mirror of https://github.com/inclusionAI/AReaL
384 lines
14 KiB
Python
384 lines
14 KiB
Python
import hashlib
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import pytest
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from sympy import (
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Abs,
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Add,
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Derivative,
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E,
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Eq,
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GreaterThan,
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I,
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Integer,
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Integral,
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LessThan,
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Limit,
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MatAdd,
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MatMul,
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Matrix,
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Max,
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Min,
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Mod,
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Mul,
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Ne,
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Pow,
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Product,
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Rational,
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S,
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StrictGreaterThan,
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StrictLessThan,
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Sum,
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Symbol,
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UnevaluatedExpr,
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acos,
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acosh,
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asin,
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asinh,
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atan,
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atanh,
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binomial,
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ceiling,
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cos,
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cosh,
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csc,
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exp,
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factorial,
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floor,
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gcd,
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lcm,
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log,
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oo,
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pi,
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root,
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sec,
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sin,
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sinh,
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sqrt,
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tan,
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tanh,
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)
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from .context import _Add, _Mul, _Pow, assert_equal, process_sympy
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x = Symbol("x", real=True)
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y = Symbol("y", real=True)
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z = Symbol("z", real=True)
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a = Symbol("a", real=True)
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b = Symbol("b", real=True)
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c = Symbol("c", real=True)
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f = Symbol("f", real=True)
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t = Symbol("t", real=True)
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k = Symbol("k", real=True)
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n = Symbol("n", real=True)
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theta = Symbol("theta", real=True)
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# shorthand definitions
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def _Abs(a):
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return Abs(a, evaluate=False)
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def _factorial(a):
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return factorial(a, evaluate=False)
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def _log(a, b):
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return log(a, b, evaluate=False)
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def pytest_generate_tests(metafunc):
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metafunc.parametrize("s, eq", metafunc.cls.GOOD_PAIRS)
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class TestAllGood(object):
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# These latex strings should parse to the corresponding SymPy expression
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GOOD_PAIRS = [
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("0", 0),
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("1", 1),
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("-3.14", -3.14),
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("5-3", _Add(5, -3)),
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("(-7.13)(1.5)", _Mul(Rational("-7.13"), Rational("1.5"))),
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(
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"\\left(-7.13\\right)\\left(1.5\\right)",
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_Mul(Rational("-7.13"), Rational("1.5")),
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),
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("x", x),
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("2x", 2 * x),
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("x^2", x**2),
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("x^{3 + 1}", x ** _Add(3, 1)),
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("x^{\\left\\{3 + 1\\right\\}}", x ** _Add(3, 1)),
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("-3y + 2x", _Add(_Mul(2, x), Mul(-1, 3, y, evaluate=False))),
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("-c", -c),
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("a \\cdot b", a * b),
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("a / b", a / b),
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("a \\div b", a / b),
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("a + b", a + b),
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("a + b - a", Add(a, b, _Mul(-1, a), evaluate=False)),
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("a^2 + b^2 = c^2", Eq(a**2 + b**2, c**2)),
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("a^2 + b^2 != 2c^2", Ne(a**2 + b**2, 2 * c**2)),
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("a\\mod b", Mod(a, b)),
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("\\sin \\theta", sin(theta)),
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("\\sin(\\theta)", sin(theta)),
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("\\sin\\left(\\theta\\right)", sin(theta)),
