Exemple #1
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def find_curve_range_intersection(curve_1, curve_2, cut_at_inflection=False):
    """
    Return intersections of x- and y-ranges of two real curves,
    which are parametric curves on the xy-plane given as 
    (x_array, y_array), a tuple of NumPy arrays.
    """
    x1, y1 = curve_1
    x2, y2 = curve_2

    if cut_at_inflection is True:
        x1_min, x1_max = sorted([x1[0], x1[-1]])
        x2_min, x2_max = sorted([x2[0], x2[-1]])

        y1_min, y1_may = sorted([y1[0], y1[-1]])
        y2_min, y2_may = sorted([y2[0], y2[-1]])
    else:
        x1_min, x1_max = numpy.sort(x1)[[0, -1]]
        x2_min, x2_max = numpy.sort(x2)[[0, -1]]

        y1_min, y1_may = numpy.sort(y1)[[0, -1]]
        y2_min, y2_may = numpy.sort(y2)[[0, -1]]

    x1_interval = Interval(x1_min, x1_max)
    x2_interval = Interval(x2_min, x2_max)

    y1_interval = Interval(y1_min, y1_may)
    y2_interval = Interval(y2_min, y2_may)

    x_range = x1_interval.intersect(x2_interval)
    y_range = y1_interval.intersect(y2_interval)

    return (x_range, y_range)
Exemple #2
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def test_complement():
    assert Interval(0, 1).complement == \
           Union(Interval(-oo, 0, True, True), Interval(1, oo, True, True))
    assert Interval(0, 1, True, False).complement == \
           Union(Interval(-oo, 0, True, False), Interval(1, oo, True, True))
    assert Interval(0, 1, False, True).complement == \
           Union(Interval(-oo, 0, True, True), Interval(1, oo, False, True))
    assert Interval(0, 1, True, True).complement == \
           Union(Interval(-oo, 0, True, False), Interval(1, oo, False, True))

    assert -S.EmptySet == S.EmptySet.complement
    assert ~S.EmptySet == S.EmptySet.complement

    assert S.EmptySet.complement == Interval(-oo, oo)

    assert Union(Interval(0, 1), Interval(2, 3)).complement == \
           Union(Interval(-oo, 0, True, True), Interval(1, 2, True, True),
                 Interval(3, oo, True, True))

    assert FiniteSet(0).complement == Union(Interval(-oo,0, True,True) ,
            Interval(0,oo, True, True))

    assert (FiniteSet(5) + Interval(S.NegativeInfinity, 0)).complement == \
            Interval(0, 5, True, True) + Interval(5, S.Infinity, True,True)

    assert FiniteSet(1,2,3).complement == Interval(S.NegativeInfinity,1, True,True) + Interval(1,2, True,True) + Interval(2,3, True,True) + Interval(3,S.Infinity, True,True)

    X = Interval(1,3)+FiniteSet(5)
    assert X.intersect(X.complement) == S.EmptySet
Exemple #3
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def test_union():
    assert Union(Interval(1, 2), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2), Interval(2, 3, True)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(2, 4)) == Interval(1, 4)
    assert Union(Interval(1, 2), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(1, 2)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(1, 2)) == \
        Interval(1, 3, False, True)
    assert Union(Interval(1, 3), Interval(1, 2, False, True)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3, True)) == \
        Interval(1, 3, True)
    assert Union(Interval(1, 2, True), Interval(1, 3, True, True)) == \
        Interval(1, 3, True, True)
    assert Union(Interval(1, 2, True, True), Interval(1, 3, True)) == \
        Interval(1, 3, True)
    assert Union(Interval(1, 3), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(2, 3)) == \
        Interval(1, 3)
    assert Union(Interval(1, 2, False, True), Interval(2, 3, True)) != \
        Interval(1, 3)
    assert Union(Interval(1, 2), S.EmptySet) == Interval(1, 2)
    assert Union(S.EmptySet) == S.EmptySet

    assert Union(Interval(0, 1), [FiniteSet(1.0/n) for n in range(1, 10)]) == \
        Interval(0, 1)

    assert Interval(1, 2).union(Interval(2, 3)) == \
        Interval(1, 2) + Interval(2, 3)

    assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)

    assert Union(Set()) == Set()

    assert FiniteSet(1) + FiniteSet(2) + FiniteSet(3) == FiniteSet(1, 2, 3)
    assert FiniteSet('ham') + FiniteSet('eggs') == FiniteSet('ham', 'eggs')
    assert FiniteSet(1, 2, 3) + S.EmptySet == FiniteSet(1, 2, 3)

    assert FiniteSet(1, 2, 3) & FiniteSet(2, 3, 4) == FiniteSet(2, 3)
    assert FiniteSet(1, 2, 3) | FiniteSet(2, 3, 4) == FiniteSet(1, 2, 3, 4)

    x = Symbol("x")
    y = Symbol("y")
    z = Symbol("z")
    assert S.EmptySet | FiniteSet(x, FiniteSet(y, z)) == \
        FiniteSet(x, FiniteSet(y, z))

    # Test that Intervals and FiniteSets play nicely
    assert Interval(1, 3) + FiniteSet(2) == Interval(1, 3)
    assert Interval(1, 3, True, True) + FiniteSet(3) == \
        Interval(1, 3, True, False)
    X = Interval(1, 3) + FiniteSet(5)
    Y = Interval(1, 2) + FiniteSet(3)
    XandY = X.intersect(Y)
    assert 2 in X and 3 in X and 3 in XandY
    assert XandY.is_subset(X) and XandY.is_subset(Y)

    raises(TypeError, lambda: Union(1, 2, 3))

    assert X.is_iterable is False
Exemple #4
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def test_measure():
    a = Symbol('a', real=True)

    assert Interval(1, 3).measure == 2
    assert Interval(0, a).measure == a
    assert Interval(1, a).measure == a - 1

    assert Union(Interval(1, 2), Interval(3, 4)).measure == 2
    assert Union(Interval(1, 2), Interval(3, 4), FiniteSet(5, 6, 7)).measure \
        == 2

    assert FiniteSet(1, 2, oo, a, -oo, -5).measure == 0

    assert S.EmptySet.measure == 0

    square = Interval(0, 10) * Interval(0, 10)
    offsetsquare = Interval(5, 15) * Interval(5, 15)
    band = Interval(-oo, oo) * Interval(2, 4)

