Use of Mathematica with Rule-based Equation Derivations

*To*: mathgroup at smc.vnet.net*Subject*: [mg61914] Use of Mathematica with Rule-based Equation Derivations*From*: mmorriss at gcn.ou.edu*Date*: Fri, 4 Nov 2005 05:11:39 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi All - I'm a many-year user of mathematica, but have always had one particular problem with it that I may have just simply missed reading about. Mathematica Version: 5.2 Problem: I would like to develop a set of re-rewite rules to apply to the Expected Value operator. For example: E[a x] = a E[x] a -> constant, x -> variable E[b + f[x]] = b + E[f[x]] , etc. The issue is how does one using Mathematica distinguish a 'constant variable (i.e. a and b)' from a variable 'variable' (i.e. 'x')? The head of a, b and x is 'Symbol' and neither a, b nor x contain a number so I can't use a_?NumberQ to identify it as a constant. This actually goes to the wider question of how does one use Mathematica for symbolic derviations where numbers are not actually substituted in the derviation? E.g. E[a + E[b x]] /. Rule2 out= a + b E[x] etc. Thanks all - Mark Morrissey University of Oklahoma

**Follow-Ups**:**Re: Use of Mathematica with Rule-based Equation Derivations***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Use of Mathematica with Rule-based Equation Derivations***From:*Daniel Lichtblau <danl@wolfram.com>