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Pattern matching "on the fly"
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