MTtranslateService/Lib/site-packages/sympy/parsing/tests/test_sympy_parser.py

# -*- coding: utf-8 -*-


import sys
import builtins
import types

from sympy.assumptions import Q
from sympy.core import Symbol, Function, Float, Rational, Integer, I, Mul, Pow, Eq
from sympy.functions import exp, factorial, factorial2, sin, Min, Max
from sympy.logic import And
from sympy.series import Limit
from sympy.testing.pytest import raises, skip

from sympy.parsing.sympy_parser import (
    parse_expr, standard_transformations, rationalize, TokenError,
    split_symbols, implicit_multiplication, convert_equals_signs,
    convert_xor, function_exponentiation, lambda_notation, auto_symbol,
    repeated_decimals, implicit_multiplication_application,
    auto_number, factorial_notation, implicit_application,
    _transformation, T
    )


def test_sympy_parser():
    x = Symbol('x')
    inputs = {
        '2*x': 2 * x,
        '3.00': Float(3),
        '22/7': Rational(22, 7),
        '2+3j': 2 + 3*I,
        'exp(x)': exp(x),
        'x!': factorial(x),
        'x!!': factorial2(x),
        '(x + 1)! - 1': factorial(x + 1) - 1,
        '3.[3]': Rational(10, 3),
        '.0[3]': Rational(1, 30),
        '3.2[3]': Rational(97, 30),
        '1.3[12]': Rational(433, 330),
        '1 + 3.[3]': Rational(13, 3),
        '1 + .0[3]': Rational(31, 30),
        '1 + 3.2[3]': Rational(127, 30),
        '.[0011]': Rational(1, 909),
        '0.1[00102] + 1': Rational(366697, 333330),
        '1.[0191]': Rational(10190, 9999),
        '10!': 3628800,
        '-(2)': -Integer(2),
        '[-1, -2, 3]': [Integer(-1), Integer(-2), Integer(3)],
        'Symbol("x").free_symbols': x.free_symbols,
        "S('S(3).n(n=3)')": 3.00,
        'factorint(12, visual=True)': Mul(
            Pow(2, 2, evaluate=False),
            Pow(3, 1, evaluate=False),
            evaluate=False),
        'Limit(sin(x), x, 0, dir="-")': Limit(sin(x), x, 0, dir='-'),
        'Q.even(x)': Q.even(x),


    }
    for text, result in inputs.items():
        assert parse_expr(text) == result

    raises(TypeError, lambda:
        parse_expr('x', standard_transformations))
    raises(TypeError, lambda:
        parse_expr('x', transformations=lambda x,y: 1))
    raises(TypeError, lambda:
        parse_expr('x', transformations=(lambda x,y: 1,)))
    raises(TypeError, lambda: parse_expr('x', transformations=((),)))
    raises(TypeError, lambda: parse_expr('x', {}, [], []))
    raises(TypeError, lambda: parse_expr('x', [], [], {}))
    raises(TypeError, lambda: parse_expr('x', [], [], {}))


def test_rationalize():
    inputs = {
        '0.123': Rational(123, 1000)
    }
    transformations = standard_transformations + (rationalize,)
    for text, result in inputs.items():
        assert parse_expr(text, transformations=transformations) == result


def test_factorial_fail():
    inputs = ['x!!!', 'x!!!!', '(!)']


    for text in inputs:
        try:
            parse_expr(text)
            assert False
        except TokenError:
            assert True


def test_repeated_fail():
    inputs = ['1[1]', '.1e1[1]', '0x1[1]', '1.1j[1]', '1.1[1 + 1]',
        '0.1[[1]]', '0x1.1[1]']


    # All are valid Python, so only raise TypeError for invalid indexing
    for text in inputs:
        raises(TypeError, lambda: parse_expr(text))


    inputs = ['0.1[', '0.1[1', '0.1[]']
    for text in inputs:
        raises((TokenError, SyntaxError), lambda: parse_expr(text))


def test_repeated_dot_only():
    assert parse_expr('.[1]') == Rational(1, 9)
    assert parse_expr('1 + .[1]') == Rational(10, 9)


def test_local_dict():
    local_dict = {
        'my_function': lambda x: x + 2
    }
    inputs = {
        'my_function(2)': Integer(4)
    }
    for text, result in inputs.items():
        assert parse_expr(text, local_dict=local_dict) == result


