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
<https://groups.google.com/g/sage-support/c/ojzZUnR46Kg> and
ask.sagemath.org
<https://ask.sagemath.org/question/78686/taylor-expansion-in-sagemath-returns-error/>
.
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