> From: Raymond Toy <toy at rtp>
> Date: 25 Sep 2001 13:04:08 -0400
>
> I now have a final question. sn has these properties:
>
> sn(u/2)^2 = (1-cn(u))/(1+dn(u))
>
> sn(2*u) = 2*sn(u)*cn(u)*dn(u)/(1-m*sn(u)^4)
>
> How do I get maxima to understand this? However, I don't want this
> applied all of the time, just like the corresponding trig functions.
>
(C1) matchdeclare(u,true);
(D1) DONE
(C2) defrule(sn_half,sn1(u/2)^2, (1-cn1(u))/(1+dn1(u)));
2 u 1 - cn1(u)
(D2) sn_half : sn1 (-) -> ----------
2 dn1(u) + 1
(C3) sn1(x/2)^2;
2 x
(D3) sn1 (-)
2
(C4) apply1(%,sn_half);
1 - cn1(x)
(D4) ----------
dn1(x) + 1
(C5) apply1(1-sn1((a+b)/2)^2,sn_half);
1 - cn1(b + a)
(D5) 1 - --------------
dn1(b + a) + 1
(C6)
--
Good luck
-Boris