= versus := and trying to speed up calculations

*To*: mathgroup at smc.vnet.net*Subject*: [mg35410] = versus := and trying to speed up calculations*From*: "Geoff Tims" <Geoff at swt.edu>*Date*: Thu, 11 Jul 2002 05:24:19 -0400 (EDT)*Organization*: Southwest Texas State University*Sender*: owner-wri-mathgroup at wolfram.com

I have the following function and it is called many many times in a program I have written. This is a bracket operator for a certain type of Lie Algebra I am looking at and it must be called over and over to test whether or not the Jacobi is actually 0 as it should be. With very low numbers for n, my program runs in a second or less. If n is around 20+ or if the coefficients are large, the program takes nearer a minute or two. That's not a long time, but I have a feeling that it's having to calculate the same Bracket many times in the program and I'm hoping to get rid of that somehow. However, I don't understand the differences between := and = enough. I've read the help files, but I don't understand the subtle differences such as I can call Bracket[stuff, something]:= somethingelse more than once, but it doesn't seem as if I can use = more than once. Bracket[a_.*e[i_], b_.*e[j_]] := Which[ i + j > n, 0, i == j, 0, i == 1, a*b*e[j + 1], i == 2 && j == 3, 14a*b*e[7], i == 3 && j == 4, 0, i < j, -a*b*Bracket[e[i + 1], e[j - 1]] + Bracket[e[1], Bracket[e[i], e[j - 1]]], i > j, -a*b*Bracket[e[j], e[i]] ]; (* bilinear function *) Bracket[mul_, expr_Plus] := Map[Bracket[mul, #] &, expr]; Bracket[expr_Plus, mul_] := Map[Bracket[#, mul] &, expr]; Bracket[0, x_] := 0 Bracket[x_, 0] := 0 Any help would be much appreciated. Geoff Tims