Complex numbers: convert SymPy to numeric (I to 1j)

Question

using symbolic calculation in Python I have

import sympy from cmath import * from mpmath import arg, cplot z = sympy.symbols('z') fhandle='z**2' g = lambda w: sympy.sympify(fhandle).evalf(subs={z: w}) g(1+2j) # Returns: -3.0 + 4.0*I # hence the next command fails, because I is expected to be 1j cplot(g, [-3,3], [-3,3])

Crawling the web I only found this which will fix the matter for the print command, but will not work with cplot.

Any suggestions?

You are abusing sympify. When you can (which is almost always) write actual code, not strings to be passed to sympify. — Krastanov
– Krastanov, Commented May 23, 2013 at 15:45
@Krastanov This is the minimum working example. fhandle will be passed as a string from the web interface. Still abusive? — arney
– arney, Commented May 23, 2013 at 16:00
Oh, not in this case, sorry. But there is now another bigger issue: sympify may parse code through eval, which means that you are exposing your app to injections. It is not an issue if you can trust the users, but it is good to know anyway. — Krastanov
– Krastanov, Commented May 23, 2013 at 16:18

DSM · Accepted Answer · 2013-05-23 14:56:26Z

One option is to wrap the result by calling complex:

>>> def g(w): ... return complex(sympy.sympify(fhandle).evalf(subs={z: w})) ... >>> g(1+2j) (-3+4j)

After which mpmath.cplot(g, [-3, 3], [-3, 3]) produces

cplot example

Note that I've used a named function here. There's not much point to using a lambda if you're going to immediately give it a name anyhow.

Note: this works because I has a method called __complex__(..).

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