AndroidRemoteController/python/py/Lib/site-packages/sympy/parsing/tests/test_latex.py

from sympy.testing.pytest import raises, XFAIL
from sympy.external import import_module

from sympy.concrete.products import Product
from sympy.concrete.summations import Sum
from sympy.core.add import Add
from sympy.core.function import (Derivative, Function)
from sympy.core.mul import Mul
from sympy.core.numbers import (E, oo)
from sympy.core.power import Pow
from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan, Unequality)
from sympy.core.symbol import Symbol
from sympy.functions.combinatorial.factorials import (binomial, factorial)
from sympy.functions.elementary.complexes import (Abs, conjugate)
from sympy.functions.elementary.exponential import (exp, log)
from sympy.functions.elementary.integers import (ceiling, floor)
from sympy.functions.elementary.miscellaneous import (root, sqrt)
from sympy.functions.elementary.trigonometric import (asin, cos, csc, sec, sin, tan)
from sympy.integrals.integrals import Integral
from sympy.series.limits import Limit

from sympy.core.relational import Eq, Ne, Lt, Le, Gt, Ge
from sympy.physics.quantum.state import Bra, Ket
from sympy.abc import x, y, z, a, b, c, t, k, n
antlr4 = import_module("antlr4")

# disable tests if antlr4-python3-runtime is not present
disabled = antlr4 is None

theta = Symbol('theta')
f = Function('f')


# shorthand definitions
def _Add(a, b):
    return Add(a, b, evaluate=False)


def _Mul(a, b):
    return Mul(a, b, evaluate=False)


def _Pow(a, b):
    return Pow(a, b, evaluate=False)


def _Sqrt(a):
    return sqrt(a, evaluate=False)


def _Conjugate(a):
    return conjugate(a, evaluate=False)


def _Abs(a):
    return Abs(a, evaluate=False)


def _factorial(a):
    return factorial(a, evaluate=False)


def _exp(a):
    return exp(a, evaluate=False)


def _log(a, b):
    return log(a, b, evaluate=False)


def _binomial(n, k):
    return binomial(n, k, evaluate=False)


def test_import():
    from sympy.parsing.latex._build_latex_antlr import (
        build_parser,
        check_antlr_version,
        dir_latex_antlr
    )
    # XXX: It would be better to come up with a test for these...
    del build_parser, check_antlr_version, dir_latex_antlr


