Converting a python numeric expression to LaTeX.

Question

I need to convert strings with valid python syntax such as:

'1+2**(x+y)'

and get the equivalent LaTeX:

$1+2^{x+y}$

I have tried sympy's latex function but it processes actual expression, rather than the string form of it:

>>> latex(1+2**(x+y))
'$1 + 2^{x + y}$'
>>> latex('1+2**(x+y)')
'$1+2**(x+y)$'

but to even do this, it requires x and y to be declared as type "symbols".

I want something more straight forward, preferably doable with the parser from the compiler module.

>>> compiler.parse('1+2**(x+y)')
Module(None, Stmt([Discard(Add((Const(1), Power((Const(2), Add((Name('x'), Name('y'))))))))]))

Last but not least, the why: I need to generate those latex snipptes so that I can show them in a webpage with mathjax.

Answer 1

You can use sympy.latex with eval:

s = "1+2**(x+y)"
sympy.latex(eval(s))   # prints '$1 + {2}^{x + y}$'

You still have to declare the variables as symbols, but if this is really a problem, it's much easier to write a parser to do this than to parse everything and generate the latex from scratch.

Answer 2

To build on tom10's answer you can define a dictionary that will generate symbols and use that when calling eval:

from collections import defaultdict
class GenerateSymbols(defaultdict):
  def __missing__(self, key):
    return sympy.Symbol(key)

Then if you use

sympy.latex(eval('1+2**(x+y)',GenerateSymbols()))

you shouldn't have to worry about pre-creating Symbols for the variables.

Answer 3

Just a little fix to Geoff Reedy excellent answer:

class GenerateSymbols(defaultdict):
    def __missing__(self, key):
        self[key] = sympy.Symbol(key)
        return self[key]

Before it would not add the new item to the dict. Now you can use this with your expression:

d= GenerateSymbols()    
eq = '(-b-sqrt(b**2-4*a*c))/(2*a)'

and you can further simplify it before converting it to LaTeX:

sympy.latex(sympy.simplify(eval(eq,d)))

and you get this:

'$- \\frac{b + \\operatorname{sqrt}\\left(- 4 a c + b^{2}\\right)}{2 a}$'

Answer 4

Here's a rather long but still incomplete method that doesn't involve sympy in any way. It's enough to cover the example of (-b-sqrt(b**2-4*a*c))/(2*a) which gets translated to \frac{- b - \sqrt{b^{2} - 4 \; a \; c}}{2 \; a} and renders as

It basically creates the AST and walks it producing the latex math the corresponds to the AST nodes. What's there should give enough of an idea how to extend it in the places it's lacking.

import ast

class LatexVisitor(ast.NodeVisitor):

    def prec(self, n):
        return getattr(self, 'prec_'+n.__class__.__name__, getattr(self, 'generic_prec'))(n)

    def visit_Call(self, n):
        func = self.visit(n.func)
        args = ', '.join(map(self.visit, n.args))
        if func == 'sqrt':
            return '\sqrt{%s}' % args
        else:
            return r'\operatorname{%s}\left(%s\right)' % (func, args)

    def prec_Call(self, n):
        return 1000

    def visit_Name(self, n):
        return n.id

    def prec_Name(self, n):
        return 1000

    def visit_UnaryOp(self, n):
        if self.prec(n.op) > self.prec(n.operand):
            return r'%s \left(%s\right)' % (self.visit(n.op), self.visit(n.operand))
        else:
            return r'%s %s' % (self.visit(n.op), self.visit(n.operand))

    def prec_UnaryOp(self, n):
        return self.prec(n.op)

    def visit_BinOp(self, n):
        if self.prec(n.op) > self.prec(n.left):
            left = r'\left(%s\right)' % self.visit(n.left)
        else:
            left = self.visit(n.left)
        if self.prec(n.op) > self.prec(n.right):
            right = r'\left(%s\right)' % self.visit(n.right)
        else:
            right = self.visit(n.right)
        if isinstance(n.op, ast.Div):
            return r'\frac{%s}{%s}' % (self.visit(n.left), self.visit(n.right))
        elif isinstance(n.op, ast.FloorDiv):
            return r'\left\lfloor\frac{%s}{%s}\right\rfloor' % (self.visit(n.left), self.visit(n.right))
        elif isinstance(n.op, ast.Pow):
            return r'%s^{%s}' % (left, self.visit(n.right))
        else:
            return r'%s %s %s' % (left, self.visit(n.op), right)

    def prec_BinOp(self, n):
        return self.prec(n.op)

    def visit_Sub(self, n):
        return '-'

    def prec_Sub(self, n):
        return 300

    def visit_Add(self, n):
        return '+'

    def prec_Add(self, n):
        return 300

    def visit_Mult(self, n):
        return '\\;'

    def prec_Mult(self, n):
        return 400

    def visit_Mod(self, n):
        return '\\bmod'

    def prec_Mod(self, n):
        return 500

    def prec_Pow(self, n):
        return 700

    def prec_Div(self, n):
        return 400

    def prec_FloorDiv(self, n):
        return 400

    def visit_LShift(self, n):
        return '\\operatorname{shiftLeft}'

    def visit_RShift(self, n):
        return '\\operatorname{shiftRight}'

    def visit_BitOr(self, n):
        return '\\operatorname{or}'

    def visit_BitXor(self, n):
        return '\\operatorname{xor}'

    def visit_BitAnd(self, n):
        return '\\operatorname{and}'

    def visit_Invert(self, n):
        return '\\operatorname{invert}'

    def prec_Invert(self, n):
        return 800

    def visit_Not(self, n):
        return '\\neg'

    def prec_Not(self, n):
        return 800

    def visit_UAdd(self, n):
        return '+'

    def prec_UAdd(self, n):
        return 800

    def visit_USub(self, n):
        return '-'

    def prec_USub(self, n):
        return 800
    def visit_Num(self, n):
        return str(n.n)

    def prec_Num(self, n):
        return 1000

    def generic_visit(self, n):
        if isinstance(n, ast.AST):
            return r'' % (n.__class__.__name__, ', '.join(map(self.visit, [getattr(n, f) for f in n._fields])))
        else:
            return str(n)

    def generic_prec(self, n):
        return 0

def py2tex(expr):
    pt = ast.parse(expr)
    return LatexVisitor().visit(pt.body[0].value)