How to Simplify an symbolic expression

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safi58
safi58 2017-4-18
评论： Andrew Newell 2017-4-23
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?
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Torsten
Torsten 2017-4-20
Or maybe this can help:
https://de.mathworks.com/help/symbolic/isequaln.html
Best wishes
Torsten.
safi58
safi58 2017-4-21
This is basically a tool for checking equivalence but that is not I am after. Thanks.

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回答（2 个）

Andrew Newell
Andrew Newell 2017-4-21
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.
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Torsten
Torsten 2017-4-21
I still don't understand why you try to transform the first expression into the second if - as you write - you are sure that both expressions yield the same values for a (at least in cases where both expressions are real-valued).
Best wishes
Torsten.
safi58
safi58 2017-4-22
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 2017-4-21
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.
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safi58
safi58 2017-4-23
Yes, without the return condition, it gives the solution.
Andrew Newell
Andrew Newell 2017-4-23
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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