How to Simplify an symbolic expression

조회 수: 3(최근 30일)
safi58
safi58 2017년 4월 18일
댓글: Andrew Newell 2017년 4월 23일
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?
  댓글 수: 7
safi58
safi58 2017년 4월 21일
This is basically a tool for checking equivalence but that is not I am after. Thanks.

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답변(2개)

Andrew Newell
Andrew Newell 2017년 4월 21일
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.
  댓글 수: 5
safi58
safi58 2017년 4월 22일
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 2017년 4월 21일
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.
  댓글 수: 8
Andrew Newell
Andrew Newell 2017년 4월 23일
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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