evaluation/math_eval/latex2sympy/tests/all_good_test.py

from .context import assert_equal, process_sympy, _Add, _Mul, _Pow
import pytest
import hashlib
from sympy import (
    E, I, oo, pi, sqrt, root, Symbol, Add, Mul, Pow, Abs, factorial, log, Eq, Ne, S, Rational, Integer, UnevaluatedExpr,
    sin, cos, tan, sinh, cosh, tanh, asin, acos, atan, asinh, acosh, atanh,
    csc, sec, Sum, Product, Limit, Integral, Derivative,
    LessThan, StrictLessThan, GreaterThan, StrictGreaterThan,
    exp, binomial, Matrix, MatMul, MatAdd,
    Mod, gcd, lcm, floor, ceiling, Max, Min
)

x = Symbol('x', real=True)
y = Symbol('y', real=True)
z = Symbol('z', real=True)
a = Symbol('a', real=True)
b = Symbol('b', real=True)
c = Symbol('c', real=True)
f = Symbol('f', real=True)
t = Symbol('t', real=True)
k = Symbol('k', real=True)
n = Symbol('n', real=True)
theta = Symbol('theta', real=True)

# shorthand definitions


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


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


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


def pytest_generate_tests(metafunc):
    metafunc.parametrize('s, eq', metafunc.cls.GOOD_PAIRS)


