Vehicle-cpp/hkpc/software/sympy/core/tests/test_symbol.py

import threading

from sympy.core.function import Function, UndefinedFunction
from sympy.core.numbers import (I, Rational, pi)
from sympy.core.relational import (GreaterThan, LessThan, StrictGreaterThan, StrictLessThan)
from sympy.core.symbol import (Dummy, Symbol, Wild, symbols)
from sympy.core.sympify import sympify  # can't import as S yet
from sympy.core.symbol import uniquely_named_symbol, _symbol, Str

from sympy.testing.pytest import raises, skip_under_pyodide
from sympy.core.symbol import disambiguate


def test_Str():
    a1 = Str('a')
    a2 = Str('a')
    b = Str('b')
    assert a1 == a2 != b
    raises(TypeError, lambda: Str())


def test_Symbol():
    a = Symbol("a")
    x1 = Symbol("x")
    x2 = Symbol("x")
    xdummy1 = Dummy("x")
    xdummy2 = Dummy("x")

    assert a != x1
    assert a != x2
    assert x1 == x2
    assert x1 != xdummy1
    assert xdummy1 != xdummy2

    assert Symbol("x") == Symbol("x")
    assert Dummy("x") != Dummy("x")
    d = symbols('d', cls=Dummy)
    assert isinstance(d, Dummy)
    c, d = symbols('c,d', cls=Dummy)
    assert isinstance(c, Dummy)
    assert isinstance(d, Dummy)
    raises(TypeError, lambda: Symbol())


def test_Dummy():
    assert Dummy() != Dummy()


def test_Dummy_force_dummy_index():
    raises(AssertionError, lambda: Dummy(dummy_index=1))
    assert Dummy('d', dummy_index=2) == Dummy('d', dummy_index=2)
    assert Dummy('d1', dummy_index=2) != Dummy('d2', dummy_index=2)
    d1 = Dummy('d', dummy_index=3)
    d2 = Dummy('d')
    # might fail if d1 were created with dummy_index >= 10**6
    assert d1 != d2
    d3 = Dummy('d', dummy_index=3)
    assert d1 == d3
    assert Dummy()._count == Dummy('d', dummy_index=3)._count


def test_lt_gt():
    S = sympify
    x, y = Symbol('x'), Symbol('y')

    assert (x >= y) == GreaterThan(x, y)
    assert (x >= 0) == GreaterThan(x, 0)
    assert (x <= y) == LessThan(x, y)
    assert (x <= 0) == LessThan(x, 0)

    assert (0 <= x) == GreaterThan(x, 0)
    assert (0 >= x) == LessThan(x, 0)
    assert (S(0) >= x) == GreaterThan(0, x)
    assert (S(0) <= x) == LessThan(0, x)

    assert (x > y) == StrictGreaterThan(x, y)
    assert (x > 0) == StrictGreaterThan(x, 0)
    assert (x < y) == StrictLessThan(x, y)
    assert (x < 0) == StrictLessThan(x, 0)

    assert (0 < x) == StrictGreaterThan(x, 0)
    assert (0 > x) == StrictLessThan(x, 0)
    assert (S(0) > x) == StrictGreaterThan(0, x)
    assert (S(0) < x) == StrictLessThan(0, x)

    e = x**2 + 4*x + 1
    assert (e >= 0) == GreaterThan(e, 0)
    assert (0 <= e) == GreaterThan(e, 0)
    assert (e > 0) == StrictGreaterThan(e, 0)
    assert (0 < e) == StrictGreaterThan(e, 0)

    assert (e <= 0) == LessThan(e, 0)
    assert (0 >= e) == LessThan(e, 0)
    assert (e < 0) == StrictLessThan(e, 0)
    assert (0 > e) == StrictLessThan(e, 0)

    assert (S(0) >= e) == GreaterThan(0, e)
    assert (S(0) <= e) == LessThan(0, e)
    assert (S(0) < e) == StrictLessThan(0, e)
    assert (S(0) > e) == StrictGreaterThan(0, e)


def test_no_len():
    # there should be no len for numbers
    x = Symbol('x')
    raises(TypeError, lambda: len(x))


def test_ineq_unequal():
    S = sympify
    x, y, z = symbols('x,y,z')

