我想用Python做一些变分微积分，我遇到了一个问题，我不太了解它的起源。我使用的是Anaconda套件，Jupyter Notebook和IPython版本5.3.0，以及python 3.6。
如果我写了
from sympy import Funtion, symbols, integrate
from IPython.display import display
t, s = symbols('t s')
f = Function('f')
c = Function('c')
计算以下表达式（它们将是失败的部分的元素）
display(f(t, s))
display(c(t, s))
display(f(c(t, s)))
display(f(c(t, s), c(t, s).diff(t)))
display(integrate( f(t, s), t))
display(integrate( f(c(t, s)), t))
display(integrate( f(c(t, s).diff(t)), t))
display(integrate( f(c(t, s),c(s,t) ), t))
出现预期的（乳胶）表达式。我看到它可以处理多个变量的派生和集成，但是当我尝试将一些东西放在一起时，如
display(integrate( f(c(t, s), c(t, s).diff(t)), t))
引发以下错误
Can't calculate 1st derivative wrt Derivative(_x1, t).
另一方面，
display(integrate( f(c(t,s), c(t,s).diff(t)), s))
显示正确的输出。有人可以解决这个问题吗？
提前谢谢
编辑：.doit（）没有帮助。错误先于
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-21-66abd1a98aff> in <module>()
11 display(integrate( f(c(t,s).diff(t)), t))
12 display(integrate( f(c(t,s), c(s,t)), t))
---> 13 display(integrate( f(c(t,s), c(t,s).diff(t)), t))
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\integrals.py in integrate(*args, **kwargs)
1278 if isinstance(integral, Integral):
1279 return integral.doit(deep=False, meijerg=meijerg, conds=conds,
-> 1280 risch=risch, manual=manual)
1281 else:
1282 return integral
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\integrals.py in doit(self, **hints)
484 function, xab[0],
485 meijerg=meijerg1, risch=risch, manual=manual,
--> 486 conds=conds)
487 if antideriv is None and meijerg1 is True:
488 ret = try_meijerg(function, xab)
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\integrals.py in _eval_integral(self, f, x, meijerg, risch, manual, conds)
885 try:
886 if conds == 'piecewise':
--> 887 h = heurisch_wrapper(g, x, hints=[])
888 else:
889 h = heurisch(g, x, hints=[])
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in heurisch_wrapper(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations)
128
129 res = heurisch(f, x, rewrite, hints, mappings, retries, degree_offset,
--> 130 unnecessary_permutations)
131 if not isinstance(res, Basic):
132 return res
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations)
672 else:
673 if retries >= 0:
--> 674 result = heurisch(f, x, mappings=mappings, rewrite=rewrite, hints=hints, retries=retries - 1, unnecessary_permutations=unnecessary_permutations)
675
676 if result is not None:
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations)
672 else:
673 if retries >= 0:
--> 674 result = heurisch(f, x, mappings=mappings, rewrite=rewrite, hints=hints, retries=retries - 1, unnecessary_permutations=unnecessary_permutations)
675
676 if result is not None:
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations)
672 else:
673 if retries >= 0:
--> 674 result = heurisch(f, x, mappings=mappings, rewrite=rewrite, hints=hints, retries=retries - 1, unnecessary_permutations=unnecessary_permutations)
675
676 if result is not None:
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in heurisch(f, x, rewrite, hints, mappings, retries, degree_offset, unnecessary_permutations)
451 mapping = list(mapping)
452 mapping = mapping + unnecessary_permutations
--> 453 diffs = [ _substitute(dcache.get_diff(g)) for g in terms ]
454 denoms = [ g.as_numer_denom()[1] for g in diffs ]
455 if all(h.is_polynomial(*V) for h in denoms) and _substitute(f).is_rational_function(*V):
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in <listcomp>(.0)
451 mapping = list(mapping)
452 mapping = mapping + unnecessary_permutations
--> 453 diffs = [ _substitute(dcache.get_diff(g)) for g in terms ]
454 denoms = [ g.as_numer_denom()[1] for g in diffs ]
455 if all(h.is_polynomial(*V) for h in denoms) and _substitute(f).is_rational_function(*V):
....\Anaconda2\envs\Py3\lib\site-packages\sympy\integrals\heurisch.py in _substitute(expr)
446
447 def _substitute(expr):
--> 448 return expr.subs(mapping)
449
450 for mapping in mappings:
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\basic.py in subs(self, *args, **kwargs)
900 rv = self
901 for old, new in sequence:
--> 902 rv = rv._subs(old, new, **kwargs)
903 if not isinstance(rv, Basic):
904 break
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\cache.py in wrapper(*args, **kwargs)
91 def wrapper(*args, **kwargs):
92 try:
---> 93 retval = cfunc(*args, **kwargs)
94 except TypeError:
95 retval = func(*args, **kwargs)
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\basic.py in _subs(self, old, new, **hints)
1014 rv = self._eval_subs(old, new)
1015 if rv is None:
-> 1016 rv = fallback(self, old, new)
1017 return rv
1018
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\basic.py in fallback(self, old, new)
986 if not hasattr(arg, '_eval_subs'):
987 continue
--> 988 arg = arg._subs(old, new, **hints)
989 if not _aresame(arg, args[i]):
990 hit = True
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\cache.py in wrapper(*args, **kwargs)
91 def wrapper(*args, **kwargs):
92 try:
---> 93 retval = cfunc(*args, **kwargs)
94 except TypeError:
95 retval = func(*args, **kwargs)
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\basic.py in _subs(self, old, new, **hints)
1012 return new
1013
-> 1014 rv = self._eval_subs(old, new)
1015 if rv is None:
1016 rv = fallback(self, old, new)
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\function.py in _eval_subs(self, old, new)
1340 variables = self_vars_front + self_vars
1341 return Derivative(new, *variables)
-> 1342 return Derivative(*(x._subs(old, new) for x in self.args))
1343
1344 def _eval_lseries(self, x, logx):
....\Anaconda2\envs\Py3\lib\site-packages\sympy\core\function.py in __new__(cls, expr, *variables, **assumptions)
1068 ordinal = 'st' if last_digit == 1 else 'nd' if last_digit == 2 else 'rd' if last_digit == 3 else 'th'
1069 raise ValueError(filldedent('''
-> 1070 Can\'t calculate %s%s derivative wrt %s.''' % (count, ordinal, v)))
1071
1072 if all_zero and not count == 0:
ValueError:
Can't calculate 1st derivative wrt Derivative(_x1, t).
答案 0 :(得分：1)
我会使用Integral来显示积分，它只构造它们而不会尝试计算它们（除非你执行doit()）。以下作品
display(Integral( f(c(t, s), c(t, s).diff(t)), t))