Parsing input

Parsing Functions Reference

sympy.parsing.sympy_parser.parse_expr(s, local_dict=None, transformations=(<function lambda_notation>, <function auto_symbol>, <function repeated_decimals>, <function auto_number>, <function factorial_notation>), global_dict=None, evaluate=True)

Converts the string s to a SymPy expression, in local_dict

Parameters

s : str

The string to parse.

local_dict : dict, optional

A dictionary of local variables to use when parsing.

global_dict : dict, optional

A dictionary of global variables. By default, this is initialized with from sympy import *; provide this parameter to override this behavior (for instance, to parse "Q & S").

transformations : tuple, optional

A tuple of transformation functions used to modify the tokens of the parsed expression before evaluation. The default transformations convert numeric literals into their SymPy equivalents, convert undefined variables into SymPy symbols, and allow the use of standard mathematical factorial notation (e.g. x!).

evaluate : bool, optional

When False, the order of the arguments will remain as they were in the string and automatic simplification that would normally occur is suppressed. (see examples)

Examples

>>> from sympy.parsing.sympy_parser import parse_expr
>>> parse_expr("1/2")
1/2
>>> type(_)
<class 'sympy.core.numbers.Half'>
>>> from sympy.parsing.sympy_parser import standard_transformations,\
... implicit_multiplication_application
>>> transformations = (standard_transformations +
...     (implicit_multiplication_application,))
>>> parse_expr("2x", transformations=transformations)
2*x

When evaluate=False, some automatic simplifications will not occur:

>>> parse_expr("2**3"), parse_expr("2**3", evaluate=False)
(8, 2**3)

In addition the order of the arguments will not be made canonical. This feature allows one to tell exactly how the expression was entered:

>>> a = parse_expr('1 + x', evaluate=False)
>>> b = parse_expr('x + 1', evaluate=0)
>>> a == b
False
>>> a.args
(1, x)
>>> b.args
(x, 1)

See also

stringify_expr, eval_expr, standard_transformations, implicit_multiplication_application

sympy.parsing.sympy_parser.stringify_expr(s, local_dict, global_dict, transformations)

Converts the string s to Python code, in local_dict

Generally, parse_expr should be used.

sympy.parsing.sympy_parser.eval_expr(code, local_dict, global_dict)

Evaluate Python code generated by stringify_expr.

Generally, parse_expr should be used.

sympy.parsing.maxima.parse_maxima(str, globals=None, name_dict={})

sympy.parsing.mathematica.mathematica(s, additional_translations=None)

Users can add their own translation dictionary # Example In [1]: mathematica(‘Log3[9]’, {‘Log3[x]’:’log(x,3)’}) Out[1]: 2 In [2]: mathematica(‘F[7,5,3]’, {‘F[x]’:’Max(*x)*Min(*x)’}) Out[2]: 21 variable-length argument needs ‘’ character

Parsing Transformations Reference

A transformation is a function that accepts the arguments tokens, local_dict, global_dict and returns a list of transformed tokens. They can be used by passing a list of functions to parse_expr() and are applied in the order given.

sympy.parsing.sympy_parser.standard_transformations = (<function lambda_notation>, <function auto_symbol>, <function repeated_decimals>, <function auto_number>, <function factorial_notation>)

Standard transformations for parse_expr(). Inserts calls to Symbol, Integer, and other SymPy datatypes and allows the use of standard factorial notation (e.g. x!).

sympy.parsing.sympy_parser.split_symbols(tokens, local_dict, global_dict)

Splits symbol names for implicit multiplication.

Intended to let expressions like xyz be parsed as x*y*z. Does not split Greek character names, so theta will not become t*h*e*t*a. Generally this should be used with implicit_multiplication.

sympy.parsing.sympy_parser.split_symbols_custom(predicate)

Creates a transformation that splits symbol names.

predicate should return True if the symbol name is to be split.

For instance, to retain the default behavior but avoid splitting certain symbol names, a predicate like this would work:

>>> from sympy.parsing.sympy_parser import (parse_expr, _token_splittable,
... standard_transformations, implicit_multiplication,
... split_symbols_custom)
>>> def can_split(symbol):
...     if symbol not in ('list', 'of', 'unsplittable', 'names'):
...             return _token_splittable(symbol)
...     return False
...
>>> transformation = split_symbols_custom(can_split)
>>> parse_expr('unsplittable', transformations=standard_transformations +
... (transformation, implicit_multiplication))
unsplittable

sympy.parsing.sympy_parser.implicit_multiplication(result, local_dict, global_dict)

Makes the multiplication operator optional in most cases.

Use this before implicit_application(), otherwise expressions like sin 2x will be parsed as x * sin(2) rather than sin(2*x).

