You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
104 lines
4.1 KiB
104 lines
4.1 KiB
from sympy.core.numbers import (I, Rational, oo)
|
|
from sympy.core.singleton import S
|
|
from sympy.core.symbol import Symbol
|
|
from sympy.functions.elementary.exponential import (exp, log)
|
|
from sympy.functions.elementary.miscellaneous import sqrt
|
|
from sympy.calculus.singularities import (
|
|
singularities,
|
|
is_increasing,
|
|
is_strictly_increasing,
|
|
is_decreasing,
|
|
is_strictly_decreasing,
|
|
is_monotonic
|
|
)
|
|
from sympy.sets import Interval, FiniteSet
|
|
from sympy.testing.pytest import raises
|
|
from sympy.abc import x, y
|
|
|
|
|
|
def test_singularities():
|
|
x = Symbol('x')
|
|
assert singularities(x**2, x) == S.EmptySet
|
|
assert singularities(x/(x**2 + 3*x + 2), x) == FiniteSet(-2, -1)
|
|
assert singularities(1/(x**2 + 1), x) == FiniteSet(I, -I)
|
|
assert singularities(x/(x**3 + 1), x) == \
|
|
FiniteSet(-1, (1 - sqrt(3) * I) / 2, (1 + sqrt(3) * I) / 2)
|
|
assert singularities(1/(y**2 + 2*I*y + 1), y) == \
|
|
FiniteSet(-I + sqrt(2)*I, -I - sqrt(2)*I)
|
|
|
|
x = Symbol('x', real=True)
|
|
assert singularities(1/(x**2 + 1), x) == S.EmptySet
|
|
assert singularities(exp(1/x), x, S.Reals) == FiniteSet(0)
|
|
assert singularities(exp(1/x), x, Interval(1, 2)) == S.EmptySet
|
|
assert singularities(log((x - 2)**2), x, Interval(1, 3)) == FiniteSet(2)
|
|
raises(NotImplementedError, lambda: singularities(x**-oo, x))
|
|
|
|
|
|
def test_is_increasing():
|
|
"""Test whether is_increasing returns correct value."""
|
|
a = Symbol('a', negative=True)
|
|
|
|
assert is_increasing(x**3 - 3*x**2 + 4*x, S.Reals)
|
|
assert is_increasing(-x**2, Interval(-oo, 0))
|
|
assert not is_increasing(-x**2, Interval(0, oo))
|
|
assert not is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3))
|
|
assert is_increasing(x**2 + y, Interval(1, oo), x)
|
|
assert is_increasing(-x**2*a, Interval(1, oo), x)
|
|
assert is_increasing(1)
|
|
|
|
assert is_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval(-2, 3)) is False
|
|
|
|
|
|
def test_is_strictly_increasing():
|
|
"""Test whether is_strictly_increasing returns correct value."""
|
|
assert is_strictly_increasing(
|
|
4*x**3 - 6*x**2 - 72*x + 30, Interval.Ropen(-oo, -2))
|
|
assert is_strictly_increasing(
|
|
4*x**3 - 6*x**2 - 72*x + 30, Interval.Lopen(3, oo))
|
|
assert not is_strictly_increasing(
|
|
4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3))
|
|
assert not is_strictly_increasing(-x**2, Interval(0, oo))
|
|
assert not is_strictly_decreasing(1)
|
|
|
|
assert is_strictly_increasing(4*x**3 - 6*x**2 - 72*x + 30, Interval.open(-2, 3)) is False
|
|
|
|
|
|
def test_is_decreasing():
|
|
"""Test whether is_decreasing returns correct value."""
|
|
b = Symbol('b', positive=True)
|
|
|
|
assert is_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
|
|
assert is_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
|
|
assert is_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
|
|
assert not is_decreasing(1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
|
|
assert not is_decreasing(-x**2, Interval(-oo, 0))
|
|
assert not is_decreasing(-x**2*b, Interval(-oo, 0), x)
|
|
|
|
|
|
def test_is_strictly_decreasing():
|
|
"""Test whether is_strictly_decreasing returns correct value."""
|
|
assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.Lopen(3, oo))
|
|
assert not is_strictly_decreasing(
|
|
1/(x**2 - 3*x), Interval.Ropen(-oo, Rational(3, 2)))
|
|
assert not is_strictly_decreasing(-x**2, Interval(-oo, 0))
|
|
assert not is_strictly_decreasing(1)
|
|
assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
|
|
assert is_strictly_decreasing(1/(x**2 - 3*x), Interval.open(1.5, 3))
|
|
|
|
|
|
def test_is_monotonic():
|
|
"""Test whether is_monotonic returns correct value."""
|
|
assert is_monotonic(1/(x**2 - 3*x), Interval.open(Rational(3,2), 3))
|
|
assert is_monotonic(1/(x**2 - 3*x), Interval.open(1.5, 3))
|
|
assert is_monotonic(1/(x**2 - 3*x), Interval.Lopen(3, oo))
|
|
assert is_monotonic(x**3 - 3*x**2 + 4*x, S.Reals)
|
|
assert not is_monotonic(-x**2, S.Reals)
|
|
assert is_monotonic(x**2 + y + 1, Interval(1, 2), x)
|
|
raises(NotImplementedError, lambda: is_monotonic(x**2 + y + 1))
|
|
|
|
|
|
def test_issue_23401():
|
|
x = Symbol('x')
|
|
expr = (x + 1)/(-1.0e-3*x**2 + 0.1*x + 0.1)
|
|
assert is_increasing(expr, Interval(1,2), x)
|