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Pattern matching "on the fly"

• To: mathgroup at smc.vnet.net
• Subject: [mg30100] Pattern matching "on the fly"
• From: "Tony MacKenzie" <mackenzi at usq.edu.au>
• Date: Sat, 28 Jul 2001 01:51:02 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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