Equation parsing in Python

Question

How can I (easily) take a string such as "sin(x)*x^2" which might be entered by a user at runtime and produce a Python function that could be evaluated for any value of x?

Quipu

Answer 1

Python's own internal compiler can parse this, if you use Python notation.

If your change the notation slightly, you'll be happier.

import compiler
eq= "sin(x)*x**2"
ast= compiler.parse( eq )

You get an abstract syntax tree that you can work with.

Ozonosphere

Can you add a sample code on how to use the derived function? – Modernistic

@Don: You don't need to use the syntax tree. Use the original function. eval("sin(x)*x**2") after setting x and using from math import *. – Ozonosphere

eval() works, but the answer doesn't actually solve the problem :( – Ferdinana

@JamesBroadhead: How does eval() not solve the problem? Can you explain what's missing? "evaluated for any value" seems to be covered by eval. What's missing? – Ozonosphere

It's not in the Answer ;). Ideally, you'd edit the answer to point that out (and the various problems associated with compiler.parse() and eval() that others have mentioned. – Ferdinana

"various problems associated with compiler.parse() and eval() that others have mentioned" seems redundant. Also. I asked the wrong question about your comment. "the answer doesn't actually solve the problem"? What more should be there -- outside of eval() which I specifically tried to avoid putting in the answer. – Ozonosphere

import compiler doesn't work with Python 3.3 Could you please update your answer + tags to make sure the reader know which one it is about. It's a good question and should have the relevant tags covered. – Amphimixis

@hagubear the replacement of the compiler module for python 3 is described here: #909592 – Bijugate

Do NOT use eval with data coming from an external source (e.g. web) as that is an easy attack vector. – Lorentz

The compiler module is deprecated since Python 2.6. This answer is obsolete – Acceptant

Answer 2

EDIT parser is deprecated in Python 3.9: https://docs.python.org/3/whatsnew/3.9.html#new-parser

You can use Python parser:

import parser
from math import sin

formula = "sin(x)*x**2"
code = parser.expr(formula).compile()
x = 10
print(eval(code))

It performs better than pure eval and, of course, avoids code injection!

Modernistic

One important thing to note is that using pure eval() on user input can be very dangerous. – Tableland

@devxeq I mean that it won't accept such things as formula = "os.system('format C:')" :) – Modernistic

@Modernistic Fair enough. :) – Cayuga

I'm not sure how this is any better than using eval on the string itself. It will still happily execute all code, not just formulas. Including bad things like os.system calls. >>> eval(parser.expr("os.system('echo evil syscall')").compile()) evil syscall – Glidebomb

parser is deprecated in python 3.9 docs.python.org/3/whatsnew/3.9.html#new-parser – Needlecraft

Answer 3

 f = parser.parse('sin(x)*x^2').to_pyfunc()

Where parser could be defined using PLY, pyparsing, builtin tokenizer, parser, ast.

Don't use eval on user input.

Vainglorious

eval on user input is indeed bad. – Camion

Could you be more specific? I have tried to import parser module in Python 3.8 but it complains: Module 'parser' has no attribute 'parse' – Enchain

@s.ouchene: "parser" here is just a stand-in for a custom module that implements the corresponding functionality (it is not literally stdlib's parser module). Here's an example for arithmetic expressions – Vainglorious

Answer 4

pyparsing might do what you want (http://pyparsing.wikispaces.com/) especially if the strings are from an untrusted source.

See also http://pyparsing.wikispaces.com/file/view/fourFn.py for a fairly full-featured calculator built with it.

Sensual

The links are no longer avaible on wikispaces. – Seize

Pyparsing is no longer hosted on wikispaces.com. Go to github.com/pyparsing/pyparsing – Dornick

Answer 5

To emphasize J.F. Sebastian's advice, 'eval' and even the 'compiler' solutions can be open to subtle security holes. How trustworthy is the input? With 'compiler' you can at least filter out things like getattr lookups from the AST, but I've found it's easier to use PLY or pyparsing for this sort of thing than it is to secure the result of letting Python help out.

Also, 'compiler' is clumsy and hard to use. It's deprecated and removed in 3.0. You should use the 'ast' module (added in 2.6, available in 2.5 as '_ast').

Overmodest

Answer 6

In agreement with vartec. I would use SymPy - in particular the lambdify function should do exactly what you want.

See: http://showmedo.com/videotutorials/video?name=7200080&fromSeriesID=720

for a very nice explanation of this.

Best wishes,

Lightner

Please include all the relevant information in the post itself, "Here is a link to a video that answers the question" is not a good answer. – Quest

Answer 7

Sage is intended as matlab replacement and in intro videos it's demonstrated how similar to yours cases are handled. They seem to be supporting a wide range of approaches. Since the code is open-source you could browse and see for yourself how the authors handle such cases.

Extrusive