Symbolic Linear Function

*To*: mathgroup at smc.vnet.net*Subject*: [mg91457] Symbolic Linear Function*From*: yatesd at mac.com*Date*: Fri, 22 Aug 2008 03:13:31 -0400 (EDT)

I could not find anything in this group or on the internet about defining a generic linear function in Mathematica. I wanted a symbolic simplification of an expression where I had an (undefined) function that I knew was linear. I did the following: SetAttributes[e,{Flat, Orderless}]; e[a_?NumericQ * x_]:= a * e[x]; e[x_Plus]:=e/@x; This seemed to work fine and gave me the insight I wanted, but I was wondering if other people have thought about this and have different solutions or have any comments on my solution. Thanks. p.s. The expression I was interested in was Variance[Log[1+x]]. I defined Variance[x_]:=e[x^2]-e[x]^2 where e is representing expectation, although I am not using any properties of expectation other than its linearity. I then looked at the Taylor expansion to order 5 with Variance[Normal[Series[Log[1+x],{x,0,5}]]]