       Help reduce this expression (Not Long)

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1977] Help reduce this expression (Not Long)
• Date: Mon, 4 Sep 1995 22:21:16 -0400
• Organization: Australian National University

```Here it is.  I didn't want to send the expression
in its glory since it is too long.  So I send this
expression and a few rules to get to the big one:

Dn[a_,k_] := Sqrt[1 - k^2 Sn[a,k]^2];

Cn[a_,k_] := Sqrt[1 - Sn[a,k]^2];

ellirule := {Sn[u_+v_,k_] -> (Sn[u,k]Cn[v,k]Dn[v,k] + Cn[u,k]Sn[v,k]Dn[u,k])/
(1-k^2 Sn[u,k]^2 Sn[v,k]^2)}

sngone := Sn[x_,k_]-> x;

In:= Sn[v, k]*Sn[2*y, k]^2 + Sn[u - v, k]*Sn[2*y, k]*Sn[u + 2*y, k] -
Sn[u, k]*Sn[2*y, k]*Sn[u - v + 2*y, k] -
k^2*Sn[u, k]*Sn[u - v, k]*Sn[v, k]*Sn[2*y, k]^2*Sn[u + 2*y, k]*
Sn[u - v + 2*y, k]

In:= % /. ellirule;

In:= % /. ellirule;

In:= % /. sngone

Out= Lots of stuff I cannot simplify to become zero.

Has anyone out there got experience working with elliptic functions
in an algebraic way?

Thanks for any help.