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("\\sin^{-1} a", asin(a)),
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("\\sin a \\cos b", _Mul(sin(a), cos(b))),
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("\\sin \\cos \\theta", sin(cos(theta))),
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("\\sin(\\cos \\theta)", sin(cos(theta))),
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("\\arcsin(a)", asin(a)),
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("\\arccos(a)", acos(a)),
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("\\arctan(a)", atan(a)),
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("\\sinh(a)", sinh(a)),
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("\\cosh(a)", cosh(a)),
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("\\tanh(a)", tanh(a)),
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("\\sinh^{-1}(a)", asinh(a)),
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("\\cosh^{-1}(a)", acosh(a)),
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("\\tanh^{-1}(a)", atanh(a)),
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("\\arcsinh(a)", asinh(a)),
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("\\arccosh(a)", acosh(a)),
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("\\arctanh(a)", atanh(a)),
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("\\arsinh(a)", asinh(a)),
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("\\arcosh(a)", acosh(a)),
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("\\artanh(a)", atanh(a)),
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("\\operatorname{arcsinh}(a)", asinh(a)),
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("\\operatorname{arccosh}(a)", acosh(a)),
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("\\operatorname{arctanh}(a)", atanh(a)),
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("\\operatorname{arsinh}(a)", asinh(a)),
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("\\operatorname{arcosh}(a)", acosh(a)),
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("\\operatorname{artanh}(a)", atanh(a)),
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("\\operatorname{gcd}(a, b)", UnevaluatedExpr(gcd(a, b))),
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("\\operatorname{lcm}(a, b)", UnevaluatedExpr(lcm(a, b))),
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("\\operatorname{gcd}(a,b)", UnevaluatedExpr(gcd(a, b))),
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("\\operatorname{lcm}(a,b)", UnevaluatedExpr(lcm(a, b))),
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("\\operatorname{floor}(a)", floor(a)),
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("\\operatorname{ceil}(b)", ceiling(b)),
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("\\cos^2(x)", cos(x) ** 2),
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("\\cos(x)^2", cos(x) ** 2),
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("\\gcd(a, b)", UnevaluatedExpr(gcd(a, b))),
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("\\lcm(a, b)", UnevaluatedExpr(lcm(a, b))),
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("\\gcd(a,b)", UnevaluatedExpr(gcd(a, b))),
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("\\lcm(a,b)", UnevaluatedExpr(lcm(a, b))),
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("\\floor(a)", floor(a)),
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("\\ceil(b)", ceiling(b)),
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("\\max(a, b)", Max(a, b)),
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("\\min(a, b)", Min(a, b)),
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("\\frac{a}{b}", a / b),
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("\\frac{a + b}{c}", _Mul(a + b, _Pow(c, -1))),
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("\\frac{7}{3}", _Mul(7, _Pow(3, -1))),
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("(\\csc x)(\\sec y)", csc(x) * sec(y)),
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("\\lim_{x \\to 3} a", Limit(a, x, 3)),
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("\\lim_{x \\rightarrow 3} a", Limit(a, x, 3)),
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("\\lim_{x \\Rightarrow 3} a", Limit(a, x, 3)),
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("\\lim_{x \\longrightarrow 3} a", Limit(a, x, 3)),
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("\\lim_{x \\Longrightarrow 3} a", Limit(a, x, 3)),
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("\\lim_{x \\to 3^{+}} a", Limit(a, x, 3, dir="+")),
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("\\lim_{x \\to 3^{-}} a", Limit(a, x, 3, dir="-")),
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("\\infty", oo),
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("\\infty\\%", oo),
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("\\$\\infty", oo),
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("-\\infty", -oo),
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("-\\infty\\%", -oo),
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("-\\$\\infty", -oo),
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("\\lim_{x \\to \\infty} \\frac{1}{x}", Limit(_Mul(1, _Pow(x, -1)), x, oo)),
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("\\frac{d}{dx} x", Derivative(x, x)),
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("\\frac{d}{dt} x", Derivative(x, t)),
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# ("f(x)", f(x)),
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# ("f(x, y)", f(x, y)),
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# ("f(x, y, z)", f(x, y, z)),
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# ("\\frac{d f(x)}{dx}", Derivative(f(x), x)),
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# ("\\frac{d\\theta(x)}{dx}", Derivative(theta(x), x)),
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("|x|", _Abs(x)),
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("\\left|x\\right|", _Abs(x)),
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("||x||", _Abs(Abs(x))),
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("|x||y|", _Abs(x) * _Abs(y)),
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("||x||y||", _Abs(_Abs(x) * _Abs(y))),
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("\\lfloor x\\rfloor", floor(x)),
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("\\lceil y\\rceil", ceiling(y)),
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("\\pi^{|xy|}", pi ** _Abs(x * y)),
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("\\frac{\\pi}{3}", _Mul(pi, _Pow(3, -1))),
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("\\sin{\\frac{\\pi}{2}}", sin(_Mul(pi, _Pow(2, -1)), evaluate=False)),
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("a+bI", a + I * b),
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("e^{I\\pi}", -1),
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("\\int x dx", Integral(x, x)),
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("\\int x d\\theta", Integral(x, theta)),
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("\\int (x^2 - y)dx", Integral(x**2 - y, x)),
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("\\int x + a dx", Integral(_Add(x, a), x)),
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("\\int da", Integral(1, a)),
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("\\int_0^7 dx", Integral(1, (x, 0, 7))),
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("\\int_a^b x dx", Integral(x, (x, a, b))),
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("\\int^b_a x dx", Integral(x, (x, a, b))),