    assert square.measure == offsetsquare.measure == 100
    assert (square + offsetsquare).measure == 175  # there is some overlap
    assert (square - offsetsquare).measure == 75
    assert (square * FiniteSet(1, 2, 3)).measure == 0
    assert (square.intersect(band)).measure == 20
    assert (square + band).measure == oo
    assert (band * FiniteSet(1, 2, 3)).measure == nan
Exemple #5
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def test_interval_symbolic():
    x = Symbol('x')
    e = Interval(0, 1)
    assert e.contains(x) == And(0 <= x, x <= 1)
    raises(TypeError, lambda: x in e)
    e = Interval(0, 1, True, True)
    assert e.contains(x) == And(0 < x, x < 1)
Exemple #6
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def test_issue_10285():
    assert FiniteSet(-x - 1).intersect(Interval.Ropen(1, 2)) == FiniteSet(x).intersect(Interval.Lopen(-3, -2))
    eq = -x - 2 * (-x - y)
    s = signsimp(eq)
    ivl = Interval.open(0, 1)
    assert FiniteSet(eq).intersect(ivl) == FiniteSet(s).intersect(ivl)
    assert FiniteSet(-eq).intersect(ivl) == FiniteSet(s).intersect(Interval.open(-1, 0))
    eq -= 1
    ivl = Interval.Lopen(1, oo)
    assert FiniteSet(eq).intersect(ivl) == FiniteSet(s).intersect(Interval.Lopen(2, oo))
def test_reduce_rational_inequalities_real_relational():
    assert reduce_rational_inequalities([], x) == False
    assert reduce_rational_inequalities(
        [[(x**2 + 3*x + 2)/(x**2 - 16) >= 0]], x, relational=False) == \
        Union(Interval.open(-oo, -4), Interval(-2, -1), Interval.open(4, oo))

    assert reduce_rational_inequalities(
        [[((-2*x - 10)*(3 - x))/((x**2 + 5)*(x - 2)**2) < 0]], x,
        relational=False) == \
        Union(Interval.open(-5, 2), Interval.open(2, 3))

    assert reduce_rational_inequalities([[(x + 1)/(x - 5) <= 0]], x,
        relational=False) == \
        Interval.Ropen(-1, 5)

    assert reduce_rational_inequalities([[(x**2 + 4*x + 3)/(x - 1) > 0]], x,
        relational=False) == \
        Union(Interval.open(-3, -1), Interval.open(1, oo))

    assert reduce_rational_inequalities([[(x**2 - 16)/(x - 1)**2 < 0]], x,
        relational=False) == \
        Union(Interval.open(-4, 1), Interval.open(1, 4))

    assert reduce_rational_inequalities([[(3*x + 1)/(x + 4) >= 1]], x,
        relational=False) == \
        Union(Interval.open(-oo, -4), Interval.Ropen(S(3)/2, oo))

    assert reduce_rational_inequalities([[(x - 8)/x <= 3 - x]], x,
        relational=False) == \
        Union(Interval.Lopen(-oo, -2), Interval.Lopen(0, 4))

    # issue sympy/sympy#10237
    assert reduce_rational_inequalities(
        [[x < oo, x >= 0, -oo < x]], x, relational=False) == Interval(0, oo)
Exemple #8
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def test_union():
    assert Union(Interval(1, 2), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2), Interval(2, 3, True)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(2, 4)) == Interval(1, 4)
    assert Union(Interval(1, 2), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(1, 2)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(1, 2)) == \
           Interval(1, 3, False, True)
    assert Union(Interval(1, 3), Interval(1, 2, False, True)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3, True)) == Interval(1, 3, True)
    assert Union(Interval(1, 2, True), Interval(1, 3, True, True)) == \
           Interval(1, 3, True, True)
    assert Union(Interval(1, 2, True, True), Interval(1, 3, True)) == \
           Interval(1, 3, True)
    assert Union(Interval(1, 3), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(2, 3)) == \
           Interval(1, 3)
    assert Union(Interval(1, 2, False, True), Interval(2, 3, True)) != \
           Interval(1, 3)
    assert Union(Interval(1, 2), S.EmptySet) == Interval(1, 2)
    assert Union(S.EmptySet) == S.EmptySet

    assert Union(Interval(0,1), [FiniteSet(1.0/n) for n in range(1,10)]) == \
            Interval(0,1)

    assert Interval(1, 2).union(Interval(2, 3)) == \
           Interval(1, 2) + Interval(2, 3)

    assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)

    assert Union(Set()) == Set()

    assert FiniteSet(1) + FiniteSet(2) + FiniteSet(3) == FiniteSet(1,2,3)
    assert FiniteSet(['ham']) + FiniteSet(['eggs']) == FiniteSet('ham', 'eggs')
    assert FiniteSet(1,2,3) + S.EmptySet == FiniteSet(1,2,3)

    assert FiniteSet(1,2,3) & FiniteSet(2,3,4) == FiniteSet(2,3)
    assert FiniteSet(1,2,3) | FiniteSet(2,3,4) == FiniteSet(1,2,3,4)


    # Test that Intervals and FiniteSets play nicely
    assert Interval(1,3) + FiniteSet(2) == Interval(1,3)
    assert Interval(1,3, True,True) + FiniteSet(3) == Interval(1,3, True,False)
    X = Interval(1,3)+FiniteSet(5)
    Y = Interval(1,2)+FiniteSet(3)
    XandY = X.intersect(Y)
    assert 2 in X and 3 in X and 3 in XandY
    assert X.subset(XandY) and Y.subset(XandY)


    raises(TypeError, "Union(1, 2, 3)")
class WordInterval(object):
    SILENCE_WORD = '#'

    def __init__(self, inf, sup, word):
        self.word = word
        self.interval = Interval(inf, sup)

    @property
    def is_silent(self):
        return self.word == WordInterval.SILENCE_WORD

    @property
    def inf(self):
        return self.interval.inf

    @property
    def sup(self):
        return self.interval.sup

    def intersect(self, another_interval):
        return self.interval.intersect(another_interval)


    def __eq__(self, other):
        return (self.interval == other.interval) and (self.word == other.word)

    def __str__(self):
        return "%s -> %s" % (self.interval, self.word)

    def __repr__(self):
        return self.__str__()
Exemple #10
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def test_complement():
    assert Interval(0, 1).complement(S.Reals) == \
        Union(Interval(-oo, 0, True, True), Interval(1, oo, True, True))
    assert Interval(0, 1, True, False).complement(S.Reals) == \
        Union(Interval(-oo, 0, True, False), Interval(1, oo, True, True))
    assert Interval(0, 1, False, True).complement(S.Reals) == \
        Union(Interval(-oo, 0, True, True), Interval(1, oo, False, True))
    assert Interval(0, 1, True, True).complement(S.Reals) == \
        Union(Interval(-oo, 0, True, False), Interval(1, oo, False, True))

    assert S.UniversalSet.complement(S.EmptySet) == S.EmptySet
    assert S.UniversalSet.complement(S.Reals) == S.EmptySet
    assert S.UniversalSet.complement(S.UniversalSet) == S.EmptySet

    assert S.EmptySet.complement(S.Reals) == S.Reals

    assert Union(Interval(0, 1), Interval(2, 3)).complement(S.Reals) == \
        Union(Interval(-oo, 0, True, True), Interval(1, 2, True, True),
              Interval(3, oo, True, True))

