Comment #11 on issue 1525 by smi...@gmail.com: No integration by
substitution
http://code.google.com/p/sympy/issues/detail?id=1525
A problem with the use of u, however, is getting rid of it later:
h[1] >>> f=Function('f');f(2*x).diff(x)
2*D(f(_u), _u)
h[2] >>> _.subs(f,cos)
2*D(cos(_u), _u)
h[3] >>> _.doit()
-2*sin(_u)
But what we want is
h[4] >>> cos(2*x).diff(x)
-2*sin(2*x)
So we need a way to replace the u with 2*x. There is no unevaluated subs,
so perhaps Limit could do the trick?
h[7] >>> 2*Limit(f(u).diff(u),u,2*x)
2*Limit(D(f(u), u), u, 2*x)
h[8] >>> _.subs(f,cos)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sympy\core\basic.py", line 958, in subs
return self._subs_old_new(old, new)
File "sympy\core\cache.py", line 101, in wrapper
func_cache_it_cache[k] = r = func(*args, **kw_args)
File "sympy\core\basic.py", line 967, in _subs_old_new
return self._eval_subs(old, new)
File "sympy\core\mul.py", line 906, in _eval_subs
return fallback()
File "sympy\core\mul.py", line 859, in fallback
self.args])
File "sympy\core\basic.py", line 973, in _eval_subs
return self.func(*[arg._eval_subs(old, new) for arg in self.args])
AttributeError: 'str' object has no attribute '_eval_subs'
h[8] >>> Limit(f(u).diff(u),u,2*x).args
(D(f(u), u), u, 2*x, '+')
OOPS. Limit has non-Basic args. That should be changed to use -1 and +1
rather than '-' and '+'. The idea is that the Limit when done with doit
should return the intended value.
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