# These LaTeX strings should parse to the corresponding SymPy expression
GOOD_PAIRS = [
    (r"0", 0),
    (r"1", 1),
    (r"-3.14", -3.14),
    (r"(-7.13)(1.5)", _Mul(-7.13, 1.5)),
    (r"x", x),
    (r"2x", 2*x),
    (r"x^2", x**2),
    (r"x^\frac{1}{2}", _Pow(x, _Pow(2, -1))),
    (r"x^{3 + 1}", x**_Add(3, 1)),
    (r"-c", -c),
    (r"a \cdot b", a * b),
    (r"a / b", a / b),
    (r"a \div b", a / b),
    (r"a + b", a + b),
    (r"a + b - a", _Add(a+b, -a)),
    (r"a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
    (r"(x + y) z", _Mul(_Add(x, y), z)),
    (r"a'b+ab'", _Add(_Mul(Symbol("a'"), b), _Mul(a, Symbol("b'")))),
    (r"y''_1", Symbol("y_{1}''")),
    (r"y_1''", Symbol("y_{1}''")),
    (r"\left(x + y\right) z", _Mul(_Add(x, y), z)),
    (r"\left( x + y\right ) z", _Mul(_Add(x, y), z)),
    (r"\left(  x + y\right ) z", _Mul(_Add(x, y), z)),
    (r"\left[x + y\right] z", _Mul(_Add(x, y), z)),
    (r"\left\{x + y\right\} z", _Mul(_Add(x, y), z)),
    (r"1+1", _Add(1, 1)),
    (r"0+1", _Add(0, 1)),
    (r"1*2", _Mul(1, 2)),
    (r"0*1", _Mul(0, 1)),
    (r"1 \times 2 ", _Mul(1, 2)),
    (r"x = y", Eq(x, y)),
    (r"x \neq y", Ne(x, y)),
    (r"x < y", Lt(x, y)),
    (r"x > y", Gt(x, y)),
    (r"x \leq y", Le(x, y)),
    (r"x \geq y", Ge(x, y)),
    (r"x \le y", Le(x, y)),
    (r"x \ge y", Ge(x, y)),
    (r"\lfloor x \rfloor", floor(x)),
    (r"\lceil x \rceil", ceiling(x)),
    (r"\langle x |", Bra('x')),
    (r"| x \rangle", Ket('x')),
    (r"\sin \theta", sin(theta)),
    (r"\sin(\theta)", sin(theta)),
    (r"\sin^{-1} a", asin(a)),
    (r"\sin a \cos b", _Mul(sin(a), cos(b))),
    (r"\sin \cos \theta", sin(cos(theta))),
    (r"\sin(\cos \theta)", sin(cos(theta))),
    (r"\frac{a}{b}", a / b),
    (r"\dfrac{a}{b}", a / b),
    (r"\tfrac{a}{b}", a / b),
    (r"\frac12", _Pow(2, -1)),
    (r"\frac12y", _Mul(_Pow(2, -1), y)),
    (r"\frac1234", _Mul(_Pow(2, -1), 34)),
    (r"\frac2{3}", _Mul(2, _Pow(3, -1))),
    (r"\frac{\sin{x}}2", _Mul(sin(x), _Pow(2, -1))),
    (r"\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
    (r"\frac{7}{3}", _Mul(7, _Pow(3, -1))),
    (r"(\csc x)(\sec y)", csc(x)*sec(y)),
    (r"\lim_{x \to 3} a", Limit(a, x, 3, dir='+-')),
    (r"\lim_{x \rightarrow 3} a", Limit(a, x, 3, dir='+-')),
    (r"\lim_{x \Rightarrow 3} a", Limit(a, x, 3, dir='+-')),
    (r"\lim_{x \longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
    (r"\lim_{x \Longrightarrow 3} a", Limit(a, x, 3, dir='+-')),
    (r"\lim_{x \to 3^{+}} a", Limit(a, x, 3, dir='+')),
    (r"\lim_{x \to 3^{-}} a", Limit(a, x, 3, dir='-')),
    (r"\lim_{x \to 3^+} a", Limit(a, x, 3, dir='+')),
    (r"\lim_{x \to 3^-} a", Limit(a, x, 3, dir='-')),
    (r"\infty", oo),
    (r"\lim_{x \to \infty} \frac{1}{x}", Limit(_Pow(x, -1), x, oo)),
    (r"\frac{d}{dx} x", Derivative(x, x)),
    (r"\frac{d}{dt} x", Derivative(x, t)),
    (r"f(x)", f(x)),
    (r"f(x, y)", f(x, y)),
    (r"f(x, y, z)", f(x, y, z)),
    (r"f'_1(x)", Function("f_{1}'")(x)),
    (r"f_{1}''(x+y)", Function("f_{1}''")(x+y)),
    (r"\frac{d f(x)}{dx}", Derivative(f(x), x)),
    (r"\frac{d\theta(x)}{dx}", Derivative(Function('theta')(x), x)),
    (r"x \neq y", Unequality(x, y)),
    (r"|x|", _Abs(x)),
    (r"||x||", _Abs(Abs(x))),
    (r"|x||y|", _Abs(x)*_Abs(y)),
    (r"||x||y||", _Abs(_Abs(x)*_Abs(y))),
    (r"\pi^{|xy|}", Symbol('pi')**_Abs(x*y)),
    (r"\int x dx", Integral(x, x)),
    (r"\int x d\theta", Integral(x, theta)),
    (r"\int (x^2 - y)dx", Integral(x**2 - y, x)),
    (r"\int x + a dx", Integral(_Add(x, a), x)),
    (r"\int da", Integral(1, a)),
    (r"\int_0^7 dx", Integral(1, (x, 0, 7))),
    (r"\int\limits_{0}^{1} x dx", Integral(x, (x, 0, 1))),
    (r"\int_a^b x dx", Integral(x, (x, a, b))),
    (r"\int^b_a x dx", Integral(x, (x, a, b))),
    (r"\int_{a}^b x dx", Integral(x, (x, a, b))),
    (r"\int^{b}_a x dx", Integral(x, (x, a, b))),
    (r"\int_{a}^{b} x dx", Integral(x, (x, a, b))),