def test_local_dict_split_implmult():
    t = standard_transformations + (split_symbols, implicit_multiplication,)
    w = Symbol('w', real=True)
    y = Symbol('y')
    assert parse_expr('yx', local_dict={'x':w}, transformations=t) == y*w


def test_local_dict_symbol_to_fcn():
    x = Symbol('x')
    d = {'foo': Function('bar')}
    assert parse_expr('foo(x)', local_dict=d) == d['foo'](x)
    d = {'foo': Symbol('baz')}
    raises(TypeError, lambda: parse_expr('foo(x)', local_dict=d))


def test_global_dict():
    global_dict = {
        'Symbol': Symbol
    }
    inputs = {
        'Q & S': And(Symbol('Q'), Symbol('S'))
    }
    for text, result in inputs.items():
        assert parse_expr(text, global_dict=global_dict) == result


def test_no_globals():

    # Replicate creating the default global_dict:
    default_globals = {}
    exec('from sympy import *', default_globals)
    builtins_dict = vars(builtins)
    for name, obj in builtins_dict.items():
        if isinstance(obj, types.BuiltinFunctionType):
            default_globals[name] = obj
    default_globals['max'] = Max
    default_globals['min'] = Min

    # Need to include Symbol or parse_expr will not work:
    default_globals.pop('Symbol')
    global_dict = {'Symbol':Symbol}

    for name in default_globals:
        obj = parse_expr(name, global_dict=global_dict)
        assert obj == Symbol(name)


def test_issue_2515():
    raises(TokenError, lambda: parse_expr('(()'))
    raises(TokenError, lambda: parse_expr('"""'))


def test_issue_7663():
    x = Symbol('x')
    e = '2*(x+1)'
    assert parse_expr(e, evaluate=0) == parse_expr(e, evaluate=False)
    assert parse_expr(e, evaluate=0).equals(2*(x+1))

def test_recursive_evaluate_false_10560():
    inputs = {
        '4*-3' : '4*-3',
        '-4*3' : '(-4)*3',
        "-2*x*y": '(-2)*x*y',
        "x*-4*x": "x*(-4)*x"
    }
    for text, result in inputs.items():
        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)


def test_function_evaluate_false():
    inputs = [
        'Abs(0)', 'im(0)', 're(0)', 'sign(0)', 'arg(0)', 'conjugate(0)',
        'acos(0)', 'acot(0)', 'acsc(0)', 'asec(0)', 'asin(0)', 'atan(0)',
        'acosh(0)', 'acoth(0)', 'acsch(0)', 'asech(0)', 'asinh(0)', 'atanh(0)',
        'cos(0)', 'cot(0)', 'csc(0)', 'sec(0)', 'sin(0)', 'tan(0)',
        'cosh(0)', 'coth(0)', 'csch(0)', 'sech(0)', 'sinh(0)', 'tanh(0)',
        'exp(0)', 'log(0)', 'sqrt(0)',
    ]
    for case in inputs:
        expr = parse_expr(case, evaluate=False)
        assert case == str(expr) != str(expr.doit())
    assert str(parse_expr('ln(0)', evaluate=False)) == 'log(0)'
    assert str(parse_expr('cbrt(0)', evaluate=False)) == '0**(1/3)'


def test_issue_10773():
    inputs = {
    '-10/5': '(-10)/5',
    '-10/-5' : '(-10)/(-5)',
    }
    for text, result in inputs.items():
        assert parse_expr(text, evaluate=False) == parse_expr(result, evaluate=False)


def test_split_symbols():
    transformations = standard_transformations + \
                      (split_symbols, implicit_multiplication,)
    x = Symbol('x')
    y = Symbol('y')
    xy = Symbol('xy')


    assert parse_expr("xy") == xy
    assert parse_expr("xy", transformations=transformations) == x*y


def test_split_symbols_function():
    transformations = standard_transformations + \
                      (split_symbols, implicit_multiplication,)
    x = Symbol('x')
    y = Symbol('y')
    a = Symbol('a')
    f = Function('f')


    assert parse_expr("ay(x+1)", transformations=transformations) == a*y*(x+1)
    assert parse_expr("af(x+1)", transformations=transformations,
                      local_dict={'f':f}) == a*f(x+1)