    assert FiniteSet(0).complement(S.Reals) ==  \
        Union(Interval(-oo, 0, True, True), Interval(0, oo, True, True))

    assert (FiniteSet(5) + Interval(S.NegativeInfinity,
                                    0)).complement(S.Reals) == \
        Interval(0, 5, True, True) + Interval(5, S.Infinity, True, True)

    assert FiniteSet(1, 2, 3).complement(S.Reals) == \
        Interval(S.NegativeInfinity, 1, True, True) + \
        Interval(1, 2, True, True) + Interval(2, 3, True, True) +\
        Interval(3, S.Infinity, True, True)

    assert FiniteSet(x).complement(S.Reals) == Complement(S.Reals, FiniteSet(x))

    assert FiniteSet(0, x).complement(S.Reals) == Complement(Interval(-oo, 0, True, True) +
                                                             Interval(0, oo, True, True)
                                                             ,FiniteSet(x), evaluate=False)

    square = Interval(0, 1) * Interval(0, 1)
    notsquare = square.complement(S.Reals*S.Reals)

    assert all(pt in square for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
    assert not any(
        pt in notsquare for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
    assert not any(pt in square for pt in [(-1, 0), (1.5, .5), (10, 10)])
    assert all(pt in notsquare for pt in [(-1, 0), (1.5, .5), (10, 10)])
Exemple #11
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def test_solve_abs():
    assert solveset_real(Abs(x) - 2, x) == FiniteSet(-2, 2)
    assert solveset_real(Abs(x + 3) - 2 * Abs(x - 3), x) == FiniteSet(1, 9)
    assert solveset_real(2 * Abs(x) - Abs(x - 1), x) == FiniteSet(-1, Rational(1, 3))

    assert solveset_real(Abs(x - 7) - 8, x) == FiniteSet(-S(1), S(15))

    # issue 9565. Note: solveset_real does not solve this as it is
    # solveset's job to handle Relationals
    assert solveset(Abs((x - 1) / (x - 5)) <= S(1) / 3, domain=S.Reals) == Interval(-1, 2)

    # issue #10069
    eq = abs(1 / (x - 1)) - 1 > 0
    u = Union(Interval.open(0, 1), Interval.open(1, 2))
    assert solveset_real(eq, x) == u
    assert solveset(eq, x, domain=S.Reals) == u

    raises(ValueError, lambda: solveset(abs(x) - 1, x))
Exemple #12
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 def __init__(self):
     self.set_str = ""
     self.interval = FiniteSet()
     self.val1 = None
     self.val2 = None
     self.left_border = True
     self.right_border = True
     self.interval_rep = 0
     self.val_lst = []
Exemple #13
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def test_solve_abs():
    assert solveset_real(Abs(x) - 2, x) == FiniteSet(-2, 2)
    assert solveset_real(Abs(x + 3) - 2*Abs(x - 3), x) == \
        FiniteSet(1, 9)
    assert solveset_real(2*Abs(x) - Abs(x - 1), x) == \
        FiniteSet(-1, Rational(1, 3))

    assert solveset_real(Abs(x - 7) - 8, x) == FiniteSet(-S(1), S(15))

    # issue 9565. Note: solveset_real does not solve this as it is
    # solveset's job to handle Relationals
    assert solveset(Abs((x - 1)/(x - 5)) <= S(1)/3, domain=S.Reals
        ) == Interval(-1, 2)

    # issue #10069
    assert solveset_real(abs(1/(x - 1)) - 1 > 0, x) == \
        ConditionSet(x, Eq((1 - Abs(x - 1))/Abs(x - 1) > 0, 0),
            S.Reals)
    assert solveset(abs(1/(x - 1)) - 1 > 0, x, domain=S.Reals
        ) == Union(Interval.open(0, 1), Interval.open(1, 2))
Exemple #14
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def test_complement():
    assert Interval(0, 1).complement == \
        Union(Interval(-oo, 0, True, True), Interval(1, oo, True, True))
    assert Interval(0, 1, True, False).complement == \
        Union(Interval(-oo, 0, True, False), Interval(1, oo, True, True))
    assert Interval(0, 1, False, True).complement == \
        Union(Interval(-oo, 0, True, True), Interval(1, oo, False, True))
    assert Interval(0, 1, True, True).complement == \
        Union(Interval(-oo, 0, True, False), Interval(1, oo, False, True))

    assert -S.EmptySet == S.EmptySet.complement
    assert ~S.EmptySet == S.EmptySet.complement

    assert S.EmptySet.complement == S.UniversalSet
    assert S.UniversalSet.complement == S.EmptySet

    assert Union(Interval(0, 1), Interval(2, 3)).complement == \
        Union(Interval(-oo, 0, True, True), Interval(1, 2, True, True),
              Interval(3, oo, True, True))

    assert FiniteSet(0).complement == Union(Interval(-oo, 0, True, True),
            Interval(0, oo, True, True))

    assert (FiniteSet(5) + Interval(S.NegativeInfinity, 0)).complement == \
        Interval(0, 5, True, True) + Interval(5, S.Infinity, True, True)

    assert FiniteSet(1, 2, 3).complement == \
        Interval(S.NegativeInfinity, 1, True, True) + Interval(1, 2, True, True) + \
        Interval(2, 3, True, True) + Interval(3, S.Infinity, True, True)

    X = Interval(1, 3) + FiniteSet(5)
    assert X.intersect(X.complement) == S.EmptySet

    square = Interval(0, 1) * Interval(0, 1)
    notsquare = square.complement

    assert all(pt in square for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
    assert not any(
        pt in notsquare for pt in [(0, 0), (.5, .5), (1, 0), (1, 1)])
    assert not any(pt in square for pt in [(-1, 0), (1.5, .5), (10, 10)])
    assert all(pt in notsquare for pt in [(-1, 0), (1.5, .5), (10, 10)])
Exemple #15
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def test_boundary_Union():
    assert (Interval(0, 1) + Interval(2, 3)).boundary == FiniteSet(0, 1, 2, 3)
    assert ((Interval(0, 1, False, True) +
             Interval(1, 2, True, False)).boundary == FiniteSet(0, 1, 2))

    assert (Interval(0, 1) + FiniteSet(2)).boundary == FiniteSet(0, 1, 2)
    assert Union(Interval(0, 10), Interval(5, 15), evaluate=False).boundary \
            == FiniteSet(0, 15)

