使用Python解决复杂的多变量函数

Question

I have a very complicated function of two variables, let's call them x and y . I want to create a Python program where the user can input two values, a and b , where a is the value of that complicated function of x and y , and b = math.atan(y/x) . This program should then output the values of x and y .

I am clueless as to where to start. I have tried to make the function into that of just one variable, then generate many random values for x and pick the closest one, but I have learnt that this is horribly inefficient and produces a result which is only accurate to about 2 significant figures, which is pretty horrible. Is there a better way to do this? Many thanks!

(PS I did not reveal the function here due to copyright issues. For the sake of example, you can consider the function

a = 4*math.atan(math.sqrt(math.tan(x)*math.tan(y)/math.tan(x+y)))

where y = x * math.tan(b) .)

Edit: After using the approach of the sympy library, it appears as though the program ignores my second equation (the complicated one). I suspect it is too complicated for sympy to handle. Thus, I am asking for another approach which does not utilise sympy .

Answer 1

You could use sympy and import the trigonometric functions from sympy.

from sympy.core.symbol import symbols
from sympy.solvers.solveset import nonlinsolve
from sympy import sqrt, tan, atan

y = symbols('y', real=True)
a,b = 4,5 # user-given values


eq2 = a - 4*atan(sqrt(tan(y/tan(b))*tan(y)/tan((y/tan(b))+y)))

S = nonlinsolve( [eq2], [y] )
print(S)

It'll return you a series of conditions ( ConditionSet object ) for possible adequate results.

If that wasn't clear enough, you can read the docs for nonlinsolve .