    e = (
        S(-1) >= x, S(-1) >= y, S(-1) >= z,
        S(-1) > x, S(-1) > y, S(-1) > z,
        S(-1) <= x, S(-1) <= y, S(-1) <= z,
        S(-1) < x, S(-1) < y, S(-1) < z,
        S(0) >= x, S(0) >= y, S(0) >= z,
        S(0) > x, S(0) > y, S(0) > z,
        S(0) <= x, S(0) <= y, S(0) <= z,
        S(0) < x, S(0) < y, S(0) < z,
        S('3/7') >= x, S('3/7') >= y, S('3/7') >= z,
        S('3/7') > x, S('3/7') > y, S('3/7') > z,
        S('3/7') <= x, S('3/7') <= y, S('3/7') <= z,
        S('3/7') < x, S('3/7') < y, S('3/7') < z,
        S(1.5) >= x, S(1.5) >= y, S(1.5) >= z,
        S(1.5) > x, S(1.5) > y, S(1.5) > z,
        S(1.5) <= x, S(1.5) <= y, S(1.5) <= z,
        S(1.5) < x, S(1.5) < y, S(1.5) < z,
        S(2) >= x, S(2) >= y, S(2) >= z,
        S(2) > x, S(2) > y, S(2) > z,
        S(2) <= x, S(2) <= y, S(2) <= z,
        S(2) < x, S(2) < y, S(2) < z,
        x >= -1, y >= -1, z >= -1,
        x > -1, y > -1, z > -1,
        x <= -1, y <= -1, z <= -1,
        x < -1, y < -1, z < -1,
        x >= 0, y >= 0, z >= 0,
        x > 0, y > 0, z > 0,
        x <= 0, y <= 0, z <= 0,
        x < 0, y < 0, z < 0,
        x >= 1.5, y >= 1.5, z >= 1.5,
        x > 1.5, y > 1.5, z > 1.5,
        x <= 1.5, y <= 1.5, z <= 1.5,
        x < 1.5, y < 1.5, z < 1.5,
        x >= 2, y >= 2, z >= 2,
        x > 2, y > 2, z > 2,
        x <= 2, y <= 2, z <= 2,
        x < 2, y < 2, z < 2,

        x >= y, x >= z, y >= x, y >= z, z >= x, z >= y,
        x > y, x > z, y > x, y > z, z > x, z > y,
        x <= y, x <= z, y <= x, y <= z, z <= x, z <= y,
        x < y, x < z, y < x, y < z, z < x, z < y,

        x - pi >= y + z, y - pi >= x + z, z - pi >= x + y,
        x - pi > y + z, y - pi > x + z, z - pi > x + y,
        x - pi <= y + z, y - pi <= x + z, z - pi <= x + y,
        x - pi < y + z, y - pi < x + z, z - pi < x + y,
        True, False
    )

    left_e = e[:-1]
    for i, e1 in enumerate( left_e ):
        for e2 in e[i + 1:]:
            assert e1 != e2


def test_Wild_properties():
    S = sympify
    # these tests only include Atoms
    x = Symbol("x")
    y = Symbol("y")
    p = Symbol("p", positive=True)
    k = Symbol("k", integer=True)
    n = Symbol("n", integer=True, positive=True)

    given_patterns = [ x, y, p, k, -k, n, -n, S(-3), S(3),
                       pi, Rational(3, 2), I ]

    integerp = lambda k: k.is_integer
    positivep = lambda k: k.is_positive
    symbolp = lambda k: k.is_Symbol
    realp = lambda k: k.is_extended_real

    S = Wild("S", properties=[symbolp])
    R = Wild("R", properties=[realp])
    Y = Wild("Y", exclude=[x, p, k, n])
    P = Wild("P", properties=[positivep])
    K = Wild("K", properties=[integerp])
    N = Wild("N", properties=[positivep, integerp])

    given_wildcards = [ S, R, Y, P, K, N ]

    goodmatch = {
        S: (x, y, p, k, n),
        R: (p, k, -k, n, -n, -3, 3, pi, Rational(3, 2)),
        Y: (y, -3, 3, pi, Rational(3, 2), I ),
        P: (p, n, 3, pi, Rational(3, 2)),
        K: (k, -k, n, -n, -3, 3),
        N: (n, 3)}

    for A in given_wildcards:
        for pat in given_patterns:
            d = pat.match(A)
            if pat in goodmatch[A]:
                assert d[A] in goodmatch[A]
            else:
                assert d is None


