Re: Rule-based programming: declare variables to be a number

*To*: mathgroup at smc.vnet.net*Subject*: [mg80776] Re: [mg80751] Rule-based programming: declare variables to be a number*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Sat, 1 Sep 2007 00:31:14 -0400 (EDT)*References*: <200708310348.XAA08008@smc.twtelecom.net>

On 31 Aug 2007, at 05:48, Hendrik van Hees wrote: > 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 > Use NumericQ instead of NumberQ. Then: NumericQ[a] = True; NumericQ[b] = True; (Note that you do not need to unprotect NumericQ !). Then you get for free: NumericQ[a*b] True NumericQ[b^a] True and so on, just as you wanted. Andrzej Kozlowski PS. I am sure NumericQ has worked like this at lest since version 5 but I no longer remember about version 4.