Re: Use of Mathematica with Rule-based Equation Derivations

*To*: mathgroup at smc.vnet.net*Subject*: [mg61932] Re: Use of Mathematica with Rule-based Equation Derivations*From*: David Bailey <dave at Remove_Thisdbailey.co.uk>*Date*: Sat, 5 Nov 2005 01:52:14 -0500 (EST)*References*: <dkfd8o$etv$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

mmorriss at gcn.ou.edu wrote: > 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 > > Hello, It seems to me that in your notation E[f[a,x]], x has a role as a dummy variable. Since Mathematica can't possible be expected to know that fact, it might make sense to use a notation that makes this explicit. Suppose you make x a second argument (a subscript might look neater). Also, since E is a built in symbol, let us use Ex (again, a script E might look neater) Ex[a x, x] /. Ex[m_ n_, x_] :> m Ex[n, x] /; FreeQ[m, x] a Ex[x,x] This will simplify any expectation value of a product where one component is a constant expression of any sort. Note that it will simplify Ex[x a,x] just as well because Times is commutative. David Bailey http://www.dbaileyconsultancy.co.uk