104 lines
4.1 KiB
Python
104 lines
4.1 KiB
Python
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from sympy.core.numbers import (I, Rational, oo)
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from sympy.core.singleton import S
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from sympy.core.symbol import Symbol
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from sympy.functions.elementary.exponential import (exp, log)
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.calculus.singularities import (
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singularities,
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is_increasing,
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is_strictly_increasing,
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is_decreasing,
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is_strictly_decreasing,
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is_monotonic
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)
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from sympy.sets import Interval, FiniteSet
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from sympy.testing.pytest import raises
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from sympy.abc import x, y
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def test_singularities():
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x = Symbol('x')
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assert singularities(x**2, x) == S.EmptySet
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assert singularities(x/(x**2 + 3*x + 2), x) == FiniteSet(-2, -1)
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assert singularities(1/(x**2 + 1), x) == FiniteSet(I, -I)
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assert singularities(x/(x**3 + 1), x) == \
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FiniteSet(-1, (1 - sqrt(3) * I) / 2, (1 + sqrt(3) * I) / 2)
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assert singularities(1/(y**2 + 2*I*y + 1), y) == \
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FiniteSet(-I + sqrt(2)*I, -I - sqrt(2)*I)
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x = Symbol('x', real=True)
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assert singularities(1/(x**2 + 1), x) == S.EmptySet
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assert singularities(exp(1/x), x, S.Reals) == FiniteSet(0)
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assert singularities(exp(1/x), x, Interval(1, 2)) == S.EmptySet
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assert singularities(log((x - 2)**2), x, Interval(1, 3)) == FiniteSet(2)
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raises(NotImplementedError, lambda: singularities(x**-oo, x))
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def test_is_increasing():
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"""Test whether is_increasing returns correct value."""
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a = Symbol('a', negative=True)
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assert is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
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assert is_increasing(-x**2, Interval(-oo, 0))
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assert not is_increasing(-x**2, Interval(0, oo))
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assert not is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
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assert is_increasing(x**2 + y, Interval(1, oo), x)
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assert is_increasing(-x**2*a, Interval(1, oo), x)
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assert is_increasing(1)
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assert is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) is False
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def test_is_strictly_increasing():
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"""Test whether is_strictly_increasing returns correct value."""
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assert is_strictly_increasing(
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4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
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assert is_strictly_increasing(
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4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
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assert not is_strictly_increasing(
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4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
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assert not is_strictly_increasing(-x**2, Interval(0, oo))
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assert not is_strictly_decreasing(1)
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assert is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) is False
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def test_is_decreasing():
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"""Test whether is_decreasing returns correct value."""
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b = Symbol('b', positive=True)
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assert is_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
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assert is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
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assert is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
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assert not is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
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assert not is_decreasing(-x**2, Interval(-oo, 0))
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assert not is_decreasing(-x**2*b, Interval(-oo, 0), x)
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def test_is_strictly_decreasing():
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"""Test whether is_strictly_decreasing returns correct value."""
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assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
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assert not is_strictly_decreasing(
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1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
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assert not is_strictly_decreasing(-x**2, Interval(-oo, 0))
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assert not is_strictly_decreasing(1)
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assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
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assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
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def test_is_monotonic():
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"""Test whether is_monotonic returns correct value."""
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assert is_monotonic(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
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assert is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
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assert is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
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assert is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
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assert not is_monotonic(-x**2, S.Reals)
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assert is_monotonic(x**2 + y + 1, Interval(1, 2), x)
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raises(NotImplementedError, lambda: is_monotonic(x**2 + y + 1))
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def test_issue_23401():
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x = Symbol('x')
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expr = (x + 1)/(-1.0e-3*x**2 + 0.1*x + 0.1)
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assert is_increasing(expr, Interval(1,2), x)
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