Re: speed of multiplying polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg72556] Re: speed of multiplying polynomials
• From: Giovanni Resta <g.restaxxx at cutTheXXXiit.cnr.it>
• Date: Tue, 9 Jan 2007 07:01:16 -0500 (EST)
• References: <enpste\$e5t\$1@smc.vnet.net>

```dmharvey at math.harvard.edu wrote:

> This is ludicrously slow compared to some other computer algebra
> systems, which can do this multiplication in about 0.0003
> seconds. I can't believe mathematica is in the order of 10000 times
> slower for this simple task. I think perhaps we are doing something
> wrong. Can anyone suggest a way of coaxing mathematica into doing this
> kind of arithmetic at a comparable pace?

I think that the point is that Mathematica multiplies the
two expression without regarding them as polynomials, but as general
expressions.
Indeed, if I have two polynomials:

a = Sum[Random[Integer,{1,1000}] x^k,{k,0,1000}];
b = Sum[Random[Integer,{1,1000}] x^k,{k,0,1000}];

And I compute the explicit product:

Timing[c = Expand[a b];]
{1.28408 Second, Null}

If I have something that is not a polynomial:
Timing[c = Expand[(a+7/x)(b+Sin[x])];]
{1.36808 Second, Null}

I got a time which is very near.
Hence, probably Mathematica is not taking advantage of the fact
that a and b are polynomials, in the first case.
In other symbolic programs you have to declare explicitly that something
is a polynomial (sometimes you can manipulate only polynomials...) so
easily the computation is faster.
I do not know if there is a way to tell mathematica that that
expressions are polynomials. Usually to perform such a simple
tasks, if I need speed, I write a specific C program
(unless coefficients are symbolic...).
g.

```

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