Re: Pattern matching "on the fly"

• To: mathgroup at smc.vnet.net
• Subject: [mg30137] Re: Pattern matching "on the fly"
• From: "Tony MacKenzie" <mackenzi at usq.edu.au>
• Date: Tue, 31 Jul 2001 04:27:11 -0400 (EDT)
• References: <9jtk77\$87r\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Thank you everyone for your help.  I think your replys more than adequately
answered the question I posted. Unfortunately (for me), this was not the
step that was slowing down my algorithm.  I will have to post a more general
question which hopefully someone will be able to help with.

Thanking you
Tony MacKenzie,
University of Southern Queensland, Australia

Tony MacKenzie <mackenzi at usq.edu.au> wrote in message
news:9jtk77\$87r\$1 at smc.vnet.net...
> Hello from down under,
>
> I am trying to use Mathematica's pattern matching abilities to achieve
> something I can do using the computer algebra software REDUCE.  I want to
do
> this because I need to take advantage of the powerful numerical algorithms
> of Mathematica.
>
> I want to set all powers of some variable greater than a certain value to
> zero, but I want mathematica to apply this pattern matching "on the fly"
> (while an expression is being evaluated, not after the expression has been
> evaluated).
>
> I'll give a quick example. I want to set all powers of x greater than 2 to
> zero i.e. x^3=>0, x^4=>0 and so on. In REDUCE I can use the following
> statement
>
> let x^3=>0;   (* This replaces x^3 with 0, x^4 with 0 and so on*)
> Then if I evaluate (1+x)^1000000, I quickly (a few seconds) find this
> expression gives 499999500000*x^2  + 1000000*x + 1.  The pattern matching
is
> done as the expression is being expanded.
>
> Now in Mathematica I have tried  x^n_ ^:=0 /; n> 2; This works, but it
only
> appears to be applied after an expression has been expanded.  For example
if
> I try
>
> x^n_ ^:=0 /; n> 2;
> Expand[(1+x)^1000000];
>
> in Mathematica, the evaluation is very slow (which I think is because the
> pattern matching is applied after the expansion and not on the fly).
>
> Any help would be greatly appreciated as I am very new to Mathematica.
>
> Tony MacKenzie
> University of Southern Queensland, Australia
>
>
>
>
>

```

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