Re: Naming Operators in Pure Function form
- To: mathgroup at smc.vnet.net
- Subject: [mg101860] Re: Naming Operators in Pure Function form
- From: earthnut at web.de (Bastian Erdnuess)
- Date: Mon, 20 Jul 2009 05:59:50 -0400 (EDT)
- References: <email@example.com>
Mathematica cannot know that you want to explain the sum of to operators pointwise, i.e. (X+T)(f) = X(f) + T(f) . You can "teach" Mathematica a simple operator algebra (@ as multiplication) with the lines Unprotect[Function]; a_Function + b_Function ^:= a[##] + b[##] & Function /: a_?NumberQ * b_Function := a * b[##] & Protect[Function]; Then your example works as you desired: X = D[ #, x ] & T = D[ #, x ] & (X + T) @ (X - T) @ f[ t, x ] --> f^(0,2) [ t, x ] - f^(2,0) [ t, x ] But be careful, I'm not sure if it is a good idea to do that. Bastian Sid <pcoords29 at gmail.com> wrote: > Dear Mathgroup, > > I am having a problem with naming differential operators wriiten as > pure functions. > > Consider the simple example (1-D wave operator) > > (D[#1, x] + D[#1, t] & ) @ (D[#1, x] - D[#1, t] & ) ... > (*) > > I want to name the diffl operators as follows : > > Let X be d/dx and T be d/dt > > Now, if I define X = D[#1, x] & and T = D[#1, t] &, that > > won't do. Also, omitting an ampersand will give zero. > > So , how should I define pure functions X and T so that (*) above > > can be written as > > (X +T ) @ (X -T ) > > (In my actual problem, I have in place of X a spherical Laplacian > plus some first-order operators and constants. ) > > > Any hints to help me suss this out will be most appreciated. > > Thanking you in advance. > > Regards. > > Sid.