Status: Accepted
Owner: ----
Labels: Type-Defect Priority-Medium Solvers
New issue 3149 by asmeu...@gmail.com: solve() doesn't work when it should
http://code.google.com/p/sympy/issues/detail?id=3149
Consider this example from the docstring of
ode.ode_1st_homogeneous_coeff_best:
In [99]: dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous_coeff_best', simplify=False)
Out[99]:
⎛ 2 ⎞
⎜ 3⋅x ⎟
log⎜───── + 1⎟
⎜ 2 ⎟
⎛f(x)⎞ ⎝f (x) ⎠
log⎜────⎟ + ────────────── = 0
⎝ C₁ ⎠ 3
If we remove the simplify flag, it is solved for f(x):
In [100]: dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous_coeff_best', simplify=True)
Out[100]:
⎡
___________________
_______________
⎢ 2 ╱
_________ 2 ⎛ ___
⎞ ╱ ______
⎢ x 3 ╱ ╱
6 x ⎜1 ╲╱ 3 ⋅ⅈ⎟ 3
╱ ╱
⎢f(x) = ─────────────────────── - ╲╱ C₃ + ╲╱ C₄ + x , f(x) =
─────────────────────────────────────── + ⎜─ + ───────⎟⋅╲╱ C₁ + ╲╱ C₂ +
⎢
___________________
___________________ ⎝2 2 ⎠
⎢ ╱ _________ ⎛
___ ⎞ ╱ _________
⎢ 3 ╱ ╱ 6 ⎜ 1 ╲╱
3 ⋅ⅈ⎟ 3 ╱ ╱ 6
⎢ ╲╱ C₁ + ╲╱ C₂ + x ⎜- ─ -
───────⎟⋅╲╱ C₃ + ╲╱ C₄ + x
⎣ ⎝ 2
2 ⎠
____
___________________⎤
___ 2 ⎛ ___ ⎞
╱ _________ ⎥
6 x ⎜1 ╲╱ 3 ⋅ⅈ⎟ 3
╱ ╱ 6 ⎥
x , f(x) = ─────────────────────────────────────── + ⎜─ - ───────⎟⋅╲╱
C₁ + ╲╱ C₂ + x ⎥
___________________ ⎝2 2
⎠ ⎥
⎛ ___ ⎞ ╱
_________ ⎥
⎜ 1 ╲╱ 3 ⋅ⅈ⎟ 3 ╱ ╱
6 ⎥
⎜- ─ + ───────⎟⋅╲╱ C₃ + ╲╱ C₄ +
x ⎥
⎝ 2 2
⎠ ⎦
But passing it straight to solve() gives a NotImplementedError:
In [98]: solve(dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous_coeff_best', simplify=False), f(x))
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call last)
/Users/aaronmeurer/Documents/Python/sympy/sympy/<ipython-input-98-0c201ee96578>
in
<module>()
----> 1 solve(dsolve(2*x*f(x) + (x**2 + f(x)**2)*f(x).diff(x), f(x),
hint='1st_homogeneous_coeff_best', simplify=False), f(x))
/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/solvers.pyc
in solve(f, *symbols, **flags)
711
###########################################################################
712 if bare_f:
--> 713 solution = _solve(f[0], *symbols, **flags)
714 else:
715 solution = _solve_system(f, symbols, **flags)
/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/solvers.pyc
in _solve(f, *symbols, **flags)
1109 if result is False:
1110 raise NotImplementedError(msg +
-> 1111 "\nNo algorithms are implemented to solve equation %s" % f)
1112
1113 if flags.get('simplify', True):
NotImplementedError: multiple generators [log(1 + 3*x**2/_F0**2),
log(_F0/C1)]
No algorithms are implemented to solve equation log(1 + 3*x**2/_F0**2)
So some kind of preprocessing or special casing is happening in dsolve()
that should also happen in solve().
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