How to avoid automatic xi symbols appearing with diff of chained functions

Mathieu Lamarre

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Aug 24, 2019, 8:13:56 PM8/24/19

to sympy

Simple example of multivariate chain rule:

print(Function('g')(Function('f')(x1,x2)).diff(x1))

Gives the expected:

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:

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

Oscar Benjamin

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Aug 24, 2019, 8:20:13 PM8/24/19

to sympy

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