class TestAllGood(object):
    # These latex strings should parse to the corresponding SymPy expression
    GOOD_PAIRS = [
        ("0", 0),
        ("1", 1),
        ("-3.14", -3.14),
        ("5-3", _Add(5, -3)),
        ("(-7.13)(1.5)", _Mul(Rational('-7.13'), Rational('1.5'))),
        ("\\left(-7.13\\right)\\left(1.5\\right)", _Mul(Rational('-7.13'), Rational('1.5'))),
        ("x", x),
        ("2x", 2 * x),
        ("x^2", x**2),
        ("x^{3 + 1}", x**_Add(3, 1)),
        ("x^{\\left\\{3 + 1\\right\\}}", x**_Add(3, 1)),
        ("-3y + 2x", _Add(_Mul(2, x), Mul(-1, 3, y, evaluate=False))),
        ("-c", -c),
        ("a \\cdot b", a * b),
        ("a / b", a / b),
        ("a \\div b", a / b),
        ("a + b", a + b),
        ("a + b - a", Add(a, b, _Mul(-1, a), evaluate=False)),
        ("a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
        ("a^2 + b^2 != 2c^2", Ne(a**2 + b**2, 2 * c**2)),
        ("a\\mod b", Mod(a, b)),
        ("\\sin \\theta", sin(theta)),
        ("\\sin(\\theta)", sin(theta)),
        ("\\sin\\left(\\theta\\right)", sin(theta)),
        ("\\sin^{-1} a", asin(a)),
        ("\\sin a \\cos b", _Mul(sin(a), cos(b))),
        ("\\sin \\cos \\theta", sin(cos(theta))),
        ("\\sin(\\cos \\theta)", sin(cos(theta))),
        ("\\arcsin(a)", asin(a)),
        ("\\arccos(a)", acos(a)),
        ("\\arctan(a)", atan(a)),
        ("\\sinh(a)", sinh(a)),
        ("\\cosh(a)", cosh(a)),
        ("\\tanh(a)", tanh(a)),
        ("\\sinh^{-1}(a)", asinh(a)),
        ("\\cosh^{-1}(a)", acosh(a)),
        ("\\tanh^{-1}(a)", atanh(a)),
        ("\\arcsinh(a)", asinh(a)),
        ("\\arccosh(a)", acosh(a)),
        ("\\arctanh(a)", atanh(a)),
        ("\\arsinh(a)", asinh(a)),
        ("\\arcosh(a)", acosh(a)),
        ("\\artanh(a)", atanh(a)),
        ("\\operatorname{arcsinh}(a)", asinh(a)),
        ("\\operatorname{arccosh}(a)", acosh(a)),
        ("\\operatorname{arctanh}(a)", atanh(a)),
        ("\\operatorname{arsinh}(a)", asinh(a)),
        ("\\operatorname{arcosh}(a)", acosh(a)),
        ("\\operatorname{artanh}(a)", atanh(a)),
        ("\\operatorname{gcd}(a, b)", UnevaluatedExpr(gcd(a, b))),
        ("\\operatorname{lcm}(a, b)", UnevaluatedExpr(lcm(a, b))),
        ("\\operatorname{gcd}(a,b)", UnevaluatedExpr(gcd(a, b))),
        ("\\operatorname{lcm}(a,b)", UnevaluatedExpr(lcm(a, b))),
        ("\\operatorname{floor}(a)", floor(a)),
        ("\\operatorname{ceil}(b)", ceiling(b)),
        ("\\cos^2(x)", cos(x)**2),
        ("\\cos(x)^2", cos(x)**2),
        ("\\gcd(a, b)", UnevaluatedExpr(gcd(a, b))),
        ("\\lcm(a, b)", UnevaluatedExpr(lcm(a, b))),
        ("\\gcd(a,b)", UnevaluatedExpr(gcd(a, b))),
        ("\\lcm(a,b)", UnevaluatedExpr(lcm(a, b))),
        ("\\floor(a)", floor(a)),
        ("\\ceil(b)", ceiling(b)),
        ("\\max(a, b)", Max(a, b)),
        ("\\min(a, b)", Min(a, b)),
        ("\\frac{a}{b}", a / b),
        ("\\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
        ("\\frac{7}{3}", _Mul(7, _Pow(3, -1))),
        ("(\\csc x)(\\sec y)", csc(x) * sec(y)),
        ("\\lim_{x \\to 3} a", Limit(a, x, 3)),
        ("\\lim_{x \\rightarrow 3} a", Limit(a, x, 3)),
        ("\\lim_{x \\Rightarrow 3} a", Limit(a, x, 3)),
        ("\\lim_{x \\longrightarrow 3} a", Limit(a, x, 3)),
        ("\\lim_{x \\Longrightarrow 3} a", Limit(a, x, 3)),
        ("\\lim_{x \\to 3^{+}} a", Limit(a, x, 3, dir='+')),
        ("\\lim_{x \\to 3^{-}} a", Limit(a, x, 3, dir='-')),
        ("\\infty", oo),
        ("\\infty\\%", oo),
        ("\\$\\infty", oo),
        ("-\\infty", -oo),
        ("-\\infty\\%", -oo),
        ("-\\$\\infty", -oo),
        ("\\lim_{x \\to \\infty} \\frac{1}{x}", Limit(_Mul(1, _Pow(x, -1)), x, oo)),
        ("\\frac{d}{dx} x", Derivative(x, x)),
        ("\\frac{d}{dt} x", Derivative(x, t)),
        # ("f(x)", f(x)),
        # ("f(x, y)", f(x, y)),
        # ("f(x, y, z)", f(x, y, z)),
        # ("\\frac{d f(x)}{dx}", Derivative(f(x), x)),
        # ("\\frac{d\\theta(x)}{dx}", Derivative(theta(x), x)),
        ("|x|", _Abs(x)),
        ("\\left|x\\right|", _Abs(x)),
        ("||x||", _Abs(Abs(x))),
        ("|x||y|", _Abs(x) * _Abs(y)),
        ("||x||y||", _Abs(_Abs(x) * _Abs(y))),
        ("\\lfloor x\\rfloor", floor(x)),
        ("\\lceil y\\rceil", ceiling(y)),
        ("\\pi^{|xy|}", pi**_Abs(x * y)),
        ("\\frac{\\pi}{3}", _Mul(pi, _Pow(3, -1))),
        ("\\sin{\\frac{\\pi}{2}}", sin(_Mul(pi, _Pow(2, -1)), evaluate=False)),
        ("a+bI", a + I * b),
        ("e^{I\\pi}", -1),
        ("\\int x dx", Integral(x, x)),
        ("\\int x d\\theta", Integral(x, theta)),
        ("\\int (x^2 - y)dx", Integral(x**2 - y, x)),