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("\\int_{a}^b x dx", Integral(x, (x, a, b))),
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("\\int^{b}_a x dx", Integral(x, (x, a, b))),
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("\\int_{a}^{b} x dx", Integral(x, (x, a, b))),
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("\\int_{ }^{}x dx", Integral(x, x)),
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("\\int^{ }_{ }x dx", Integral(x, x)),
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("\\int^{b}_{a} x dx", Integral(x, (x, a, b))),
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# ("\\int_{f(a)}^{f(b)} f(z) dz", Integral(f(z), (z, f(a), f(b)))),
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("\\int (x+a)", Integral(_Add(x, a), x)),
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("\\int a + b + c dx", Integral(Add(a, b, c, evaluate=False), x)),
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("\\int \\frac{dz}{z}", Integral(Pow(z, -1), z)),
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("\\int \\frac{3 dz}{z}", Integral(3 * Pow(z, -1), z)),
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("\\int \\frac{1}{x} dx", Integral(Pow(x, -1), x)),
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(
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"\\int \\frac{1}{a} + \\frac{1}{b} dx",
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Integral(_Add(_Pow(a, -1), Pow(b, -1)), x),
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),
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(
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"\\int \\frac{3 \\cdot d\\theta}{\\theta}",
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Integral(3 * _Pow(theta, -1), theta),
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),
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("\\int \\frac{1}{x} + 1 dx", Integral(_Add(_Pow(x, -1), 1), x)),
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("x_0", Symbol("x_0", real=True)),
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("x_{1}", Symbol("x_1", real=True)),
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("x_a", Symbol("x_a", real=True)),
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("x_{b}", Symbol("x_b", real=True)),
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("h_\\theta", Symbol("h_{\\theta}", real=True)),
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("h_\\theta ", Symbol("h_{\\theta}", real=True)),
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("h_{\\theta}", Symbol("h_{\\theta}", real=True)),
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# ("h_{\\theta}(x_0, x_1)", Symbol('h_{theta}', real=True)(Symbol('x_{0}', real=True), Symbol('x_{1}', real=True))),
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("x!", _factorial(x)),
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("100!", _factorial(100)),
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("\\theta!", _factorial(theta)),
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("(x + 1)!", _factorial(_Add(x, 1))),
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("\\left(x + 1\\right)!", _factorial(_Add(x, 1))),
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("(x!)!", _factorial(_factorial(x))),
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("x!!!", _factorial(_factorial(_factorial(x)))),
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("5!7!", _Mul(_factorial(5), _factorial(7))),
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("\\sqrt{x}", sqrt(x)),
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("\\sqrt{x + b}", sqrt(_Add(x, b))),
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("\\sqrt[3]{\\sin x}", root(sin(x), 3)),
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("\\sqrt[y]{\\sin x}", root(sin(x), y)),
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("\\sqrt[\\theta]{\\sin x}", root(sin(x), theta)),
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("x < y", StrictLessThan(x, y)),
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("x \\leq y", LessThan(x, y)),
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("x > y", StrictGreaterThan(x, y)),
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("x \\geq y", GreaterThan(x, y)),
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("\\sum_{k = 1}^{3} c", Sum(c, (k, 1, 3))),
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("\\sum_{k = 1}^3 c", Sum(c, (k, 1, 3))),
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("\\sum^{3}_{k = 1} c", Sum(c, (k, 1, 3))),
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("\\sum^3_{k = 1} c", Sum(c, (k, 1, 3))),
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("\\sum_{k = 1}^{10} k^2", Sum(k**2, (k, 1, 10))),
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(
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"\\sum_{n = 0}^{\\infty} \\frac{1}{n!}",
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Sum(_Pow(_factorial(n), -1), (n, 0, oo)),
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),
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("\\prod_{a = b}^{c} x", Product(x, (a, b, c))),
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("\\prod_{a = b}^c x", Product(x, (a, b, c))),
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("\\prod^{c}_{a = b} x", Product(x, (a, b, c))),
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("\\prod^c_{a = b} x", Product(x, (a, b, c))),
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("\\ln x", _log(x, E)),
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("\\ln xy", _log(x * y, E)),
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("\\log x", _log(x, 10)),
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("\\log xy", _log(x * y, 10)),
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# ("\\log_2 x", _log(x, 2)),
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("\\log_{2} x", _log(x, 2)),
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# ("\\log_a x", _log(x, a)),
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("\\log_{a} x", _log(x, a)),
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("\\log_{11} x", _log(x, 11)),
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("\\log_{a^2} x", _log(x, _Pow(a, 2))),
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("[x]", x),
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("[a + b]", _Add(a, b)),
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("\\frac{d}{dx} [ \\tan x ]", Derivative(tan(x), x)),
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("2\\overline{x}", 2 * Symbol("xbar", real=True)),
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("2\\overline{x}_n", 2 * Symbol("xbar_n", real=True)),
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("\\frac{x}{\\overline{x}_n}", x / Symbol("xbar_n", real=True)),
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(
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"\\frac{\\sin(x)}{\\overline{x}_n}",
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sin(Symbol("x", real=True)) / Symbol("xbar_n", real=True),
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),
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("2\\bar{x}", 2 * Symbol("xbar", real=True)),
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("2\\bar{x}_n", 2 * Symbol("xbar_n", real=True)),
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("\\sin\\left(\\theta\\right) \\cdot4", sin(theta) * 4),
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("\\ln\\left(\\theta\\right)", _log(theta, E)),
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("\\ln\\left(x-\\theta\\right)", _log(x - theta, E)),