def test_symbols():
    x = Symbol('x')
    y = Symbol('y')
    z = Symbol('z')

    assert symbols('x') == x
    assert symbols('x ') == x
    assert symbols(' x ') == x
    assert symbols('x,') == (x,)
    assert symbols('x, ') == (x,)
    assert symbols('x ,') == (x,)

    assert symbols('x , y') == (x, y)

    assert symbols('x,y,z') == (x, y, z)
    assert symbols('x y z') == (x, y, z)

    assert symbols('x,y,z,') == (x, y, z)
    assert symbols('x y z ') == (x, y, z)

    xyz = Symbol('xyz')
    abc = Symbol('abc')

    assert symbols('xyz') == xyz
    assert symbols('xyz,') == (xyz,)
    assert symbols('xyz,abc') == (xyz, abc)

    assert symbols(('xyz',)) == (xyz,)
    assert symbols(('xyz,',)) == ((xyz,),)
    assert symbols(('x,y,z,',)) == ((x, y, z),)
    assert symbols(('xyz', 'abc')) == (xyz, abc)
    assert symbols(('xyz,abc',)) == ((xyz, abc),)
    assert symbols(('xyz,abc', 'x,y,z')) == ((xyz, abc), (x, y, z))

    assert symbols(('x', 'y', 'z')) == (x, y, z)
    assert symbols(['x', 'y', 'z']) == [x, y, z]
    assert symbols({'x', 'y', 'z'}) == {x, y, z}

    raises(ValueError, lambda: symbols(''))
    raises(ValueError, lambda: symbols(','))
    raises(ValueError, lambda: symbols('x,,y,,z'))
    raises(ValueError, lambda: symbols(('x', '', 'y', '', 'z')))

    a, b = symbols('x,y', real=True)
    assert a.is_real and b.is_real

    x0 = Symbol('x0')
    x1 = Symbol('x1')
    x2 = Symbol('x2')

    y0 = Symbol('y0')
    y1 = Symbol('y1')

    assert symbols('x0:0') == ()
    assert symbols('x0:1') == (x0,)
    assert symbols('x0:2') == (x0, x1)
    assert symbols('x0:3') == (x0, x1, x2)

    assert symbols('x:0') == ()
    assert symbols('x:1') == (x0,)
    assert symbols('x:2') == (x0, x1)
    assert symbols('x:3') == (x0, x1, x2)

    assert symbols('x1:1') == ()
    assert symbols('x1:2') == (x1,)
    assert symbols('x1:3') == (x1, x2)

    assert symbols('x1:3,x,y,z') == (x1, x2, x, y, z)

    assert symbols('x:3,y:2') == (x0, x1, x2, y0, y1)
    assert symbols(('x:3', 'y:2')) == ((x0, x1, x2), (y0, y1))

    a = Symbol('a')
    b = Symbol('b')
    c = Symbol('c')
    d = Symbol('d')

    assert symbols('x:z') == (x, y, z)
    assert symbols('a:d,x:z') == (a, b, c, d, x, y, z)
    assert symbols(('a:d', 'x:z')) == ((a, b, c, d), (x, y, z))

    aa = Symbol('aa')
    ab = Symbol('ab')
    ac = Symbol('ac')
    ad = Symbol('ad')

    assert symbols('aa:d') == (aa, ab, ac, ad)
    assert symbols('aa:d,x:z') == (aa, ab, ac, ad, x, y, z)
    assert symbols(('aa:d','x:z')) == ((aa, ab, ac, ad), (x, y, z))

    assert type(symbols(('q:2', 'u:2'), cls=Function)[0][0]) == UndefinedFunction  # issue 23532