        ("\\int x + a dx", Integral(_Add(x, a), x)),
        ("\\int da", Integral(1, a)),
        ("\\int_0^7 dx", Integral(1, (x, 0, 7))),
        ("\\int_a^b x dx", Integral(x, (x, a, b))),
        ("\\int^b_a x dx", Integral(x, (x, a, b))),
        ("\\int_{a}^b x dx", Integral(x, (x, a, b))),
        ("\\int^{b}_a x dx", Integral(x, (x, a, b))),
        ("\\int_{a}^{b} x dx", Integral(x, (x, a, b))),
        ("\\int_{  }^{}x dx", Integral(x, x)),
        ("\\int^{  }_{ }x dx", Integral(x, x)),
        ("\\int^{b}_{a} x dx", Integral(x, (x, a, b))),
        # ("\\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
        ("\\int (x+a)", Integral(_Add(x, a), x)),
        ("\\int a + b + c dx", Integral(Add(a, b, c, evaluate=False), x)),
        ("\\int \\frac{dz}{z}", Integral(Pow(z, -1), z)),
        ("\\int \\frac{3 dz}{z}", Integral(3 * Pow(z, -1), z)),
        ("\\int \\frac{1}{x} dx", Integral(Pow(x, -1), x)),
        ("\\int \\frac{1}{a} + \\frac{1}{b} dx", Integral(_Add(_Pow(a, -1), Pow(b, -1)), x)),
        ("\\int \\frac{3 \\cdot d\\theta}{\\theta}", Integral(3 * _Pow(theta, -1), theta)),
        ("\\int \\frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
        ("x_0", Symbol('x_0', real=True)),
        ("x_{1}", Symbol('x_1', real=True)),
        ("x_a", Symbol('x_a', real=True)),
        ("x_{b}", Symbol('x_b', real=True)),
        ("h_\\theta", Symbol('h_{\\theta}', real=True)),
        ("h_\\theta ", Symbol('h_{\\theta}', real=True)),
        ("h_{\\theta}", Symbol('h_{\\theta}', real=True)),
        # ("h_{\\theta}(x_0, x_1)", Symbol('h_{theta}', real=True)(Symbol('x_{0}', real=True), Symbol('x_{1}', real=True))),
        ("x!", _factorial(x)),
        ("100!", _factorial(100)),
        ("\\theta!", _factorial(theta)),
        ("(x + 1)!", _factorial(_Add(x, 1))),
        ("\\left(x + 1\\right)!", _factorial(_Add(x, 1))),
        ("(x!)!", _factorial(_factorial(x))),
        ("x!!!", _factorial(_factorial(_factorial(x)))),
        ("5!7!", _Mul(_factorial(5), _factorial(7))),
        ("\\sqrt{x}", sqrt(x)),
        ("\\sqrt{x + b}", sqrt(_Add(x, b))),
        ("\\sqrt[3]{\\sin x}", root(sin(x), 3)),
        ("\\sqrt[y]{\\sin x}", root(sin(x), y)),
        ("\\sqrt[\\theta]{\\sin x}", root(sin(x), theta)),
        ("x < y", StrictLessThan(x, y)),
        ("x \\leq y", LessThan(x, y)),
        ("x > y", StrictGreaterThan(x, y)),
        ("x \\geq y", GreaterThan(x, y)),
        ("\\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
        ("\\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
        ("\\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
        ("\\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
        ("\\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
        ("\\sum_{n = 0}^{\\infty} \\frac{1}{n!}", Sum(_Pow(_factorial(n), -1), (n, 0, oo))),
        ("\\prod_{a = b}^{c} x", Product(x, (a, b, c))),
        ("\\prod_{a = b}^c x", Product(x, (a, b, c))),
        ("\\prod^{c}_{a = b} x", Product(x, (a, b, c))),
        ("\\prod^c_{a = b} x", Product(x, (a, b, c))),
        ("\\ln x", _log(x, E)),
        ("\\ln xy", _log(x * y, E)),
        ("\\log x", _log(x, 10)),
        ("\\log xy", _log(x * y, 10)),
        # ("\\log_2 x", _log(x, 2)),
        ("\\log_{2} x", _log(x, 2)),
        # ("\\log_a x", _log(x, a)),
        ("\\log_{a} x", _log(x, a)),
        ("\\log_{11} x", _log(x, 11)),
        ("\\log_{a^2} x", _log(x, _Pow(a, 2))),
        ("[x]", x),
        ("[a + b]", _Add(a, b)),
        ("\\frac{d}{dx} [ \\tan x ]", Derivative(tan(x), x)),
        ("2\\overline{x}", 2 * Symbol('xbar', real=True)),
        ("2\\overline{x}_n", 2 * Symbol('xbar_n', real=True)),
        ("\\frac{x}{\\overline{x}_n}", x / Symbol('xbar_n', real=True)),
        ("\\frac{\\sin(x)}{\\overline{x}_n}", sin(Symbol('x', real=True)) / Symbol('xbar_n', real=True)),
        ("2\\bar{x}", 2 * Symbol('xbar', real=True)),
        ("2\\bar{x}_n", 2 * Symbol('xbar_n', real=True)),
        ("\\sin\\left(\\theta\\right) \\cdot4", sin(theta) * 4),
        ("\\ln\\left(\\theta\\right)", _log(theta, E)),
        ("\\ln\\left(x-\\theta\\right)", _log(x - theta, E)),
        ("\\ln\\left(\\left(x-\\theta\\right)\\right)", _log(x - theta, E)),
        ("\\ln\\left(\\left[x-\\theta\\right]\\right)", _log(x - theta, E)),
        ("\\ln\\left(\\left\\{x-\\theta\\right\\}\\right)", _log(x - theta, E)),
        ("\\ln\\left(\\left|x-\\theta\\right|\\right)", _log(_Abs(x - theta), E)),
        ("\\frac{1}{2}xy(x+y)", Mul(_Pow(2, -1), x, y, (x + y), evaluate=False)),
        ("\\frac{1}{2}\\theta(x+y)", Mul(_Pow(2, -1), theta, (x + y), evaluate=False)),
        ("1-f(x)", 1 - f * x),

