the enormous product before
> truncating.  Please cc to tombell at stanford.edu, and thanks in advance
> for any suggestions.
> 
>