Comment #8 on issue 1525 by asmeurer: No integration by substitution
http://code.google.com/p/sympy/issues/detail?id=1525
To put things in perspective in the commit log, btw, 2361dd == c20062e7~1.
See https://github.com/sympy/sympy/pull/134.
By the way, other than tests testing the
In [1]: f(g(x)).diff(x)
Out[1]:
d d
─────(f(g(x)))⋅──(g(x))
dg(x) dx
behavior two doctests fail in my fdiff_revert branch (the one from the pull
request):
________ sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_indep_div_dep
________
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line
1761, in sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_indep_div_dep
Failed example:
pprint(dsolve(genform, f(x),
hint='1st_homogeneous_coeff_subs_indep_div_dep_Integral'))
Exception raised:
Traceback (most recent call last):
File "/sw/lib/python2.7/doctest.py", line 1254, in __run
compileflags, 1) in test.globs
File "<doctest
sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_indep_div_dep[5]>", line
2, in <module>
hint='1st_homogeneous_coeff_subs_indep_div_dep_Integral'))
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line 401, in dsolve
hints = classify_ode(eq, func, dict=True)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line 684, in classify_ode
if r[d] != 0 and simplify(r[d].diff(y)) == simplify(r[e].diff(x)):
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/expr.py",
line 1499, in diff
return Derivative(self, *new_symbols, **assumptions)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 602, in __new__
obj = expr._eval_derivative(s)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 276, in _eval_derivative
df = self.fdiff(i)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 474, in fdiff
return Derivative(self,self.args[argindex-1],evaluate=False)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 565, in __new__
raise ValueError('Derivative expects Symbol [, Integer] args but
got %s, %s' % (s, count))
ValueError: Derivative expects Symbol [, Integer] args but got x/_y, 1
________________________________________________________________________________
________ sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_dep_div_indep
________
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line
1680, in sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_dep_div_indep
Failed example:
pprint(dsolve(genform, f(x),
hint='1st_homogeneous_coeff_subs_dep_div_indep_Integral'))
Exception raised:
Traceback (most recent call last):
File "/sw/lib/python2.7/doctest.py", line 1254, in __run
compileflags, 1) in test.globs
File "<doctest
sympy.solvers.ode.ode_1st_homogeneous_coeff_subs_dep_div_indep[5]>", line
2, in <module>
hint='1st_homogeneous_coeff_subs_dep_div_indep_Integral'))
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line 401, in dsolve
hints = classify_ode(eq, func, dict=True)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/solvers/ode.py",
line 684, in classify_ode
if r[d] != 0 and simplify(r[d].diff(y)) == simplify(r[e].diff(x)):
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/expr.py",
line 1499, in diff
return Derivative(self, *new_symbols, **assumptions)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 602, in __new__
obj = expr._eval_derivative(s)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 276, in _eval_derivative
df = self.fdiff(i)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 474, in fdiff
return Derivative(self,self.args[argindex-1],evaluate=False)
File "/Users/aaronmeurer/Documents/Python/sympy/sympy/sympy/core/function.py",
line 565, in __new__
raise ValueError('Derivative expects Symbol [, Integer] args but
got %s, %s' % (s, count))
ValueError: Derivative expects Symbol [, Integer] args but got _y/x, 1
See
http://docs.sympy.org/dev/modules/solvers/ode.html#st-homogeneous-coeff-subs-dep-div-indep.
Just something to keep in mind when considering what to do for the problem
discussed in comment 6.
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