    # issue 6675
    def sym(s):
        return str(symbols(s))
    assert sym('a0:4') == '(a0, a1, a2, a3)'
    assert sym('a2:4,b1:3') == '(a2, a3, b1, b2)'
    assert sym('a1(2:4)') == '(a12, a13)'
    assert sym('a0:2.0:2') == '(a0.0, a0.1, a1.0, a1.1)'
    assert sym('aa:cz') == '(aaz, abz, acz)'
    assert sym('aa:c0:2') == '(aa0, aa1, ab0, ab1, ac0, ac1)'
    assert sym('aa:ba:b') == '(aaa, aab, aba, abb)'
    assert sym('a:3b') == '(a0b, a1b, a2b)'
    assert sym('a-1:3b') == '(a-1b, a-2b)'
    assert sym(r'a:2\,:2' + chr(0)) == '(a0,0%s, a0,1%s, a1,0%s, a1,1%s)' % (
        (chr(0),)*4)
    assert sym('x(:a:3)') == '(x(a0), x(a1), x(a2))'
    assert sym('x(:c):1') == '(xa0, xb0, xc0)'
    assert sym('x((:a)):3') == '(x(a)0, x(a)1, x(a)2)'
    assert sym('x(:a:3') == '(x(a0, x(a1, x(a2)'
    assert sym(':2') == '(0, 1)'
    assert sym(':b') == '(a, b)'
    assert sym(':b:2') == '(a0, a1, b0, b1)'
    assert sym(':2:2') == '(00, 01, 10, 11)'
    assert sym(':b:b') == '(aa, ab, ba, bb)'

    raises(ValueError, lambda: symbols(':'))
    raises(ValueError, lambda: symbols('a:'))
    raises(ValueError, lambda: symbols('::'))
    raises(ValueError, lambda: symbols('a::'))
    raises(ValueError, lambda: symbols(':a:'))
    raises(ValueError, lambda: symbols('::a'))


def test_symbols_become_functions_issue_3539():
    from sympy.abc import alpha, phi, beta, t
    raises(TypeError, lambda: beta(2))
    raises(TypeError, lambda: beta(2.5))
    raises(TypeError, lambda: phi(2.5))
    raises(TypeError, lambda: alpha(2.5))
    raises(TypeError, lambda: phi(t))


def test_unicode():
    xu = Symbol('x')
    x = Symbol('x')
    assert x == xu

    raises(TypeError, lambda: Symbol(1))


def test_uniquely_named_symbol_and_Symbol():
    F = uniquely_named_symbol
    x = Symbol('x')
    assert F(x) == x
    assert F('x') == x
    assert str(F('x', x)) == 'x0'
    assert str(F('x', (x + 1, 1/x))) == 'x0'
    _x = Symbol('x', real=True)
    assert F(('x', _x)) == _x
    assert F((x, _x)) == _x
    assert F('x', real=True).is_real
    y = Symbol('y')
    assert F(('x', y), real=True).is_real
    r = Symbol('x', real=True)
    assert F(('x', r)).is_real
    assert F(('x', r), real=False).is_real
    assert F('x1', Symbol('x1'),
        compare=lambda i: str(i).rstrip('1')).name == 'x0'
    assert F('x1', Symbol('x1'),
        modify=lambda i: i + '_').name == 'x1_'
    assert _symbol(x, _x) == x


def test_disambiguate():
    x, y, y_1, _x, x_1, x_2 = symbols('x y y_1 _x x_1 x_2')
    t1 = Dummy('y'), _x, Dummy('x'), Dummy('x')
    t2 = Dummy('x'), Dummy('x')
    t3 = Dummy('x'), Dummy('y')
    t4 = x, Dummy('x')
    t5 = Symbol('x', integer=True), x, Symbol('x_1')

    assert disambiguate(*t1) == (y, x_2, x, x_1)
    assert disambiguate(*t2) == (x, x_1)
    assert disambiguate(*t3) == (x, y)
    assert disambiguate(*t4) == (x_1, x)
    assert disambiguate(*t5) == (t5[0], x_2, x_1)
    assert disambiguate(*t5)[0] != x  # assumptions are retained

    t6 = _x, Dummy('x')/y
    t7 = y*Dummy('y'), y

    assert disambiguate(*t6) == (x_1, x/y)
    assert disambiguate(*t7) == (y*y_1, y_1)
    assert disambiguate(Dummy('x_1'), Dummy('x_1')
        ) == (x_1, Symbol('x_1_1'))


@skip_under_pyodide("Cannot create threads under pyodide.")
def test_issue_gh_16734():
    # https://github.com/sympy/sympy/issues/16734

    syms = list(symbols('x, y'))

    def thread1():
        for n in range(1000):
            syms[0], syms[1] = symbols(f'x{n}, y{n}')
            syms[0].is_positive # Check an assumption in this thread.
        syms[0] = None

    def thread2():
        while syms[0] is not None:
            # Compare the symbol in this thread.
            result = (syms[0] == syms[1])  # noqa

    # Previously this would be very likely to raise an exception:
    thread = threading.Thread(target=thread1)
    thread.start()
    thread2()
    thread.join()