def test_issue_10198():
assert reduce_inequalities(-1 + 1 / abs(1 / x - 1) < 0) == Or(
And(-oo < x, x < 0), And(S(0) < x, x < S(1) / 2))
assert reduce_inequalities(abs(1 / sqrt(x)) - 1, x) == Eq(x, 1)
assert reduce_abs_inequality(-3 + 1/abs(1 - 1/x), '<', x) == \
Or(And(-oo < x, x < 0),
And(S(0) < x, x < S(3)/4), And(S(3)/2 < x, x < oo))
raises(
ValueError,
lambda: reduce_abs_inequality(-3 + 1 / abs(1 - 1 / sqrt(x)), '<', x))
def test_issue_10198():
assert reduce_inequalities(-1 + 1 / abs(1 / x - 1) < 0) == Or(
And(-oo < x, x < 0), And(S.Zero < x, x < S.Half))
assert reduce_inequalities(abs(1 / sqrt(x)) - 1, x) == Eq(x, 1)
assert reduce_abs_inequality(-3 + 1/abs(1 - 1/x), '<', x) == \
Or(And(-oo < x, x < 0),
And(S.Zero < x, x < Rational(3, 4)), And(Rational(3, 2) < x, x < oo))
raises(
ValueError,
lambda: reduce_abs_inequality(-3 + 1 / abs(1 - 1 / sqrt(x)), '<', x))
def test_issue_10198():
assert reduce_inequalities(
-1 + 1/abs(1/x - 1) < 0) == Or(
And(-oo < x, x < 0), And(S(0) < x, x < S(1)/2)
)
assert reduce_inequalities(abs(1/sqrt(x)) - 1, x) == Eq(x, 1)
assert reduce_abs_inequality(-3 + 1/abs(1 - 1/x), '<', x) == \
Or(And(-oo < x, x < 0),
And(S(0) < x, x < S(3)/4), And(S(3)/2 < x, x < oo))
raises(ValueError,lambda: reduce_abs_inequality(-3 + 1/abs(
1 - 1/sqrt(x)), '<', x))
def test_issue_8545():
from sympy import refine
eq = 1 - x - abs(1 - x)
ans = And(Lt(1, x), Lt(x, oo))
assert reduce_abs_inequality(eq, '<', x) == ans
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_inequalities(refine(eq) < 0) == ans
def test_issue_8545():
from sympy import refine
eq = 1 - x - abs(1 - x)
ans = And(Lt(1, x), Lt(x, oo))
assert reduce_abs_inequality(eq, '<', x) == ans
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_inequalities(refine(eq) < 0) == ans
def test_issue_8545():
eq = 1 - x - abs(1 - x)
ans = And(Lt(1, x), Lt(x, oo))
assert reduce_abs_inequality(eq, '<', x) == ans
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_inequalities(eq < 0) == ans
def test_issue_8545():
eq = 1 - x - abs(1 - x)
ans = And(Lt(1, x), Lt(x, oo))
assert reduce_abs_inequality(eq, '<', x) == ans
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_inequalities(eq < 0) == ans
def test_issue_8545():
x = Symbol('x', real=True)
eq = 1 - x - sqrt((1 - x)**2)
assert reduce_abs_inequality(eq, '<', x) == And(Lt(1, x), Lt(x, oo))