    assert Union(Interval(0, 10), Interval(0, 1), evaluate=False).boundary \
            == FiniteSet(0, 10)
    assert Union(Interval(0, 10, True, True),
                 Interval(10, 15, True, True), evaluate=False).boundary \
            == FiniteSet(0, 10, 15)
Exemple #16
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def test_boundary_ProductSet_line():
    line_in_r2 = Interval(0, 1) * FiniteSet(0)
    assert line_in_r2.boundary == line_in_r2
Exemple #17
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def test_union_boundary_of_joining_sets():
    """ Testing the boundary of unions is a hard problem """
    assert Union(Interval(0, 10), Interval(10, 15), evaluate=False).boundary \
            == FiniteSet(0, 15)
Exemple #18
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def test_Union_of_ProductSets_shares():
    line = Interval(0, 2)
    points = FiniteSet(0, 1, 2)
    assert Union(line * line, line * points) == line * line
Exemple #19
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def test_product_basic():
    H, T = 'H', 'T'
    unit_line = Interval(0, 1)
    d6 = FiniteSet(1, 2, 3, 4, 5, 6)
    d4 = FiniteSet(1, 2, 3, 4)
    coin = FiniteSet(H, T)

    square = unit_line * unit_line

    assert (0, 0) in square
    assert 0 not in square
    assert (H, T) in coin**2
    assert (.5, .5, .5) in square * unit_line
    assert (H, 3, 3) in coin * d6 * d6
    HH, TT = sympify(H), sympify(T)
    assert set(coin**2) == set(((HH, HH), (HH, TT), (TT, HH), (TT, TT)))

    assert (d4 * d4).is_subset(d6 * d6)

    assert square.complement(Interval(-oo, oo) * Interval(-oo, oo)) == Union(
        (Interval(-oo, 0, True, True) + Interval(1, oo, True, True)) *
        Interval(-oo, oo),
        Interval(-oo, oo) *
        (Interval(-oo, 0, True, True) + Interval(1, oo, True, True)))

    assert (Interval(-5, 5)**3).is_subset(Interval(-10, 10)**3)
    assert not (Interval(-10, 10)**3).is_subset(Interval(-5, 5)**3)
    assert not (Interval(-5, 5)**2).is_subset(Interval(-10, 10)**3)

    assert (Interval(.2, .5) * FiniteSet(.5)).is_subset(
        square)  # segment in square

    assert len(coin * coin * coin) == 8
    assert len(S.EmptySet * S.EmptySet) == 0
    assert len(S.EmptySet * coin) == 0
    raises(TypeError, lambda: len(coin * Interval(0, 2)))
Exemple #20
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def test_image_piecewise():
    f = Piecewise((x, x <= -1), (1 / x**2, x <= 5), (x**3, True))
    f1 = Piecewise((0, x <= 1), (1, x <= 2), (2, True))
    assert imageset(x, f, Interval(-5, 5)) == Union(Interval(-5, -1),
                                                    Interval(S(1) / 25, oo))
    assert imageset(x, f1, Interval(1, 2)) == FiniteSet(0, 1)
Exemple #21
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def test_is_closed():
    assert Interval(0, 1, False, False).is_closed
    assert not Interval(0, 1, True, False).is_closed
    assert FiniteSet(1, 2, 3).is_closed
Exemple #22
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def test_solve_poly_inequality():
    assert psolve(Poly(0, x), '==') == [S.Reals]
    assert psolve(Poly(1, x), '==') == [S.EmptySet]
    assert psolve(PurePoly(x + 1, x), ">") == [Interval(-1, oo, True, False)]
Exemple #23
0
    def generate_interval(self, A, OP):
        if OP == '\setminus':
            if len(A.interval) == 1:
                self.interval_rep = 1
                self.val1 = choice([A.val_lst[0], -oo, oo])
                if self.val1 == -oo or self.val1 == oo:
                    self.val2 = A.val_lst[0]
                else:
                    self.val2 = choice([-oo, oo])
            else:
                self.interval_rep = 0
                self.val1 = choice(A.val_lst)
                self.val2 = self.val1
            self.left_border = choice([True, False])
            self.left_border = choice([True, False])
                
        elif OP == '\cap':
            self.interval_rep = 0
            if len(A.val_lst) == 1:
                if randint(0, 1) == 0:
                    self.val1 = randint(-25, A.val_lst[0])
                    self.val2 = A.val_lst[0] + randint(0, 2)
                else:
                    self.val1 = A.val_lst[-1]-randint(0, 2)
                    self.val2 = randint(A.val_lst[-1], 25)
            else:
                if randint(0, 1) == 0:
                    self.val1 = randint(-25, A.val_lst[1])
                    self.val2 = A.val_lst[1] + randint(0, 2)
                else:
                    self.val1 = A.val_lst[-1] - randint(0, 2)
                    self.val2 = randint(A.val_lst[-1], 25)
        else:
            self.interval_rep = 2
            tmp_lst = [-5, -4, -3, -2, -1, 1, 2, 3, 4, 5]
            tmp_lst.extend(A.val_lst)
            for i in range(0, randint(1, 5)):
                self.val_lst.append(choice(tmp_lst))
        
        if self.interval_rep == 0:
            self.interval = Interval(self.val1, self.val2, self.left_border, self.right_border)
            self.set_str += "\{r \ | \ r \in \mathbb{R} \wedge \ "+str(self.val1)
            self.set_str += '<' if self.left_border == True else '\leq'
            self.set_str += ' \ r'
            self.set_str += '<' if self.right_border == True else '\leq'
            self.set_str += str(self.val2)
            self.set_str += '\}'
            if isinstance(self.interval, EmptySet):
                self.interval = FiniteSet(self.val1)
                self.set_str = '\{'+str(self.val1)+'\}'
        elif self.interval_rep == 1:
            self.interval = Interval(self.val1, self.val2, self.left_border, self.right_border)
            self.set_str +=  "\{r \ | \ r \in \mathbb{R} \wedge \ r"
            if self.val1 == -oo or self.val1 == oo:
                if self.val1 == -oo:
                    self.set_str += '<' if self.left_border == True else '\leq'
                else: 
                    self.set_str += '>' if self.left_border == True else '\geq'
                #if self.val1 == oo:
                #    self.set_str += '<' if self.left_border == True else '\leq'
                #else: 
                #    self.set_str += '>' if self.left_border == True else '\geq'
                self.set_str += str(self.val2)+'\}'
            else:
                if self.val2 == -oo:
                    self.set_str += '<' if self.left_border == True else '\leq'
                else: 
                    self.set_str += '>' if self.left_border == True else '\geq'
                #if self.val2 == oo:
                #    self.set_str += '<' if self.left_border == True else '\leq'
                #else:
                #    self.set_str += '>' if self.left_border == True else '\geq'
                self.set_str += str(self.val1)+'\}'

