Problem with `series`

[emanuel.c...@gmail.com]

The series method of a (large) expressin doesn’t return :

from sympy import * x1, x2, x3, x4, w1, w2, w3, w4, w5, w5, w6 = symbols("x1, x2, x3, x4, w1, w2, w3, w4, w5, w5, w6") g= 1/4*((w1**2*w3**2*x1**4*x2**6*x3**8 + 2*(w1**2*w3**2*x1**4*x2**6 + w1**2*w3*x1**3*x2**5)*x3**7 + (w1**2*w3**2*x1**4*x2**6 + 2*w1**2*w3*x1**3*x2**5 + 2*w1**2*x1**2*x2**4)*x3**6)*x4**6 + 2*((w1**2*w3**2*x1**4*x2**6 + (w1**2*w3**2*x1**4 + (2*w1**2*w3 + w1*w3**2)*x1**3)*x2**5)*x3**7 + 2*(w1**2*w3**2*x1**4*x2**6 + (w1**2*w3**2*x1**4 + (3*w1**2*w3 + w1*w3**2)*x1**3)*x2**5 + (w1**2*w3*x1**3 + (w1**2 + w1*w3)*x1**2)*x2**4)*x3**6 + (w1**2*w3**2*x1**4*x2**6 + (w1**2*w3**2*x1**4 + (4*w1**2*w3 + w1*w3**2)*x1**3)*x2**5 + 2*(w1**2*w3*x1**3 + (2*w1**2 + w1*w3)*x1**2)*x2**4 + 2*(w1**2*x1**2 + w1*x1)*x2**3)*x3**5)*x4**5 + ((w1**2*w3**2*x1**4*x2**6 + 2*(w1**2*w3**2*x1**4 + (3*w1**2*w3 + 2*w1*w3**2)*x1**3)*x2**5 + (w1**2*w3**2*x1**4 + 2*(3*w1**2*w3 + 2*w1*w3**2)*x1**3 + 2*(3*w1**2 + 6*w1*w3 + w3**2)*x1**2)*x2**4)*x3**6 + 2*(w1**2*w3**2*x1**4*x2**6 + (2*w1**2*w3**2*x1**4 + (7*w1**2*w3 + 4*w1*w3**2)*x1**3)*x2**5 + (w1**2*w3**2*x1**4 + 4*(2*w1**2*w3 + w1*w3**2)*x1**3 + (9*w1**2 + 16*w1*w3 + 2*w3**2)*x1**2)*x2**4 + (w1**2*w3*x1**3 + (3*w1**2 + 4*w1*w3)*x1**2 + 2*(3*w1 + w3)*x1)*x2**3)*x3**5 + (w1**2*w3**2*x1**4*x2**6 + 2*(w1**2*w3**2*x1**4 + 2*(2*w1**2*w3 + w1*w3**2)*x1**3)*x2**5 + (w1**2*w3**2*x1**4 + 2*(5*w1**2*w3 + 2*w1*w3**2)*x1**3 + 2*(7*w1**2 + 10*w1*w3 + w3**2)*x1**2)*x2**4 + 2*(w1**2*w3*x1**3 + (5*w1**2 + 4*w1*w3)*x1**2 + 2*(5*w1 + w3)*x1)*x2**3 + 2*(w1**2*x1**2 + 4*w1*x1 + 2)*x2**2)*x3**4)*x4**4 + 2*(((w1**2*w3 + w1*w3**2)*x1**3*x2**5 + (2*(w1**2*w3 + w1*w3**2)*x1**3 + (3*w1**2 + 10*w1*w3 + 2*w3**2)*x1**2)*x2**4 + ((w1**2*w3 + w1*w3**2)*x1**3 + (3*w1**2 + 10*w1*w3 + 2*w3**2)*x1**2 + 4*(3*w1 + 2*w3)*x1)*x2**3)*x3**5 + (2*(w1**2*w3 + w1*w3**2)*x1**3*x2**5 + (4*(w1**2*w3 + w1*w3**2)*x1**3 + (7*w1**2 + 22*w1*w3 + 4*w3**2)*x1**2)*x2**4 + 2*((w1**2*w3 + w1*w3**2)*x1**3 + 2*(2*w1**2 + 6*w1*w3 + w3**2)*x1**2 + (17*w1 + 10*w3)*x1)*x2**3 + ((w1**2 + 2*w1*w3)*x1**2 + 2*(5*w1 + 2*w3)*x1 + 8)*x2**2)*x3**4 + ((w1**2*w3 + w1*w3**2)*x1**3*x2**5 + 2*((w1**2*w3 + w1*w3**2)*x1**3 + (2*w1**2 + 6*w1*w3 + w3**2)*x1**2)*x2**4 + ((w1**2*w3 + w1*w3**2)*x1**3 + (5*w1**2 + 14*w1*w3 + 2*w3**2)*x1**2 + 12*(2*w1 + w3)*x1)*x2**3 + ((w1**2 + 2*w1*w3)*x1**2 + 2*(7*w1 + 2*w3)*x1 + 