def test_functional_exponent():
    t = standard_transformations + (convert_xor, function_exponentiation)
    x = Symbol('x')
    y = Symbol('y')
    a = Symbol('a')
    yfcn = Function('y')
    assert parse_expr("sin^2(x)", transformations=t) == (sin(x))**2
    assert parse_expr("sin^y(x)", transformations=t) == (sin(x))**y
    assert parse_expr("exp^y(x)", transformations=t) == (exp(x))**y
    assert parse_expr("E^y(x)", transformations=t) == exp(yfcn(x))
    assert parse_expr("a^y(x)", transformations=t) == a**(yfcn(x))


def test_match_parentheses_implicit_multiplication():
    transformations = standard_transformations + \
                      (implicit_multiplication,)
    raises(TokenError, lambda: parse_expr('(1,2),(3,4]',transformations=transformations))


def test_convert_equals_signs():
    transformations = standard_transformations + \
                        (convert_equals_signs, )
    x = Symbol('x')
    y = Symbol('y')
    assert parse_expr("1*2=x", transformations=transformations) == Eq(2, x)
    assert parse_expr("y = x", transformations=transformations) == Eq(y, x)
    assert parse_expr("(2*y = x) = False",
        transformations=transformations) == Eq(Eq(2*y, x), False)


def test_parse_function_issue_3539():
    x = Symbol('x')
    f = Function('f')
    assert parse_expr('f(x)') == f(x)


def test_split_symbols_numeric():
    transformations = (
        standard_transformations +
        (implicit_multiplication_application,))

    n = Symbol('n')
    expr1 = parse_expr('2**n * 3**n')
    expr2 = parse_expr('2**n3**n', transformations=transformations)
    assert expr1 == expr2 == 2**n*3**n

    expr1 = parse_expr('n12n34', transformations=transformations)
    assert expr1 == n*12*n*34


def test_unicode_names():
    assert parse_expr('α') == Symbol('α')


def test_python3_features():
    # Make sure the tokenizer can handle Python 3-only features
    if sys.version_info < (3, 7):
        skip("test_python3_features requires Python 3.7 or newer")


    assert parse_expr("123_456") == 123456
    assert parse_expr("1.2[3_4]") == parse_expr("1.2[34]") == Rational(611, 495)
    assert parse_expr("1.2[012_012]") == parse_expr("1.2[012012]") == Rational(400, 333)
    assert parse_expr('.[3_4]') == parse_expr('.[34]') == Rational(34, 99)
    assert parse_expr('.1[3_4]') == parse_expr('.1[34]') == Rational(133, 990)
    assert parse_expr('123_123.123_123[3_4]') == parse_expr('123123.123123[34]') == Rational(12189189189211, 99000000)


def test_issue_19501():
    x = Symbol('x')
    eq = parse_expr('E**x(1+x)', local_dict={'x': x}, transformations=(
        standard_transformations +
        (implicit_multiplication_application,)))
    assert eq.free_symbols == {x}


def test_parsing_definitions():
    from sympy.abc import x
    assert len(_transformation) == 12  # if this changes, extend below
    assert _transformation[0] == lambda_notation
    assert _transformation[1] == auto_symbol
    assert _transformation[2] == repeated_decimals
    assert _transformation[3] == auto_number
    assert _transformation[4] == factorial_notation
    assert _transformation[5] == implicit_multiplication_application
    assert _transformation[6] == convert_xor
    assert _transformation[7] == implicit_application
    assert _transformation[8] == implicit_multiplication
    assert _transformation[9] == convert_equals_signs
    assert _transformation[10] == function_exponentiation
    assert _transformation[11] == rationalize
    assert T[:5] == T[0,1,2,3,4] == standard_transformations
    t = _transformation
    assert T[-1, 0] == (t[len(t) - 1], t[0])
    assert T[:5, 8] == standard_transformations + (t[8],)
    assert parse_expr('0.3x^2', transformations='all') == 3*x**2/10
    assert parse_expr('sin 3x', transformations='implicit') == sin(3*x)


def test_builtins():
    cases = [
        ('abs(x)', 'Abs(x)'),
        ('max(x, y)', 'Max(x, y)'),
        ('min(x, y)', 'Min(x, y)'),
        ('pow(x, y)', 'Pow(x, y)'),
    ]
    for built_in_func_call, sympy_func_call in cases:
        assert parse_expr(built_in_func_call) == parse_expr(sympy_func_call)
    assert str(parse_expr('pow(38, -1, 97)')) == '23'


def test_issue_22822():
    raises(ValueError, lambda: parse_expr('x', {'': 1}))
    data = {'some_parameter': None}
    assert parse_expr('some_parameter is None', data) is True