Updates:
Status: Started
Labels: Milestone-Release0.7.0
Comment #13 on issue 326 by mattpap: sympy.roots_.sturm(...) hangs
http://code.google.com/p/sympy/issues/detail?id=326
... and (almost) two years later we arrive with the following session
(using my
development branch):
In [2]: f = sympify('(-1/625) + (1/62500)*x - 4096/625*pi**(-8)*x**4 -
128/625*pi**(-4)*x**2 + \
...: (32/15625)*pi**(-4)*x**3 + (1024/15625)*pi**(-8)*x**5')
In [3]: f
Out[3]:
2 3 4 5
x 128⋅x 32⋅x 4096⋅x 1024⋅x
-1/625 + ───── - ────── + ──────── - ─────── + ────────
62500 4 4 8 8
625⋅π 15625⋅π 625⋅π 15625⋅π
In [4]: sturm(f, x)
Out[4]:
⎡ 4 4 4 ⎛ 4⎞ 4
4 8 12⎤
⎢ 2 3 25⋅π x⋅π 2 π ⎜ π ⎟
25⋅π -
3686400000000⋅π - 11520000⋅π - 9⋅π ⎥
⎢- 100⋅x + x - ───── + ────, -200⋅x + 3⋅x + ──, x⋅⎜20000/9 - ──⎟ + ─────,
────────────────────────────────────────⎥
⎢ 16 64 64 ⎝ 96⎠ 18
4 8 ⎥
⎣
26214400000000 - 245760000⋅π + 576⋅π ⎦
In [5]: %time s = sturm(f, x)
CPU times: user 0.31 s, sys: 0.00 s, total: 0.31 s
Wall time: 0.39 s
In [7]: %time s = sturm(f, x)
CPU times: user 0.30 s, sys: 0.00 s, total: 0.30 s
Wall time: 0.38 s
A bit slow but with gmpy will be better.
In [9]: from sympy.polys.rootfinding import number_of_real_roots
In [10]: number_of_real_roots(f, x)
Out[10]: 1
In [11]: factor(f)
Out[11]:
2
⎛ 2⎞
⎜ 64⋅x ⎟
-⎜1 + ─────⎟ ⋅(100 - x)
⎜ 4 ⎟
⎝ π ⎠
───────────────────────
62500
In [12]: roots(f, x)
Out[12]:
⎧ 2 2 ⎫
⎪ -ⅈ⋅π ⅈ⋅π ⎪
⎨100: 1, ─────: 2, ────: 2⎬
⎪ 8 8 ⎪
⎩ ⎭
And we're done. Lets now use gmpy as ZZ and QQ ground types:
m...@neutrino ~/repo/git/sympy $ SYMPY_GROUND_TYPES=gmpy isympy
Python 2.6.2 console for SymPy 0.7.0-git (cache: off)
In [1]: f = sympify('(-1/625) + (1/62500)*x - 4096/625*pi**(-8)*x**4 -
128/625*pi**(-4)*x**2 + \
...: (32/15625)*pi**(-4)*x**3 + (1024/15625)*pi**(-8)*x**5')
In [2]: %time s = sturm(f, x)
CPU times: user 0.18 s, sys: 0.00 s, total: 0.18 s
Wall time: 0.22 s
In [4]: %time s = sturm(f, x)
CPU times: user 0.18 s, sys: 0.00 s, total: 0.18 s
Wall time: 0.22 s
Almost two times faster than with int and Fraction (2.6).
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