0) I have recently discovered Sympy to myself and am pleased using it.
It is already rich with many interesting capabilities. Thanks a lot
for it!
1) I am trying to solve symbolically an eigen-problem depending on a
small parameter. For my 2x2 matrix this takes couple of hours. For a
3x3 matrix the eigen-problem becomes an ewig-problem: I have never
managed to wait till the end.
Q1) Is there a way how to simplify the problem by retaining only a few
leading terms in the small parameter expansion?
2) I tried to use .series() function for simplifying eigenvalues and
eigenvectors of a 2x2 matrix. It takes very long. In the example below
I would expect an immediate result for the expansion, not several
minutes. It seems I am using Sympy not in the best way.
Q2) How can I better deal with small parameters? Do you have docs/
examples?
Thank you in advance!
Example: **************
d, na, nb, e, dna, dnb, nanb= symbols('d na nb e dna dnb nanb')
d2, na2, nb2= symbols('d2 na2 nb2', positive=True)
aaa = d2 + dna*e + dnb*e - (8*d2*dna*e + 8*d2*dnb*e + 4*d2**2 +
e**4*na2**2 + e**4*nb2**2 + 4*e**4*nanb**2 + 8*dna**2*e**2 +
8*dnb**2*e**2 + 8*d2*nanb*e**2 - 4*dna*nb2*e**3 - 4*dnb*na2*e**3 +
4*dna*na2*e**3 + 4*dnb*nb2*e**3 + 8*dna*nanb*e**3 + 8*dnb*nanb*e**3 -
2*na2*nb2*e**4)**(sympify(1)/2)/2 + na2*e**2/2 + nb2*e**2/2
aaa.series(e,0,3)
********** the last command takes several minutes to complete.
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