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MathGroup Archive 1995

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Help reduce this expression (Not Long)

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1977] Help reduce this expression (Not Long)
  • From: Vlad.Fridkin at manuel.anu.edu.au
  • 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[1]:= 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[2]:= % /. ellirule;

In[3]:= % /. ellirule;

In[4]:= % /. sngone

Out[4]= 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.
Vlad.
        
--

                             ___________________________ 
    Vlad.Fridkin at anu.edu.au  || ||| || ||| || ||| || ||| 
       http://wwwmaths.anu.edu.au/~vxf661/Vlad_Fridkin.html


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