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Re: Pattern matching "on the fly"


Tony,
Not a general solution, but for your example we get


(1+x)^1000000 +O[x]^3//Normal//Timing

{0.27*Second, 1 + 1000000*x + 499999500000*x^2}
--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"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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