    (r"\int^{b}_{a} x dx", Integral(x, (x, a, b))),
    (r"\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
    (r"\int (x+a)", Integral(_Add(x, a), x)),
    (r"\int a + b + c dx", Integral(_Add(_Add(a, b), c), x)),
    (r"\int \frac{dz}{z}", Integral(Pow(z, -1), z)),
    (r"\int \frac{3 dz}{z}", Integral(3*Pow(z, -1), z)),
    (r"\int \frac{1}{x} dx", Integral(Pow(x, -1), x)),
    (r"\int \frac{1}{a} + \frac{1}{b} dx",
     Integral(_Add(_Pow(a, -1), Pow(b, -1)), x)),
    (r"\int \frac{3 \cdot d\theta}{\theta}",
     Integral(3*_Pow(theta, -1), theta)),
    (r"\int \frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
    (r"x_0", Symbol('x_{0}')),
    (r"x_{1}", Symbol('x_{1}')),
    (r"x_a", Symbol('x_{a}')),
    (r"x_{b}", Symbol('x_{b}')),
    (r"h_\theta", Symbol('h_{theta}')),
    (r"h_{\theta}", Symbol('h_{theta}')),
    (r"h_{\theta}(x_0, x_1)",
     Function('h_{theta}')(Symbol('x_{0}'), Symbol('x_{1}'))),
    (r"x!", _factorial(x)),
    (r"100!", _factorial(100)),
    (r"\theta!", _factorial(theta)),
    (r"(x + 1)!", _factorial(_Add(x, 1))),
    (r"(x!)!", _factorial(_factorial(x))),
    (r"x!!!", _factorial(_factorial(_factorial(x)))),
    (r"5!7!", _Mul(_factorial(5), _factorial(7))),
    (r"\sqrt{x}", sqrt(x)),
    (r"\sqrt{x + b}", sqrt(_Add(x, b))),
    (r"\sqrt[3]{\sin x}", root(sin(x), 3)),
    (r"\sqrt[y]{\sin x}", root(sin(x), y)),
    (r"\sqrt[\theta]{\sin x}", root(sin(x), theta)),
    (r"\sqrt{\frac{12}{6}}", _Sqrt(_Mul(12, _Pow(6, -1)))),
    (r"\overline{z}", _Conjugate(z)),
    (r"\overline{\overline{z}}", _Conjugate(_Conjugate(z))),
    (r"\overline{x + y}", _Conjugate(_Add(x, y))),
    (r"\overline{x} + \overline{y}", _Conjugate(x) + _Conjugate(y)),
    (r"x < y", StrictLessThan(x, y)),
    (r"x \leq y", LessThan(x, y)),
    (r"x > y", StrictGreaterThan(x, y)),
    (r"x \geq y", GreaterThan(x, y)),
    (r"\mathit{x}", Symbol('x')),
    (r"\mathit{test}", Symbol('test')),
    (r"\mathit{TEST}", Symbol('TEST')),
    (r"\mathit{HELLO world}", Symbol('HELLO world')),
    (r"\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
    (r"\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
    (r"\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
    (r"\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
    (r"\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
    (r"\sum_{n = 0}^{\infty} \frac{1}{n!}",
     Sum(_Pow(_factorial(n), -1), (n, 0, oo))),
    (r"\prod_{a = b}^{c} x", Product(x, (a, b, c))),
    (r"\prod_{a = b}^c x", Product(x, (a, b, c))),
    (r"\prod^{c}_{a = b} x", Product(x, (a, b, c))),
    (r"\prod^c_{a = b} x", Product(x, (a, b, c))),
    (r"\exp x", _exp(x)),
    (r"\exp(x)", _exp(x)),
    (r"\lg x", _log(x, 10)),
    (r"\ln x", _log(x, E)),
    (r"\ln xy", _log(x*y, E)),
    (r"\log x", _log(x, E)),
    (r"\log xy", _log(x*y, E)),
    (r"\log_{2} x", _log(x, 2)),
    (r"\log_{a} x", _log(x, a)),
    (r"\log_{11} x", _log(x, 11)),
    (r"\log_{a^2} x", _log(x, _Pow(a, 2))),
    (r"[x]", x),
    (r"[a + b]", _Add(a, b)),
    (r"\frac{d}{dx} [ \tan x ]", Derivative(tan(x), x)),
    (r"\binom{n}{k}", _binomial(n, k)),
    (r"\tbinom{n}{k}", _binomial(n, k)),
    (r"\dbinom{n}{k}", _binomial(n, k)),
    (r"\binom{n}{0}", _binomial(n, 0)),
    (r"x^\binom{n}{k}", _Pow(x, _binomial(n, k))),
    (r"a \, b", _Mul(a, b)),
    (r"a \thinspace b", _Mul(a, b)),
    (r"a \: b", _Mul(a, b)),
    (r"a \medspace b", _Mul(a, b)),
    (r"a \; b", _Mul(a, b)),
    (r"a \thickspace b", _Mul(a, b)),
    (r"a \quad b", _Mul(a, b)),
    (r"a \qquad b", _Mul(a, b)),
    (r"a \! b", _Mul(a, b)),
    (r"a \negthinspace b", _Mul(a, b)),
    (r"a \negmedspace b", _Mul(a, b)),
    (r"a \negthickspace b", _Mul(a, b)),
    (r"\int x \, dx", Integral(x, x)),
    (r"\log_2 x", _log(x, 2)),
    (r"\log_a x", _log(x, a)),
    (r"5^0 - 4^0", _Add(_Pow(5, 0), _Mul(-1, _Pow(4, 0)))),
    (r"3x - 1", _Add(_Mul(3, x), -1))
]


