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Rule-based programming: declare variables to be a number

• To: mathgroup at smc.vnet.net
• Subject: [mg80751] Rule-based programming: declare variables to be a number
• From: Hendrik van Hees <hees at comp.tamu.edu>
• Date: Thu, 30 Aug 2007 23:48:51 -0400 (EDT)

I still work with Mathematica 4.0. I hope, somebody can answer my
question despite this.

I have written a simple rule-based program to evaluate traces of
SU(2)-Lie algebra (Pauli matrices) to help me to obtain the Lagrangian
of a chiral model, but that's not so important for my question.

My problem is the following: To get the usual rules with algebraic
expressions containing numbers and Lie-algebra variables, one needs to
define what happens when a Lie-algebra variable is multiplied by a
number. This works fine as long as I use really constant numbers like
1, 2, 1/2, etc.

However, of course, one needs this feature also for variable numbers,
say a coupling constant g. So I wrote Unprotect[NumberQ] and then said

NumberQ[g]:=True,

but then NumberQ[g^2] evaluates to False. So I have written a whole
bunch of rules to make powers of g also numbers. It works already quite
well, but is there a possibility to just declare a variable (like g) to
be a number, and then make Mathematica know, that expressions like g^2,
Sqrt[g], 1+g, etc. are also numbers?
 
-- 
Hendrik van Hees                        Texas A&M University
Phone:  +1 979/845-1411                 Cyclotron Institute, MS-3366
Fax:    +1 979/845-1899                 College Station, TX 77843-3366
http://theory.gsi.de/~vanhees/faq       mailto:hees at comp.tamu.edu