12)*x2**2 + 2*(w1*x1 + 2)*x2)*x3**3)*x4**3 + 24*(x2**2 + 2*x2 + 1)*x3**2 + 2*(((w1**2 + 4*w1*w3 + w3**2)*x1**2*x2**4 + 2*((w1**2 + 4*w1*w3 + w3**2)*x1**2 + (8*w1 + 7*w3)*x1)*x2**3 + ((w1**2 + 4*w1*w3 + w3**2)*x1**2 + 2*(8*w1 + 7*w3)*x1 + 20)*x2**2)*x3**4 + 2*((w1**2 + 4*w1*w3 + w3**2)*x1**2*x2**4 + (2*(w1**2 + 4*w1*w3 + w3**2)*x1**2 + 3*(6*w1 + 5*w3)*x1)*x2**3 + ((w1**2 + 4*w1*w3 + w3**2)*x1**2 + 4*(5*w1 + 4*w3)*x1 + 27)*x2**2 + ((2*w1 + w3)*x1 + 7)*x2)*x3**3 + ((w1**2 + 4*w1*w3 + w3**2)*x1**2*x2**4 + 2*((w1**2 + 4*w1*w3 + w3**2)*x1**2 + 2*(5*w1 + 4*w3)*x1)*x2**3 + ((w1**2 + 4*w1*w3 + w3**2)*x1**2 + 6*(4*w1 + 3*w3)*x1 + 36)*x2**2 + 2*((2*w1 + w3)*x1 + 9)*x2 + 2)*x3**2)*x4**2 + 24*x2**2 + 48*(x2**2 + 2*x2 + 1)*x3 + 12*(((w1 + w3)*x1*x2**3 + (2*(w1 + w3)*x1 + 5)*x2**2 + ((w1 + w3)*x1 + 5)*x2)*x3**3 + (2*(w1 + w3)*x1*x2**3 + (4*(w1 + w3)*x1 + 11)*x2**2 + 2*((w1 + w3)*x1 + 6)*x2 + 1)*x3**2 + ((w1 + w3)*x1*x2**3 + 2*((w1 + w3)*x1 + 3)*x2**2 + ((w1 + w3)*x1 + 7)*x2 + 1)*x3)*x4 + 48*x2 + 24)*exp(-w2*x1*x2*x3*x4)/((x2**3*x3**6*exp(w5*x1*x2) + 3*x2**3*x3**5*exp(w5*x1*x2) + 3*x2**3*x3**4*exp(w5*x1*x2) + x2**3*x3**3*exp(w5*x1*x2))*x4**3*exp(w6*x1*x2*x3) + 3*((x2**3 + x2**2)*x3**5*exp(w5*x1*x2) + 3*(x2**3 + x2**2)*x3**4*exp(w5*x1*x2) + 3*(x2**3 + x2**2)*x3**3*exp(w5*x1*x2) + (x2**3 + x2**2)*x3**2*exp(w5*x1*x2))*x4**2*exp(w6*x1*x2*x3) + 3*((x2**3 + 2*x2**2 + x2)*x3**4*exp(w5*x1*x2) + 3*(x2**3 + 2*x2**2 + x2)*x3**3*exp(w5*x1*x2) + 3*(x2**3 + 2*x2**2 + x2)*x3**2*exp(w5*x1*x2) + (x2**3 + 2*x2**2 + x2)*x3*exp(w5*x1*x2))*x4*exp(w6*x1*x2*x3) + ((x2**3 + 3*x2**2 + 3*x2 + 1)*x3**3*exp(w5*x1*x2) + 3*(x2**3 + 3*x2**2 + 3*x2 + 1)*x3**2*exp(w5*x1*x2) + 3*(x2**3 + 3*x2**2 + 3*x2 + 1)*x3*exp(w5*x1*x2) + (x2**3 + 3*x2**2 + 3*x2 + 1)*exp(w5*x1*x2))*exp(w6*x1*x2*x3)) from time import time as stime t0=stime() foo=g.series(x4, 0, 7) t1=stime() print(t1-t0)

“never” returns (i. e. doesn’t return after 40 minutes).

FWIW, this series can be computed without problems and in short times with Giac, Mathematica and Sage (using Sage’s series in the latter case). Maxima standalone can compute it via taylor, but fails when called from Sage.

Relevant posts/threads in sage-support and ask.sagemath.org.

​

[Oscar Benjamin]

The general approach for computing series in SymPy is algorithmically
misdesigned.

See:
https://github.com/sympy/sympy/issues/26957

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