Python - solve polynomial for y
I'm taking in a function (e.g. y = x**2) and need to solve for x. I know I can painstakingly solve this manually, but I'm trying to find instead a method to use. I've browsed numpy, scipy and sympy, but can't seem to find what I'm looking for. Currently I'm making a lambda out of the function so it'd be nice if i'm able to keep that format for the the method, but not necessary.
Thanks!
Answer
If you are looking for numerical solutions (i.e. just interested in the numbers, not the symbolic closed form solutions), then there are a few options for you in the SciPy.optimize module. For something simple, the newton is a pretty good start for simple polynomials, but you can take it from there.
For symbolic solutions (which is to say to get y = x**2 -> x = +/- sqrt(y)) SymPy solver gives you roughly what you need. The whole SymPy package is directed at doing symbolic manipulation.
Here is an example using the Python interpreter to solve the equation that is mentioned in the question. You will need to make sure that SymPy package is installed, then:
>>>> from sympy import * # we are importing everything for ease of use
>>>> x = Symbol("x")
>>>> y = Symbol("y") # create the two variables
>>>> equation = Eq(x ** 2, y) # create the equation
>>>> solve(equation, x)
[y**(1/2), -y**(1/2)]
As you see the basics are fairly workable, even as an interactive algebra system. Not nearly as nice as Mathematica, but then again, it is free and you can incorporate it into your own programs. Make sure to read the Gotchas and Pitfalls section of the SymPy documentation on how to encode the appropriate equations.
If all this was to get a quick and dirty solutions to equations then there is always Wolfram Alpha.