Simplyfing Sum[Mod[f(k),y],{k,k0,n}] type expressions? (Newbie question)

*To*: mathgroup at smc.vnet.net*Subject*: [mg40202] Simplyfing Sum[Mod[f(k),y],{k,k0,n}] type expressions? (Newbie question)*From*: prodogoss at btinternet.com (prodogoss)*Date*: Tue, 25 Mar 2003 14:50:20 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

I'm dealing with a problem that requires lots of summations of (x mod y) type expressions. I had hoped that Mathematica (which I've just started using) could simplify these but it doesn't seem to work. E.g., why won't (can't?) Mathematica simplify the expression: Sum[Mod[3n-k-4, 3],{k, 2n-1,d}] ? By *hand* I can show that if S = SUM((3n-k-4) mod 3, k = 2n-1 to d) and G = d - 2n + 2, then S = f(t) where t = (n - 2 - G) mod 3, and (f(0), f(1), f(2)) = ({1, 0, 0}, {0, 1, 0}, {0, 0, 1})(G-1, G, G) ie 3x1 matrix = (3rd order unit matix) x (3x1 matrix) Hence, given values of d & n, S can be expressed in such a way that its calculation is possible without having to labourously evaluate S for each step, k. I had heard so much about Mathematica and thought it would excel at handling problems like this involving summations of Mod[] etc.? Is there another way of doing this? Any help would be great! Thanks in advance!

**Follow-Ups**:**Re: Simplyfing Sum[Mod[f(k),y],{k,k0,n}] type expressions? (Newbie question)***From:*Dr Bob <drbob@bigfoot.com>

**Re: Simplyfing Sum[Mod[f(k),y],{k,k0,n}] type expressions? (Newbie question)***From:*Daniel Lichtblau <danl@wolfram.com>