        else:
            for i in range(len(self.val_lst)):
                self.interval = self.interval.union(FiniteSet(self.val_lst[i]))
            self.set_str = '\{'+str(self.interval)+'\}'
Exemple #24
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def test_factor_terms():
    A = Symbol('A', commutative=False)
    assert factor_terms(9*(x + x*y + 1) + (3*x + 3)**(2 + 2*x)) == \
        9*x*y + 9*x + _keep_coeff(S(3), x + 1)**_keep_coeff(S(2), x + 1) + 9
    assert factor_terms(9*(x + x*y + 1) + (3)**(2 + 2*x)) == \
        _keep_coeff(S(9), 3**(2*x) + x*y + x + 1)
    assert factor_terms(3**(2 + 2*x) + a*3**(2 + 2*x)) == \
        9*3**(2*x)*(a + 1)
    assert factor_terms(x + x*A) == \
        x*(1 + A)
    assert factor_terms(sin(x + x*A)) == \
        sin(x*(1 + A))
    assert factor_terms((3*x + 3)**((2 + 2*x)/3)) == \
        _keep_coeff(S(3), x + 1)**_keep_coeff(S(2)/3, x + 1)
    assert factor_terms(x + (x*y + x)**(3*x + 3)) == \
        x + (x*(y + 1))**_keep_coeff(S(3), x + 1)
    assert factor_terms(a*(x + x*y) + b*(x*2 + y*x*2)) == \
        x*(a + 2*b)*(y + 1)
    i = Integral(x, (x, 0, oo))
    assert factor_terms(i) == i

    assert factor_terms(x / 2 + y) == x / 2 + y
    # fraction doesn't apply to integer denominators
    assert factor_terms(x / 2 + y, fraction=True) == x / 2 + y
    # clear *does* apply to the integer denominators
    assert factor_terms(x / 2 + y, clear=True) == Mul(S.Half,
                                                      x + 2 * y,
                                                      evaluate=False)

    # check radical extraction
    eq = sqrt(2) + sqrt(10)
    assert factor_terms(eq) == eq
    assert factor_terms(eq, radical=True) == sqrt(2) * (1 + sqrt(5))
    eq = root(-6, 3) + root(6, 3)
    assert factor_terms(eq,
                        radical=True) == 6**(S(1) / 3) * (1 + (-1)**(S(1) / 3))

    eq = [x + x * y]
    ans = [x * (y + 1)]
    for c in [list, tuple, set]:
        assert factor_terms(c(eq)) == c(ans)
    assert factor_terms(Tuple(x + x * y)) == Tuple(x * (y + 1))
    assert factor_terms(Interval(0, 1)) == Interval(0, 1)
    e = 1 / sqrt(a / 2 + 1)
    assert factor_terms(e, clear=False) == 1 / sqrt(a / 2 + 1)
    assert factor_terms(e, clear=True) == sqrt(2) / sqrt(a + 2)

    eq = x / (x + 1 / x) + 1 / (x**2 + 1)
    assert factor_terms(eq, fraction=False) == eq
    assert factor_terms(eq, fraction=True) == 1

    assert factor_terms((1/(x**3 + x**2) + 2/x**2)*y) == \
        y*(2 + 1/(x + 1))/x**2

    # if not True, then processesing for this in factor_terms is not necessary
    assert gcd_terms(-x - y) == -x - y
    assert factor_terms(-x - y) == Mul(-1, x + y, evaluate=False)

    # if not True, then "special" processesing in factor_terms is not necessary
    assert gcd_terms(exp(Mul(-1, x + 1))) == exp(-x - 1)
    e = exp(-x - 2) + x
    assert factor_terms(e) == exp(Mul(-1, x + 2, evaluate=False)) + x
    assert factor_terms(e, sign=False) == e
    assert factor_terms(exp(-4 * x - 2) -
                        x) == -x + exp(Mul(-2, 2 * x + 1, evaluate=False))

    # sum/integral tests
    for F in (Sum, Integral):
        assert factor_terms(F(x, (y, 1, 10))) == x * F(1, (y, 1, 10))
        assert factor_terms(F(x, (y, 1, 10)) + x) == x * (1 + F(1, (y, 1, 10)))
        assert factor_terms(F(x * y + x * y**2,
                              (y, 1, 10))) == x * F(y * (y + 1), (y, 1, 10))
Exemple #25
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def test_reduce_rational_inequalities_real_relational():
    assert reduce_rational_inequalities([], x) == False
    assert reduce_rational_inequalities(
        [[(x**2 + 3*x + 2)/(x**2 - 16) >= 0]], x, relational=False) == \
        Union(Interval.open(-oo, -4), Interval(-2, -1), Interval.open(4, oo))

    assert reduce_rational_inequalities(
        [[((-2*x - 10)*(3 - x))/((x**2 + 5)*(x - 2)**2) < 0]], x,
        relational=False) == \
        Union(Interval.open(-5, 2), Interval.open(2, 3))

    assert reduce_rational_inequalities([[(x + 1)/(x - 5) <= 0]], x,
        relational=False) == \
        Interval.Ropen(-1, 5)

    assert reduce_rational_inequalities([[(x**2 + 4*x + 3)/(x - 1) > 0]], x,
        relational=False) == \
        Union(Interval.open(-3, -1), Interval.open(1, oo))

    assert reduce_rational_inequalities([[(x**2 - 16)/(x - 1)**2 < 0]], x,
        relational=False) == \
        Union(Interval.open(-4, 1), Interval.open(1, 4))

    assert reduce_rational_inequalities([[(3*x + 1)/(x + 4) >= 1]], x,
        relational=False) == \
        Union(Interval.open(-oo, -4), Interval.Ropen(S(3)/2, oo))

    assert reduce_rational_inequalities([[(x - 8)/x <= 3 - x]], x,
        relational=False) == \
        Union(Interval.Lopen(-oo, -2), Interval.Lopen(0, 4))

    # issue sympy/sympy#10237
    assert reduce_rational_inequalities([[x < oo, x >= 0, -oo < x]],
                                        x,
                                        relational=False) == Interval(0, oo)
Exemple #26
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def test_issue_10326():
    assert Contains(oo, Interval(-oo, oo)) == False
    assert Contains(-oo, Interval(-oo, oo)) == False
Exemple #27
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def test_interior():
    assert Interval(0, 1, False, True).interior == Interval(0, 1, True, True)
Exemple #28
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def test_closure():
    assert Interval(0, 1, False, True).closure == Interval(0, 1, False, False)
Exemple #29
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 def create_ui_set(self, X):
     result = None
     nums = []
     allowed = "-0123456789{},()[]o"
     if not all(c in allowed for c in X):
         return False
     if len(X) < 3 and X != '{}':
         return False
     if (X[0] == '(' or X[0] == '[') and  (X[-1] == ')' or X[-1] == ']'):
         nums = re.findall("[-\d]+", X)
         if '-' in nums:
             nums.remove('-')
         if len(nums) == 1:
             if '-oo' in X or 'oo' in X:
                 if '-oo' in X:
                     nums.append(nums[0])
                     nums[0] = -oo
                 elif 'oo' in X:
                     nums.append(oo)
                 else:
                     return False
         if len(nums) != 2:
             return False
         commata = re.findall(",", X)
         if len(commata) != 1:
             return False
         for i in range(len(X)):
             if X[i] == ',' and not (((X[i-1].isdigit() or X[i+1].isdigit()) or (X[i-1] == 'o' or X[i+1] == 'o'))): 
                 return False
         left = True if X[0] == '(' else False
         right = True if X[-1] == ')' else False
         if oo in nums or -oo in nums:
             if oo in nums:
                 result = Interval(int(nums[0]), oo, left, right)
                 return result
             else:
                 result = Interval(-oo, int(nums[1]), left, right)
                 return result
         else:
             if nums[0] <= nums[1]:
                 result = Interval(int(nums[0]), int(nums[1]), left, right)
                 return result
             else:
                 return False
         