Examples

>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_multiplication)
>>> transformations = standard_transformations + (implicit_multiplication,)
>>> parse_expr('3 x y', transformations=transformations)
3*x*y

sympy.parsing.sympy_parser.implicit_application(result, local_dict, global_dict)

Makes parentheses optional in some cases for function calls.

Use this after implicit_multiplication(), otherwise expressions like sin 2x will be parsed as x * sin(2) rather than sin(2*x).

Examples

>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_application)
>>> transformations = standard_transformations + (implicit_application,)
>>> parse_expr('cot z + csc z', transformations=transformations)
cot(z) + csc(z)

sympy.parsing.sympy_parser.function_exponentiation(tokens, local_dict, global_dict)

Allows functions to be exponentiated, e.g. cos**2(x).

Examples

>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, function_exponentiation)
>>> transformations = standard_transformations + (function_exponentiation,)
>>> parse_expr('sin**4(x)', transformations=transformations)
sin(x)**4

sympy.parsing.sympy_parser.implicit_multiplication_application(result, local_dict, global_dict)

Allows a slightly relaxed syntax.

• Parentheses for single-argument method calls are optional.

• Multiplication is implicit.

• Symbol names can be split (i.e. spaces are not needed between symbols).

• Functions can be exponentiated.

Examples

>>> from sympy.parsing.sympy_parser import (parse_expr,
... standard_transformations, implicit_multiplication_application)
>>> parse_expr("10sin**2 x**2 + 3xyz + tan theta",
... transformations=(standard_transformations +
... (implicit_multiplication_application,)))
3*x*y*z + 10*sin(x**2)**2 + tan(theta)

sympy.parsing.sympy_parser.rationalize(tokens, local_dict, global_dict)

Converts floats into Rational. Run AFTER auto_number.

sympy.parsing.sympy_parser.convert_xor(tokens, local_dict, global_dict)

Treats XOR, ^, as exponentiation, **.

These are included in :data:sympy.parsing.sympy_parser.standard_transformations and generally don’t need to be manually added by the user.

sympy.parsing.sympy_parser.lambda_notation(tokens, local_dict, global_dict)

Substitutes “lambda” with its Sympy equivalent Lambda(). However, the conversion doesn’t take place if only “lambda” is passed because that is a syntax error.

sympy.parsing.sympy_parser.auto_symbol(tokens, local_dict, global_dict)

Inserts calls to Symbol/Function for undefined variables.

sympy.parsing.sympy_parser.repeated_decimals(tokens, local_dict, global_dict)

Allows 0.2[1] notation to represent the repeated decimal 0.2111… (19/90)

Run this before auto_number.

sympy.parsing.sympy_parser.auto_number(tokens, local_dict, global_dict)

Converts numeric literals to use SymPy equivalents.

Complex numbers use I, integer literals use Integer, and float literals use Float.

sympy.parsing.sympy_parser.factorial_notation(tokens, local_dict, global_dict)

Allows standard notation for factorial.

Experimental \(\LaTeX\) Parsing

\(\LaTeX\) parsing was ported from latex2sympy. While functional and its API should remain stable, the parsing behavior or backend may change in future releases.

\(\LaTeX\) Parsing Caveats

The current implementation is experimental. The behavior, parser backend and API might change in the future. Unlike some of the other parsers, \(\LaTeX\) is designed as a type-setting language, not a computer algebra system and so can contain typographical conventions that might be interpreted multiple ways.

In its current definition, the parser will at times will fail to fully parse the expression, but not throw a warning:

parse_latex(r'x -')

Will simply find x. What is covered by this behavior will almost certainly change between releases, and become stricter, more relaxed, or some mix.

\(\LaTeX\) Parsing Functions Reference

sympy.parsing.latex.parse_latex(s)

Converts the string s to a SymPy Expr

Parameters

s : str

The LaTeX string to parse. In Python source containing LaTeX, raw strings (denoted with r", like this one) are preferred, as LaTeX makes liberal use of the \ character, which would trigger escaping in normal Python strings.

Examples

>>> from sympy.parsing.latex import parse_latex  # doctest: +SKIP
>>> expr = parse_latex(r"\frac {1 + \sqrt {\a}} {\b}")  # doctest: +SKIP
>>> expr  # doctest: +SKIP
(sqrt(a) + 1)/b
>>> expr.evalf(4, subs=dict(a=5, b=2))  # doctest: +SKIP
1.618

\(\LaTeX\) Parsing Exceptions Reference

class sympy.parsing.latex.LaTeXParsingError

Runtime Installation

The currently-packaged parser backend is partially generated with ANTLR4, but to use the parser, you only need the antlr4 Python package available.

Depending on your package manager, you can install the right package with, for example, pip3 (Python 3 only):

$ pip3 install antlr4-python3-runtime

or pip (Python 2 only):

$ pip install antlr4-python2-runtime

or conda (Python 2 or Python 3):

$ conda install --channel=conda-forge antlr-python-runtime