CODEWITHSUNDEEP
pythondesign-patternswolfram-mathematicasympy
ajlopez
ajlopez

Reputation: 11

Sympy patterns for functions

In Wolfram Research Mathematica it is possible to define a sustitution rule of the type

sustitution = g_[arg___] -> g[Sequence @@ Reverse[{arg}]]

Then it is possible to apply it to different expressions involving functions with the following results:

f[x, y] /. sustitution   >>  f[y,x]
g[x1,x2,x3]              >>  g[x3,x2,x1]
h[1,z,w,t]/.sustitution  >>  h[t,w,z,1]

As it is possible to use a pattern with name, g_, for the name of the function and another pattern, arg___, for the arguments, the same sustitution rule is valid no matter the name of the function that appears in the expression.

Is it possible to use WildFunction symbols along with replace to obtain a similar efect with Sympy?

Upvotes: 1

Views: 211

Answers (1)

smichr
smichr

Reputation: 19145

The arg__ is not necessary for a SymPy type arg-remapping function since the args can be retrieved from the function call itself:

>>> from sympy.abc import x,y,z
>>> from sympy import Function
>>> f = Function('f')
>>> g_ = lambda f: f.func(*list(reversed(f.args)))
>>> g_(f(x,y,z))
f(z, y, x)

Another way of changing all user-defined functions the same way within an expression is to use replace as follows:

>>> from sympy.abc import *
>>> from sympy import Function, AppliedUndef
>>> f,g,h,F=symbols('f,g,h,F',cls=Function)
>>> eq=f(x,y,z)+g(y,x,w)*h(1,u,t)**cos(F(x,y,1,w))
>>> eq.replace(
... lambda x: isinstance(x, AppliedUndef),
... lambda x: x.func(*list(reversed(x.args))))
f(z, y, x) + g(w, x, y)*h(t, u, 1)**cos(F(w, 1, y, x))

If you wanted to apply such a transformation to all functions then use Function instead of AppliedUndef.

Upvotes: 2

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