Hello, I am new to both Python and Sympy. I've been going through the
documentation with some test problems and have questions regarding how
much expansion/simplification/factoring etc. is possible within Sympy
compared with CAS products like Mathematica. I have occasional access
to Mathematica but would prefer the open source approach. I use the
anaconda distribution and ipythoin on a Mac
Here is a toy problem involving some quotients of complex numbers that come
up in optics.
from sympy import *
var('A,B,C,D,u,v,qi,qf')
qi = 1/(u-I*v)
qf = (A+B/qi)/(C+D/qi)
I'd like to get an expansion of 1/qf. My hand calculation and Mathematica
both give:
(A C)/((A+B u)^2+B^2 v^2)+(B C u)/((A+B u)^2+B^2 v^2)+(A D u)/((A+B
u)^2+B^2 v^2)+(B D u^2)/((A+B u)^2+B^2 v^2)+(B D v^2)/((A+B u)^2+B^2
v^2)+I ((B C v)/((A+B u)^2+B^2 v^2)-(A D v)/((A+B u)^2+B^2 v^2))
It is simply taking 1/qf, multiplying top and bottom by the complex
conjugate of the denominator, and collecting terms. The real and imaginary
parts each relate to a physical parameter of a Gaussian laser beam.
I've tried this in iPython/Sympy a few different ways. Definitions as
above:
In [4]:
1/qf
Out[4]:
(C + D*(u - I*v))/(A + B*(u - I*v))
In [5]:
expand(1/qf)
Out[5]:
C/(A + B*u - I*B*v) + D*u/(A + B*u - I*B*v) - I*D*v/(A + B*u - I*B*v)
In [10]:
(expand(1/qf, complex=True))
Out[10]: A massive expression. I can provide it if there's interest but there
are hundreds of terms.
I've also tried simplify, expand, factor, etc. in various combinations.
Nothing quite as simple as what the hand
calculation/Mathematica provide.
I'd appreciate suggestions including opinions on whether or not sympy is an
appropriate choice for what I have in mind.
Thanks,
JBB
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