     elif X[0] == '{' and X[-1] == '}':
         if len(X) == 2:
             return EmptySet()
         else:
             nums = re.findall("[-\d]+", X)
             if len(re.findall(",", X)) != len(nums)-1:
                 return False
             num_count = 0    
             for i in range(len(nums)):
                 if X[i] == ',' and not X.index(nums[num_count]) < i and X[i+1]  == ',':
                     return False
                 num_count += 1
             result = FiniteSet()
             for i in range(len(nums)):
                 result = result.union(FiniteSet(int(nums[i])))
             return result
     else:
         return False
Exemple #30
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def test_image_interval():
    from sympy.core.numbers import Rational
    x = Symbol('x', real=True)
    a = Symbol('a', real=True)
    assert imageset(x, 2 * x, Interval(-2, 1)) == Interval(-4, 2)
    assert imageset(x, 2*x, Interval(-2, 1, True, False)) == \
        Interval(-4, 2, True, False)
    assert imageset(x, x**2, Interval(-2, 1, True, False)) == \
        Interval(0, 4, False, True)
    assert imageset(x, x**2, Interval(-2, 1)) == Interval(0, 4)
    assert imageset(x, x**2, Interval(-2, 1, True, False)) == \
        Interval(0, 4, False, True)
    assert imageset(x, x**2, Interval(-2, 1, True, True)) == \
        Interval(0, 4, False, True)
    assert imageset(x, (x - 2)**2, Interval(1, 3)) == Interval(0, 1)
    assert imageset(x, 3*x**4 - 26*x**3 + 78*x**2 - 90*x, Interval(0, 4)) == \
        Interval(-35, 0)  # Multiple Maxima
    assert imageset(x, x + 1/x, Interval(-oo, oo)) == Interval(-oo, -2) \
        + Interval(2, oo)  # Single Infinite discontinuity
    assert imageset(x, 1/x + 1/(x-1)**2, Interval(0, 2, True, False)) == \
        Interval(Rational(3, 2), oo, False)  # Multiple Infinite discontinuities

    # Test for Python lambda
    assert imageset(lambda x: 2 * x, Interval(-2, 1)) == Interval(-4, 2)

    assert imageset(Lambda(x, a*x), Interval(0, 1)) == \
            ImageSet(Lambda(x, a*x), Interval(0, 1))

    assert imageset(Lambda(x, sin(cos(x))), Interval(0, 1)) == \
            ImageSet(Lambda(x, sin(cos(x))), Interval(0, 1))
Exemple #31
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def test_image_Intersection():
    x = Symbol('x', real=True)
    y = Symbol('y', real=True)
    assert imageset(x, x**2, Interval(-2, 0).intersect(Interval(x, y))) == \
           Interval(0, 4).intersect(Interval(Min(x**2, y**2), Max(x**2, y**2)))
Exemple #32
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 def __init__(self, inf, sup, word):
     self.word = word
     self.interval = Interval(inf, sup)
Exemple #33
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def test_reduce_poly_inequalities_real_interval():
    assert reduce_rational_inequalities([[Eq(x**2, 0)]], x,
                                        relational=False) == FiniteSet(0)
    assert reduce_rational_inequalities([[Le(x**2, 0)]], x,
                                        relational=False) == FiniteSet(0)
    assert reduce_rational_inequalities([[Lt(x**2, 0)]], x,
                                        relational=False) == S.EmptySet
    assert reduce_rational_inequalities(
        [[Ge(x**2, 0)]], x, relational=False) == \
        S.Reals if x.is_real else Interval(-oo, oo)
    assert reduce_rational_inequalities(
        [[Gt(x**2, 0)]], x, relational=False) == \
        FiniteSet(0).complement(S.Reals)
    assert reduce_rational_inequalities(
        [[Ne(x**2, 0)]], x, relational=False) == \
        FiniteSet(0).complement(S.Reals)

    assert reduce_rational_inequalities([[Eq(x**2, 1)]], x,
                                        relational=False) == FiniteSet(-1, 1)
    assert reduce_rational_inequalities([[Le(x**2, 1)]], x,
                                        relational=False) == Interval(-1, 1)
    assert reduce_rational_inequalities([[Lt(x**2, 1)]], x,
                                        relational=False) == Interval(
                                            -1, 1, True, True)
    assert reduce_rational_inequalities(
        [[Ge(x**2, 1)]], x, relational=False) == \
        Union(Interval(-oo, -1), Interval(1, oo))
    assert reduce_rational_inequalities(
        [[Gt(x**2, 1)]], x, relational=False) == \
        Interval(-1, 1).complement(S.Reals)
    assert reduce_rational_inequalities(
        [[Ne(x**2, 1)]], x, relational=False) == \
        FiniteSet(-1, 1).complement(S.Reals)
    assert reduce_rational_inequalities([[Eq(x**2, 1.0)]], x,
                                        relational=False) == FiniteSet(
                                            -1.0, 1.0).evalf()
    assert reduce_rational_inequalities([[Le(x**2, 1.0)]], x,
                                        relational=False) == Interval(
                                            -1.0, 1.0)
    assert reduce_rational_inequalities([[Lt(x**2, 1.0)]], x,
                                        relational=False) == Interval(
                                            -1.0, 1.0, True, True)
    assert reduce_rational_inequalities(
        [[Ge(x**2, 1.0)]], x, relational=False) == \
        Union(Interval(-inf, -1.0), Interval(1.0, inf))
    assert reduce_rational_inequalities(
        [[Gt(x**2, 1.0)]], x, relational=False) == \
        Union(Interval(-inf, -1.0, right_open=True),
        Interval(1.0, inf, left_open=True))
    assert reduce_rational_inequalities([[Ne(
        x**2, 1.0)]], x, relational=False) == \
        FiniteSet(-1.0, 1.0).complement(S.Reals)

    s = sqrt(2)