def test_parseable():
    from sympy.parsing.latex import parse_latex
    for latex_str, sympy_expr in GOOD_PAIRS:
        assert parse_latex(latex_str) == sympy_expr, latex_str

# These bad LaTeX strings should raise a LaTeXParsingError when parsed
BAD_STRINGS = [
    r"(",
    r")",
    r"\frac{d}{dx}",
    r"(\frac{d}{dx})",
    r"\sqrt{}",
    r"\sqrt",
    r"\overline{}",
    r"\overline",
    r"{",
    r"}",
    r"\mathit{x + y}",
    r"\mathit{21}",
    r"\frac{2}{}",
    r"\frac{}{2}",
    r"\int",
    r"!",
    r"!0",
    r"_",
    r"^",
    r"|",
    r"||x|",
    r"()",
    r"((((((((((((((((()))))))))))))))))",
    r"-",
    r"\frac{d}{dx} + \frac{d}{dt}",
    r"f(x,,y)",
    r"f(x,y,",
    r"\sin^x",
    r"\cos^2",
    r"@",
    r"#",
    r"$",
    r"%",
    r"&",
    r"*",
    r"" "\\",
    r"~",
    r"\frac{(2 + x}{1 - x)}",
]

def test_not_parseable():
    from sympy.parsing.latex import parse_latex, LaTeXParsingError
    for latex_str in BAD_STRINGS:
        with raises(LaTeXParsingError):
            parse_latex(latex_str)

# At time of migration from latex2sympy, should fail but doesn't
FAILING_BAD_STRINGS = [
    r"\cos 1 \cos",
    r"f(,",
    r"f()",
    r"a \div \div b",
    r"a \cdot \cdot b",
    r"a // b",
    r"a +",
    r"1.1.1",
    r"1 +",
    r"a / b /",
]

@XFAIL
def test_failing_not_parseable():
    from sympy.parsing.latex import parse_latex, LaTeXParsingError
    for latex_str in FAILING_BAD_STRINGS:
        with raises(LaTeXParsingError):
            parse_latex(latex_str)

# In strict mode, FAILING_BAD_STRINGS would fail
def test_strict_mode():
    from sympy.parsing.latex import parse_latex, LaTeXParsingError
    for latex_str in FAILING_BAD_STRINGS:
        with raises(LaTeXParsingError):
            parse_latex(latex_str, strict=True)