I would say that you should use doit but I just tried that and it crashed:
In [*9*]: e=Function('g')(Function('f')(x1,x2),Function('h'
)(x1,x2)).diff(x1)
In [*10*]: e
Out[*10*]:
⎛ ∂ ⎞│ ⎛ ∂ ⎞│ ⎛
∂ ⎞│ ⎛ ∂
⎜───(f(ξ₁, x[2]))⎟│ ⋅⎜───(g(ξ₁, h(x[1], x[2])))⎟│ +
⎜───(g(f(x[1], x[2]), ξ₂))⎟│ ⋅⎜───(h(ξ₁
⎝∂ξ₁ ⎠│ξ₁=x[1] ⎝∂ξ₁ ⎠│ξ₁=f(x[1], x[2])
⎝∂ξ₂ ⎠│ξ₂=h(x[1], x[2]) ⎝∂ξ₁
⎞│
, x[2]))⎟│
⎠│ξ₁=x[1]
In [*11*]: e.doit()
Fatal Python error: Cannot recover from stack overflow.
Thread 0x000070000994b000 (most recent call first):
File "/Users/enojb/.local/lib/python3.5/threading.py", line 293 in wait
File "/Users/enojb/.local/lib/python3.5/threading.py", line 549 in wait
File
"/Users/enojb/current/sympy/35venv/lib/python3.5/site-packages/IPython/core/history.py",
line 829 in run
File
"/Users/enojb/current/sympy/35venv/lib/python3.5/site-packages/IPython/core/history.py",
line 58 in needs_sqlite
File
"</Users/enojb/current/sympy/35venv/lib/python3.5/site-packages/decorator.py:decorator-gen-24>",
line 2 in run
File "/Users/enojb/.local/lib/python3.5/threading.py", line 914 in
_bootstrap_inner
File "/Users/enojb/.local/lib/python3.5/threading.py", line 882 in
_bootstrap
Current thread 0x00007fffae5cf380 (most recent call first):
File "/Users/enojb/current/sympy/sympy/sympy/core/symbol.py", line 284 in
assumptions0
File "/Users/enojb/current/sympy/sympy/sympy/core/symbol.py", line 274 in
_hashable_content
File "/Users/enojb/current/sympy/sympy/sympy/core/symbol.py", line 381 in
_hashable_content
File "/Users/enojb/current/sympy/sympy/sympy/core/expr.py", line 133 in
__eq__
File "/Users/enojb/current/sympy/sympy/sympy/core/basic.py", line 343 in
__eq__
File "/Users/enojb/current/sympy/sympy/sympy/core/containers.py", line 97
in __eq__
File "/Users/enojb/current/sympy/sympy/sympy/core/expr.py", line 134 in
__eq__
File "/Users/enojb/current/sympy/sympy/sympy/core/cache.py", line 94 in
wrapper
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2291
in <listcomp>
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2291
in _hashable_content
File "/Users/enojb/current/sympy/sympy/sympy/core/expr.py", line 109 in
__hash__
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2286
in __hash__
File "/Users/enojb/current/sympy/sympy/sympy/core/cache.py", line 94 in
wrapper
File "/Users/enojb/current/sympy/sympy/sympy/core/expr.py", line 196 in
__mul__
File "/Users/enojb/current/sympy/sympy/sympy/core/decorators.py", line
129 in binary_op_wrapper
File "/Users/enojb/current/sympy/sympy/sympy/core/decorators.py", line 91
in __sympifyit_wrapper
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 618
in _eval_derivative
File "/Users/enojb/current/sympy/sympy/sympy/core/basic.py", line 1724 in
_visit_eval_derivative_scalar
File "/Users/enojb/current/sympy/sympy/sympy/core/basic.py", line 1719 in
_accept_eval_derivative
File "/Users/enojb/current/sympy/sympy/sympy/core/basic.py", line 1743 in
_eval_derivative_n_times
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1427
in __new__
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1598
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1600
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1600
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1600
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1600
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
...
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 2242
in doit
File "/Users/enojb/current/sympy/sympy/sympy/core/function.py", line 1600
in doit
...
Abort trap: 6
On Sun, 25 Aug 2019 at 01:13, Mathieu Lamarre <mathieu.lama...@gmail.com>
wrote:
> Simple example of multivariate chain rule:
> print(Function('g')(Function('f')(x1,x2)).diff(x1))
>
> Gives the expected:
>
> [image: diff1.PNG]
>
> Derivative(f(x1, x2), x1)*Derivative(g(f(x1, x2)), f(x1, x2))
>
>
> Adding another function h:
>
> print(Function('g')(Function('f')(x1,x2),Function('h')(x1,x2)).diff(x1))
>
> Gives the expected answer but with extra _xi_1 and _xi_2 symbols:
>
> [image: diff.PNG]
>
> Derivative(f(x1, x2), x1)*Subs(Derivative(g(_xi_1, h(x1, x2)), _xi_1), _xi_1,
> f(x1, x2)) + Derivative(h(x1, x2), x1)*Subs(Derivative(g(f(x1, x2), _xi_2),
> _xi_2), _xi_2, h(x1, x2))
>
>
> This is annoying for subsequent substitutions, for instance to switch from
> the function notation to simple symbols.
> Also, for more complex equations, the numbering of the automatic xi
> symbols is hard to predict.
>
> Is there a way to change this behavior? i.e. do not get the Subs and
> _xi_%d above
>
> Thanks
>
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