    assert reduce_rational_inequalities(
        [[Lt(x**2 - 1, 0), Gt(x**2 - 1, 0)]], x,
        relational=False) == S.EmptySet
    assert reduce_rational_inequalities(
        [[Le(x**2 - 1, 0), Ge(x**2 - 1, 0)]], x,
        relational=False) == FiniteSet(-1, 1)
    assert reduce_rational_inequalities(
        [[Le(x**2 - 2, 0), Ge(x**2 - 1, 0)]], x,
        relational=False) == Union(Interval(-s, -1, False, False),
                                   Interval(1, s, False, False))
    assert reduce_rational_inequalities(
        [[Le(x**2 - 2, 0), Gt(x**2 - 1, 0)]], x,
        relational=False) == Union(Interval(-s, -1, False, True),
                                   Interval(1, s, True, False))
    assert reduce_rational_inequalities(
        [[Lt(x**2 - 2, 0), Ge(x**2 - 1, 0)]], x,
        relational=False) == Union(Interval(-s, -1, True, False),
                                   Interval(1, s, False, True))
    assert reduce_rational_inequalities(
        [[Lt(x**2 - 2, 0), Gt(x**2 - 1, 0)]], x,
        relational=False) == Union(Interval(-s, -1, True, True),
                                   Interval(1, s, True, True))
    assert reduce_rational_inequalities(
        [[Lt(x**2 - 2, 0), Ne(x**2 - 1, 0)]], x,
        relational=False) == Union(Interval(-s, -1, True, True),
                                   Interval(-1, 1, True, True),
                                   Interval(1, s, True, True))
Exemple #34
0
def test_is_open():
    assert not Interval(0, 1, False, False).is_open
    assert not Interval(0, 1, True, False).is_open
    assert Interval(0, 1, True, True).is_open
    assert not FiniteSet(1, 2, 3).is_open
Exemple #35
0
#!/usr/bin/env python

from sympy import Interval
from sympy.abc import a, b, x
from sympy import factor

e = Interval.map(Interval(10, 12), Interval(-1, 1), x)
print(e.subs(x, 10))
print(e.subs(x, 11))
print(e.subs(x, 12))

e = Interval.map(Interval(a, b), Interval(-1, 1), x)
print(factor(e))
Exemple #36
0
 def set(self):
     if self.is_symbolic:
         return Intersection(S.Naturals0, Interval(0, self.n))
     return set(self.dict.keys())
Exemple #37
0
def test_Interval_free_symbols():
    # issue 6211
    assert Interval(0, 1).free_symbols == set()
    x = Symbol('x', real=True)
    assert Interval(0, x).free_symbols == set([x])
Exemple #38
0
def test_image_Union():
    x = Symbol('x', real=True)
    assert imageset(x, x**2, Interval(-2, 0) + FiniteSet(1, 2, 3)) == \
            (Interval(0, 4) + FiniteSet(9))
Exemple #39
0
f = FiniteSet(s, hello)

print f

for a in f:
    print a, isinstance(a,String)
    
    
print hello + world
print hello + ' ' + Rational(3,4) 

t = Tuple(hello, f)
print t
print t[0]

Doubles = Interval(-1e300,1e300)
print Doubles
v = S(1e300)
print type(v),v,Doubles.contains(v)

print type(Doubles * Doubles)


x = Symbol('x', real = True, bounded = True)

print ( Interval(x+2,100) | Interval(x+3,100) ).contains(x+4.0) & (x < 90)
print Interval(x+4.0,100) & Interval(x+3,100)

print x.is_bounded

print Interval(sin(x),100)
Exemple #40
0
def test_Union_as_relational():
    x = Symbol('x')
    assert (Interval(0, 1) + FiniteSet(2)).as_relational(x) == \
        Or(And(Le(0, x), Le(x, 1)), Eq(x, 2))
    assert (Interval(0, 1, True, True) + FiniteSet(1)).as_relational(x) == \
        And(Lt(0, x), Le(x, 1))
Exemple #41
0
#!/usr/bin/python

from sympy.solvers import solveset
from sympy import Symbol, Interval, pprint

x = Symbol('x')

sol = solveset(x**2 - 1, x, Interval(0, 100))
print(sol) 
Exemple #42
0
def test_piecewise_integrate():
    x, y = symbols('x y', real=True, finite=True)

    # XXX Use '<=' here! '>=' is not yet implemented ..
    f = Piecewise(((x - 2)**2, 0 <= x), (1, True))
    assert integrate(f, (x, -2, 2)) == Rational(14, 3)

    g = Piecewise(((x - 5)**5, 4 <= x), (f, True))
    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
    assert integrate(g, (x, -2, 5)) == Rational(43, 6)

    g = Piecewise(((x - 5)**5, 4 <= x), (f, x < 4))
    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
    assert integrate(g, (x, -2, 5)) == Rational(43, 6)

    g = Piecewise(((x - 5)**5, 2 <= x), (f, x < 2))
    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
    assert integrate(g, (x, -2, 5)) == -Rational(701, 6)

    g = Piecewise(((x - 5)**5, 2 <= x), (f, True))
    assert integrate(g, (x, -2, 2)) == Rational(14, 3)
    assert integrate(g, (x, -2, 5)) == -Rational(701, 6)

    g = Piecewise(((x - 5)**5, 2 <= x), (2 * f, True))
    assert integrate(g, (x, -2, 2)) == 2 * Rational(14, 3)
    assert integrate(g, (x, -2, 5)) == -Rational(673, 6)

    g = Piecewise((1, x > 0), (0, Eq(x, 0)), (-1, x < 0))
    assert integrate(g, (x, -1, 1)) == 0

    g = Piecewise((1, x - y < 0), (0, True))
    assert integrate(g, (y, -oo, 0)) == -Min(0, x)
    assert integrate(g, (y, 0, oo)) == oo - Max(0, x)
    assert integrate(g, (y, -oo, oo)) == oo - x

    g = Piecewise((0, x < 0), (x, x <= 1), (1, True))
    assert integrate(g, (x, -5, 1)) == Rational(1, 2)
    assert integrate(g, (x, -5, y)).subs(y, 1) == Rational(1, 2)
    assert integrate(g, (x, y, 1)).subs(y, -5) == Rational(1, 2)
    assert integrate(g, (x, 1, -5)) == -Rational(1, 2)
    assert integrate(g, (x, 1, y)).subs(y, -5) == -Rational(1, 2)
    assert integrate(g, (x, y, -5)).subs(y, 1) == -Rational(1, 2)
    assert integrate(g, (x, -5, y)) == Piecewise(
        (0, y < 0), (y**2 / 2, y <= 1), (y - 0.5, True))
    assert integrate(g, (x, y, 1)) == Piecewise(
        (0.5, y < 0), (0.5 - y**2 / 2, y <= 1), (1 - y, True))