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("\\ln\\left(\\left(x-\\theta\\right)\\right)", _log(x - theta, E)),
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("\\ln\\left(\\left[x-\\theta\\right]\\right)", _log(x - theta, E)),
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("\\ln\\left(\\left\\{x-\\theta\\right\\}\\right)", _log(x - theta, E)),
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("\\ln\\left(\\left|x-\\theta\\right|\\right)", _log(_Abs(x - theta), E)),
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("\\frac{1}{2}xy(x+y)", Mul(_Pow(2, -1), x, y, (x + y), evaluate=False)),
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("\\frac{1}{2}\\theta(x+y)", Mul(_Pow(2, -1), theta, (x + y), evaluate=False)),
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("1-f(x)", 1 - f * x),
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("\\begin{matrix}1&2\\\\3&4\\end{matrix}", Matrix([[1, 2], [3, 4]])),
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(
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"\\begin{matrix}x&x^2\\\\\\sqrt{x}&x\\end{matrix}",
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Matrix([[x, x**2], [_Pow(x, S.Half), x]]),
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),
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(
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"\\begin{matrix}\\sqrt{x}\\\\\\sin(\\theta)\\end{matrix}",
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Matrix([_Pow(x, S.Half), sin(theta)]),
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),
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("\\begin{pmatrix}1&2\\\\3&4\\end{pmatrix}", Matrix([[1, 2], [3, 4]])),
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("\\begin{bmatrix}1&2\\\\3&4\\end{bmatrix}", Matrix([[1, 2], [3, 4]])),
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# scientific notation
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("2.5\\times 10^2", 250),
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("1,500\\times 10^{-1}", 150),
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# e notation
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("2.5E2", 250),
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("1,500E-1", 150),
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# multiplication without cmd
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("2x2y", Mul(2, x, 2, y, evaluate=False)),
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("2x2", Mul(2, x, 2, evaluate=False)),
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("x2", x * 2),
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# lin alg processing
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(
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"\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}",
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MatMul(theta, Matrix([[1, 2], [3, 4]]), evaluate=False),
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),
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(
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"\\theta\\begin{matrix}1\\\\3\\end{matrix} - \\begin{matrix}-1\\\\2\\end{matrix}",
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MatAdd(
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MatMul(theta, Matrix([[1], [3]]), evaluate=False),
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MatMul(-1, Matrix([[-1], [2]]), evaluate=False),
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evaluate=False,
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),
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),
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(
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"\\theta\\begin{matrix}1&0\\\\0&1\\end{matrix}*\\begin{matrix}3\\\\-2\\end{matrix}",
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MatMul(theta, Matrix([[1, 0], [0, 1]]), Matrix([3, -2]), evaluate=False),
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),
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(
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"\\frac{1}{9}\\theta\\begin{matrix}1&2\\\\3&4\\end{matrix}",
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MatMul(
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Pow(9, -1, evaluate=False),
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theta,
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Matrix([[1, 2], [3, 4]]),
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evaluate=False,
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),
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),
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(
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"\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}",
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[Matrix([1, 2, 3]), Matrix([4, 3, 1])],
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),
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(
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"\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix};\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}",
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[Matrix([1, 2, 3]), Matrix([4, 3, 1])],
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),
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(
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"\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix}\\right\\}",
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[Matrix([1, 2, 3]), Matrix([4, 3, 1])],
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),
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(
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"\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix},\\begin{pmatrix}4\\\\3\\\\1\\end{pmatrix},\\begin{pmatrix}1\\\\1\\\\1\\end{pmatrix}\\right\\}",
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[Matrix([1, 2, 3]), Matrix([4, 3, 1]), Matrix([1, 1, 1])],
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),
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(
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"\\left\\{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right\\}",
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Matrix([1, 2, 3]),
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),
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("\\left{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}\\right}", Matrix([1, 2, 3])),
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("{\\begin{pmatrix}1\\\\2\\\\3\\end{pmatrix}}", Matrix([1, 2, 3])),
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# us dollars
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("\\$1,000.00", 1000),
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("\\$543.21", 543.21),
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("\\$0.009", 0.009),
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# percentages
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("100\\%", 1),
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("1.5\\%", 0.015),
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("0.05\\%", 0.0005),
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# empty set
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("\\emptyset", S.EmptySet),
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]
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def test_good_pair(self, s, eq):
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assert_equal(s, eq)
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