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    <p>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 <a href="http://www.scipy.org/doc/api_docs/SciPy.optimize.html" rel="nofollow noreferrer">SciPy.optimize</a> module. For something simple, the <a href="http://www.scipy.org/doc/api_docs/SciPy.optimize.minpack.html#newton" rel="nofollow noreferrer"><code>newton</code></a> is a pretty good start for simple polynomials, but you can take it from there.</p> <p>For symbolic solutions (which is to say to get y = x**2 -> x = +/- sqrt(y)) <a href="http://sympy.org" rel="nofollow noreferrer">SymPy</a> <a href="http://docs.sympy.org/dev/modules/solvers/solvers.html" rel="nofollow noreferrer">solver</a> gives you roughly what you need. The whole SymPy package is directed at doing symbolic manipulation.</p> <p>Here is an example using the <em>Python</em> interpreter to solve the equation that is mentioned in the question. You will need to make sure that SymPy package is installed, then:</p> <pre><code>&gt;&gt;&gt;&gt; from sympy import * # we are importing everything for ease of use &gt;&gt;&gt;&gt; x = Symbol("x") &gt;&gt;&gt;&gt; y = Symbol("y") # create the two variables &gt;&gt;&gt;&gt; equation = Eq(x ** 2, y) # create the equation &gt;&gt;&gt;&gt; solve(equation, x) [y**(1/2), -y**(1/2)] </code></pre> <p>As you see the basics are fairly workable, even as an interactive algebra system. Not nearly as nice as <a href="http://www.wolfram.com/mathematica/" rel="nofollow noreferrer">Mathematica</a>, but then again, it is free and you can incorporate it into your own programs. Make sure to read the <a href="http://docs.sympy.org/dev/gotchas.html" rel="nofollow noreferrer"><em>Gotchas and Pitfalls</em></a> section of the SymPy documentation on how to encode the appropriate equations.</p> <p>If all this was to get a quick and dirty solutions to equations then there is always <a href="http://www.wolframalpha.com/input/?i=solve+x**2+%3D+y+for+x" rel="nofollow noreferrer">Wolfram Alpha</a>.</p>
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    1. COthanks, but I would like the function to be returned ( e.g. INPUT: y = x**2 OUTPUT: sqrt(y) or x = sqrt(y) )
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    2. CO@Nona see my updated answer about SymPy. @kindall also gave you the answer.
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    3. COcool, i see it now, `pde.pde_separate`. i dont follow the argument's it requires though, separate(eq,fun,sep), what's the partial differential equation? fun i assume would be my lambda, sep is just a placeholder for the results? strategy looks like i would actually use 'add'. I'm trying to follow the example, but I think I'm getting lost with `u, X, T = map(Function, 'uXT')` .... Thanks again!!
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