Re: Mupad Rules...

Peter Pein wrote: 


Salut Raymond,

make use of the option Steps=... in Simplify:


Simplify(f0(B),SelectRules = simpSin,Steps=1000);

- 4*sin(1/4*B)^2 + 2*sin(1/2*B) + sin(B)*ln(2*sin(1/4*B)^2 -
2*sin(3/4*B)^2 - 2*sin(B) + sin(1/2*B) + sin(3/2*B)) -
sin(B)*ln(2*sin(1/4*B)^2 - 2*sin(3/4*B)^2 + 2*sin(B) + sin(1/2*B) +
sin(3/2*B)) - ln(2*sin(1/4*B)^2 - 2*sin(3/4*B)^2 - 2*sin(B))*sin(B) +
ln(2*sin(1/4*B)^2 - 2*sin(3/4*B)^2 + 2*sin(B))*sin(B) + 2

simplify(%,sin);

2*cos(1/2*B) + 2*sin(1/2*B) + sin(B)*ln(cos(3/2*B) - cos(1/2*B) -
2*sin(B) + sin(1/2*B) + sin(3/2*B)) - sin(B)*ln(2*sin(B) - cos(1/2*B) +
cos(3/2*B) + sin(1/2*B) + sin(3/2*B)) - sin(B)*ln(cos(3/2*B) -
cos(1/2*B) - 2*sin(B)) + sin(B)*ln(2*sin(B) - cos(1/2*B) + cos(3/2*B))

Simplify(%,Steps=1000);
[gives no further improvement]

With Mathematica's help I got:

2*c-arctanh(2*c/(2+sin(b)))*sin(b), with c=sin(b/2)+cos(b/2)



  Hallo Peter,

Many thanks for the Steps trick (531 were really required!) and the very nice Mathematica simplification!

	   Raymond
.