    g = Piecewise((1 - x, Interval(0, 1).contains(x)),
                  (1 + x, Interval(-1, 0).contains(x)), (0, True))
    assert integrate(g, (x, -5, 1)) == 1
    assert integrate(g, (x, -5, y)).subs(y, 1) == 1
    assert integrate(g, (x, y, 1)).subs(y, -5) == 1
    assert integrate(g, (x, 1, -5)) == -1
    assert integrate(g, (x, 1, y)).subs(y, -5) == -1
    assert integrate(g, (x, y, -5)).subs(y, 1) == -1
    assert integrate(g, (x, -5, y)) == Piecewise(
        (-y**2 / 2 + y + 0.5, Interval(0, 1).contains(y)),
        (y**2 / 2 + y + 0.5, Interval(-1, 0).contains(y)), (0, y <= -1),
        (1, True))
    assert integrate(g, (x, y, 1)) == Piecewise(
        (y**2 / 2 - y + 0.5, Interval(0, 1).contains(y)),
        (-y**2 / 2 - y + 0.5, Interval(-1, 0).contains(y)), (1, y <= -1),
        (0, True))

    g = Piecewise((0, Or(x <= -1, x >= 1)), (1 - x, x > 0), (1 + x, True))
    assert integrate(g, (x, -5, 1)) == 1
    assert integrate(g, (x, -5, y)).subs(y, 1) == 1
    assert integrate(g, (x, y, 1)).subs(y, -5) == 1
    assert integrate(g, (x, 1, -5)) == -1
    assert integrate(g, (x, 1, y)).subs(y, -5) == -1
    assert integrate(g, (x, y, -5)).subs(y, 1) == -1
    assert integrate(g, (x, -5, y)) == Piecewise((0, y <= -1), (1, y >= 1),
                                                 (-y**2 / 2 + y + 0.5, y > 0),
                                                 (y**2 / 2 + y + 0.5, True))
    assert integrate(g, (x, y, 1)) == Piecewise((1, y <= -1), (0, y >= 1),
                                                (y**2 / 2 - y + 0.5, y > 0),
                                                (-y**2 / 2 - y + 0.5, True))
Exemple #43
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def test_issue_8715():
    eq = x + 1 / x > -2 + 1 / x
    assert solveset(eq, x, S.Reals) == (Interval.open(-2, oo) - FiniteSet(0))
    assert solveset(eq.subs(x, log(x)), x, S.Reals) == Interval.open(exp(-2), oo) - FiniteSet(1)
Exemple #44
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def test_piecewise_solve2():
    f = Piecewise(((x - 2)**2, x >= 0), (0, True))
    assert solve(f, x) == [2, Interval(0, oo, True, True)]
Exemple #45
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def test_Intersection_as_relational():
    x = Symbol('x')
    assert (Intersection(Interval(0, 1), FiniteSet(2),
                         evaluate=False).as_relational(x) == And(
                             And(Le(0, x), Le(x, 1)), Eq(x, 2)))
Exemple #46
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def test_as_expr_set_pairs():
    assert Piecewise((x, x > 0), (-x, x <= 0)).as_expr_set_pairs() == \
        [(x, Interval(0, oo, True, True)), (-x, Interval(-oo, 0))]

    assert Piecewise(((x - 2)**2, x >= 0), (0, True)).as_expr_set_pairs() == \
        [((x - 2)**2, Interval(0, oo)), (0, Interval(-oo, 0, True, True))]
Exemple #47
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 def set(self):
     if self.is_symbolic:
         return Intersection(S.Naturals0, Interval(0, self.n))
     return set(map(Integer, list(range(0, self.n + 1))))
Exemple #48
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def test_issue_5724_7680():
    assert I not in S.Reals  # issue 7680
    assert Interval(-oo, oo).contains(I) is S.false
Exemple #49
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 def set(self):
     N, m, n = self.N, self.m, self.n
     if self.is_symbolic:
         return Intersection(S.Naturals0, Interval(self.low, self.high))
     return set([i for i in range(max(0, n + m - N), min(n, m) + 1)])
Exemple #50
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def test_union():
    assert Union(Interval(1, 2), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2), Interval(2, 3, True)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(2, 4)) == Interval(1, 4)
    assert Union(Interval(1, 2), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3), Interval(1, 2)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(1, 2)) == \
        Interval(1, 3, False, True)
    assert Union(Interval(1, 3), Interval(1, 2, False, True)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3)) == Interval(1, 3)
    assert Union(Interval(1, 2, True), Interval(1, 3, True)) == \
        Interval(1, 3, True)
    assert Union(Interval(1, 2, True), Interval(1, 3, True, True)) == \
        Interval(1, 3, True, True)
    assert Union(Interval(1, 2, True, True), Interval(1, 3, True)) == \
        Interval(1, 3, True)
    assert Union(Interval(1, 3), Interval(2, 3)) == Interval(1, 3)
    assert Union(Interval(1, 3, False, True), Interval(2, 3)) == \
        Interval(1, 3)
    assert Union(Interval(1, 2, False, True), Interval(2, 3, True)) != \
        Interval(1, 3)
    assert Union(Interval(1, 2), S.EmptySet) == Interval(1, 2)
    assert Union(S.EmptySet) == S.EmptySet

    assert Union(Interval(0, 1), [FiniteSet(1.0/n) for n in range(1, 10)]) == \
        Interval(0, 1)

    assert Interval(1, 2).union(Interval(2, 3)) == \
        Interval(1, 2) + Interval(2, 3)

    assert Interval(1, 2).union(Interval(2, 3)) == Interval(1, 3)

    assert Union(Set()) == Set()

    assert FiniteSet(1) + FiniteSet(2) + FiniteSet(3) == FiniteSet(1, 2, 3)
    assert FiniteSet('ham') + FiniteSet('eggs') == FiniteSet('ham', 'eggs')
    assert FiniteSet(1, 2, 3) + S.EmptySet == FiniteSet(1, 2, 3)

    assert FiniteSet(1, 2, 3) & FiniteSet(2, 3, 4) == FiniteSet(2, 3)
    assert FiniteSet(1, 2, 3) | FiniteSet(2, 3, 4) == FiniteSet(1, 2, 3, 4)

    x = Symbol("x")
    y = Symbol("y")
    z = Symbol("z")
    assert S.EmptySet | FiniteSet(x, FiniteSet(y, z)) == \
        FiniteSet(x, FiniteSet(y, z))

    # Test that Intervals and FiniteSets play nicely
    assert Interval(1, 3) + FiniteSet(2) == Interval(1, 3)
    assert Interval(1, 3, True, True) + FiniteSet(3) == \
        Interval(1, 3, True, False)
    X = Interval(1, 3) + FiniteSet(5)
    Y = Interval(1, 2) + FiniteSet(3)
    XandY = X.intersect(Y)
    assert 2 in X and 3 in X and 3 in XandY
    assert XandY.is_subset(X) and XandY.is_subset(Y)

    raises(TypeError, lambda: Union(1, 2, 3))

    assert X.is_iterable is False

    # issue 7843
    assert Union(S.EmptySet, FiniteSet(-sqrt(-I), sqrt(-I))) == \
        FiniteSet(-sqrt(-I), sqrt(-I))