How to Simplify an symbolic expression

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safi58
safi58 on 18 Apr 2017
Commented: Andrew Newell on 23 Apr 2017
Hi all, I want to simplify this equation
a= 2 atan((-2+Sqrt(4-gama^2 *l^2* M^2-4* gama *l* M^2 *tan(gama/2)+4* tan(gama/2)^2-4 *M^2 *tan(gama/2)^2))/(gama* l* M+2* tan(gama/2)+2* M* tan(gama/2)))
into this form
a= (gama/2)-asin(((gama*l*M)/2)*cos(gama/2)+M*sin(gama/2))
Can anyone help?
  7 Comments
safi58
safi58 on 21 Apr 2017
This is basically a tool for checking equivalence but that is not I am after. Thanks.

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Answers (2)

Andrew Newell
Andrew Newell on 21 Apr 2017
If I define
a= 2*atan((-2+sqrt(4-gama^2 *l^2* M^2-4* gama *l* M^2 *tan(gama/2)+4* tan(gama/2)^2-4 *M^2 *tan(gama/2)^2))/(gama* l* M+2* tan(gama/2)+2* M* tan(gama/2)));
b = (gama/2)-asin(((gama*l*M)/2)*cos(gama/2)+M*sin(gama/2));
and substitute pi for gama,
subs(a,gama,pi)
subs(b,gama,pi)
I get a==NaN and b==pi/2 - asin(M). So they are not the same. I find that applying simplify to a does not change it significantly.
  5 Comments
safi58
safi58 on 22 Apr 2017
Hi Torsten,
I want to transform the first expression because second one is more compact and easy to read.

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Walter Roberson
Walter Roberson on 21 Apr 2017
I randomly substituted M=2, l=3. With those two values, the two expressions are not equal. One of the two goes complex from about gama = pi to gama = 17*pi/16 . From 17*pi/16 to roughly 48*Pi/41 the difference between the two is real valued . After that the difference has a real component of 2*pi and an increasing imaginary component.
  8 Comments
Andrew Newell
Andrew Newell on 23 Apr 2017
To summarize what Walter and I are saying, the two expressions are clearly not always equal, and the conditions under which they are equal are hard to pin down. Perhaps you should look more closely at how they did it in the article. Not that published work is always 100% correct.

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