Thank you, Peter but there is not quite what I was looking for.
Technically your result simply proves that the square root of the square of a
real number x is the absolute value of x (\sqrt{x^2} = |x| for x \in reals).
Or in your terms:
test = |sin(INC)|/\sqrt{sin(INC)^2} for INC real
is always, identically, equal to 1.
For my case, sin(INC)/|sin(INC)| is what I am looking at (i.e., the numerator
has no absolute value), and it is equal to 1 for my assumptions but how can
sympy know that without knowing that I've restricted INC to the range [0,\pi]?
If, for example, INC were in the range [\pi,2\pi] then sin(INC)/|sin(INC)| =
-1.
If there is a way to say something like:
INC = sm.symbols(‘INC’, real=True,range=[0,pi])
then I say that the result is proved. But I can't anything like this in the
documentation (perhaps I simply don't know where to look).
Conrad
________________________________
From: [email protected] <[email protected]> on behalf of
[email protected] <[email protected]>
Sent: Tuesday, January 21, 2025 9:39 AM
To: [email protected] <[email protected]>
Subject: RE: [sympy] trigsimp, assumptions, and vector magnitudes
I guess sympy does not know that INC is real and sin(INC) > 0.
I just tried:
INC = sm.symbols(‘INC’, real=True)
test = sympy.Abs(sympy.sin(INC)) / sympy.sqrt(sympy.sin**2(INC))
test = 1 was the result, as expected
From: 'Conrad Schiff' via sympy <[email protected]>
Sent: Tuesday, January 21, 2025 2:57 PM
To: [email protected]
Subject: [sympy] trigsimp, assumptions, and vector magnitudes
I am writing a textbook on orbital mechanics and I would like to use sympy for
certain calculations (e.g., deriving expressions for certain vectors in terms
of Keplerian orbital elements) so that the readers realize the power of sympy.
I have a specific problem I am hoping this group could help me with as I am
also fairly new to sympy. Here is a minimum working example:
********************************
from sympy import *
A, INC = symbols('A INC')
zxh = Matrix([[-sin(A)*sin(INC)], [cos(A)*sin(INC)], [0]])
********************************
At this point, I want to unitize 'zxh' so that the sin(INC) divides out. This
is a legitimate step since the range of INC is restricted to 0 to \pi and the
sin(INC) is always non-negative (I am ignoring the singularities on the
boundaries of 0 and \pi). I tried the following but I get the errors below.
Some help in coaxing sympy to do what I know can be done would be appreciated.
********************************
mag2_zxh = trigsimp(zxh.dot(zxh))
-> gives sin**2(INC)
mag_zxh = sqrt(mag2_zxh)
-> gives sqrt(sin(INC)**2)
zxh/mag_zxh
-> gives Matrix([[-sin(A)*sin(INC)/sqrt(sin(INC)**2)],
[sin(INC)*cos(A)/sqrt(sin(INC)**2)], [0]])
********************************
How can I coax sympy into recognizing that "sin(INC)/sqrt(sin(INC)**2) = 1"?
Thanks for any help,
Conrad Schiff, PhD
Professor of Physics
Capitol Technology University
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