CODEWITHSUNDEEP
wildcardsympy
Andrew Mir
Andrew Mir

Reputation: 125

How to work with the result of the wild sympy

I have the following code:

f=tan(x)*x**2
q=Wild('q')
s=f.match(tan(q))
s={q_ : x}

How to work with the result of the "wild"? How to not address the array, for example, s[0], s{0}?

Upvotes: 1

Views: 300

Answers (1)

JohanC
JohanC

Reputation: 80329

Wild can be used when you have an expression which is the result of some complicated calculation, but you know it has to be of the form sin(something) times something else. Then s[q] will be the sympy expression for the "something". And s[p] for the "something else". This could be used to investigate both p and q. Or to further work with a simplified version of f, substituting p and q with new variables, especially if p and q would be complex expressions involving multiple variables.

Many more use cases are possible.

Here is an example:

from sympy import *
from sympy.abc import x, y, z

p = Wild('p')
q = Wild('q')
f = tan(x) * x**2
s = f.match(p*tan(q))
print(f'f is the tangent of "{s[q]}" multiplied by "{s[p]}"')
g = f.xreplace({s[q]: y, s[p]:z})
print(f'f rewritten in simplified form as a function of y and z: "{g}"')
h = s[p] * s[q]
print(f'a new function h, combining parts of f: "{h}"')

Output:

f is the tangent of "x" multiplied by "x**2"
f rewritten in simplified form as a function of y and z: "z*tan(y)"
a new function h, combining parts of f: "x**3"

If you're interested in all arguments from tan that appear in f written as a product, you might try:

from sympy import *
from sympy.abc import x

f = tan(x+2)*tan(x*x+1)*7*(x+1)*tan(1/x)

if f.func == Mul:
    all_tan_args = [a.args[0] for a in f.args if a.func == tan]
    # note: the [0] is needed because args give a tupple of arguments and
    #   in the case of tan you'ld want the first (there is only one)
elif f.func == tan:
    all_tan_args = [f.args[0]]
else:
    all_tan_args = []

prod = 1
for a in all_tan_args:
    prod *= a

print(f'All the tangent arguments are: {all_tan_args}')
print(f'Their product is: {prod}')

Output:

All the tangent arguments are: [1/x, x**2 + 1, x + 2]
Their product is: (x + 2)*(x**2 + 1)/x

Note that neither method would work for f = tan(x)**2. For that, you'ld need to write another match and decide whether you'ld want to take the same power of the arguments.

Upvotes: 1

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