        ("\\begin{matrix}1&2\\\\3&4\\end{matrix}", Matrix([[1, 2], [3, 4]])),
        ("\\begin{matrix}x&x^2\\\\\\sqrt{x}&x\\end{matrix}", Matrix([[x, x**2], [_Pow(x, S.Half), x]])),
        ("\\begin{matrix}\\sqrt{x}\\\\\\sin(\\theta)\\end{matrix}", Matrix([_Pow(x, S.Half), sin(theta)])),
        ("\\begin{pmatrix}1&2\\\\3&4\\end{pmatrix}", Matrix([[1, 2], [3, 4]])),
        ("\\begin{bmatrix}1&2\\\\3&4\\end{bmatrix}", Matrix([[1, 2], [3, 4]])),

        # scientific notation
        ("2.5\\times 10^2", 250),
        ("1,500\\times 10^{-1}", 150),

        # e notation
        ("2.5E2", 250),
        ("1,500E-1", 150),

        # multiplication without cmd
        ("2x2y", Mul(2, x, 2, y, evaluate=False)),
        ("2x2", Mul(2, x, 2, evaluate=False)),
        ("x2", x * 2),

        # lin alg processing
        ("\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}", MatMul(theta, Matrix([[1, 2], [3, 4]]), evaluate=False)),
        ("\\theta\\begin{matrix}1\\\\3\\end{matrix} - \\begin{matrix}-1\\\\2\\end{matrix}", MatAdd(MatMul(theta, Matrix([[1], [3]]), evaluate=False), MatMul(-1, Matrix([[-1], [2]]), evaluate=False), evaluate=False)),
        ("\\theta\\begin{matrix}1&0\\\\0&1\\end{matrix}*\\begin{matrix}3\\\\-2\\end{matrix}", MatMul(theta, Matrix([[1, 0], [0, 1]]), Matrix([3, -2]), evaluate=False)),
        ("\\frac{1}{9}\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}", MatMul(Pow(9, -1, evaluate=False), theta, Matrix([[1, 2], [3, 4]]), evaluate=False)),
        ("\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
        ("\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix};\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
        ("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}\\right\\}", [Matrix([1, 2, 3]), Matrix([4, 3, 1])]),
        ("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix},\\begin{pmatrix}1\\\\1\\\\1\\end{pmatrix}\\right\\}", [Matrix([1, 2, 3]), Matrix([4, 3, 1]), Matrix([1, 1, 1])]),
        ("\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right\\}", Matrix([1, 2, 3])),
        ("\\left{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right}", Matrix([1, 2, 3])),
        ("{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}}", Matrix([1, 2, 3])),

        # us dollars
        ("\\$1,000.00", 1000),
        ("\\$543.21", 543.21),
        ("\\$0.009", 0.009),

        # percentages
        ("100\\%", 1),
        ("1.5\\%", 0.015),
        ("0.05\\%", 0.0005),

        # empty set
        ("\\emptyset", S.EmptySet)
    ]

    def test_good_pair(self, s, eq):
        assert_equal(s, eq)