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image-handler/image-handler10.0/venv/lib/site-packages/sympy/assumptions/tests/test_query.py

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from sympy.abc import t, w, x, y, z, n, k, m, p, i
from sympy.assumptions import (ask, AssumptionsContext, Q, register_handler,
remove_handler)
from sympy.assumptions.assume import assuming, global_assumptions, Predicate
from sympy.assumptions.cnf import CNF, Literal
from sympy.assumptions.facts import (single_fact_lookup,
get_known_facts, generate_known_facts_dict, get_known_facts_keys)
from sympy.assumptions.handlers import AskHandler
from sympy.assumptions.ask_generated import (get_all_known_facts,
get_known_facts_dict)
from sympy.core.add import Add
from sympy.core.numbers import (I, Integer, Rational, oo, zoo, pi)
from sympy.core.singleton import S
from sympy.core.power import Pow
from sympy.core.symbol import Str, symbols, Symbol
from sympy.functions.combinatorial.factorials import factorial
from sympy.functions.elementary.complexes import (Abs, im, re, sign)
from sympy.functions.elementary.exponential import (exp, log)
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.elementary.trigonometric import (
acos, acot, asin, atan, cos, cot, sin, tan)
from sympy.logic.boolalg import Equivalent, Implies, Xor, And, to_cnf
from sympy.matrices import Matrix, SparseMatrix
from sympy.testing.pytest import (XFAIL, slow, raises, warns_deprecated_sympy,
_both_exp_pow)
import math
def test_int_1():
z = 1
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is True
assert ask(Q.rational(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is True
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_int_11():
z = 11
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is True
assert ask(Q.rational(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is True
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is True
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_int_12():
z = 12
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is True
assert ask(Q.rational(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is True
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is True
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_float_1():
z = 1.0
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is None
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is None
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
z = 7.2123
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is None
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is None
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
# test for issue #12168
assert ask(Q.rational(math.pi)) is None
def test_zero_0():
z = Integer(0)
assert ask(Q.nonzero(z)) is False
assert ask(Q.zero(z)) is True
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is True
assert ask(Q.rational(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is False
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is True
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is True
def test_negativeone():
z = Integer(-1)
assert ask(Q.nonzero(z)) is True
assert ask(Q.zero(z)) is False
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is True
assert ask(Q.rational(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is False
assert ask(Q.negative(z)) is True
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is True
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_infinity():
assert ask(Q.commutative(oo)) is True
assert ask(Q.integer(oo)) is False
assert ask(Q.rational(oo)) is False
assert ask(Q.algebraic(oo)) is False
assert ask(Q.real(oo)) is False
assert ask(Q.extended_real(oo)) is True
assert ask(Q.complex(oo)) is False
assert ask(Q.irrational(oo)) is False
assert ask(Q.imaginary(oo)) is False
assert ask(Q.positive(oo)) is False
assert ask(Q.extended_positive(oo)) is True
assert ask(Q.negative(oo)) is False
assert ask(Q.even(oo)) is False
assert ask(Q.odd(oo)) is False
assert ask(Q.finite(oo)) is False
assert ask(Q.infinite(oo)) is True
assert ask(Q.prime(oo)) is False
assert ask(Q.composite(oo)) is False
assert ask(Q.hermitian(oo)) is False
assert ask(Q.antihermitian(oo)) is False
assert ask(Q.positive_infinite(oo)) is True
assert ask(Q.negative_infinite(oo)) is False
def test_neg_infinity():
mm = S.NegativeInfinity
assert ask(Q.commutative(mm)) is True
assert ask(Q.integer(mm)) is False
assert ask(Q.rational(mm)) is False
assert ask(Q.algebraic(mm)) is False
assert ask(Q.real(mm)) is False
assert ask(Q.extended_real(mm)) is True
assert ask(Q.complex(mm)) is False
assert ask(Q.irrational(mm)) is False
assert ask(Q.imaginary(mm)) is False
assert ask(Q.positive(mm)) is False
assert ask(Q.negative(mm)) is False
assert ask(Q.extended_negative(mm)) is True
assert ask(Q.even(mm)) is False
assert ask(Q.odd(mm)) is False
assert ask(Q.finite(mm)) is False
assert ask(Q.infinite(oo)) is True
assert ask(Q.prime(mm)) is False
assert ask(Q.composite(mm)) is False
assert ask(Q.hermitian(mm)) is False
assert ask(Q.antihermitian(mm)) is False
assert ask(Q.positive_infinite(-oo)) is False
assert ask(Q.negative_infinite(-oo)) is True
def test_complex_infinity():
assert ask(Q.commutative(zoo)) is True
assert ask(Q.integer(zoo)) is False
assert ask(Q.rational(zoo)) is False
assert ask(Q.algebraic(zoo)) is False
assert ask(Q.real(zoo)) is False
assert ask(Q.extended_real(zoo)) is False
assert ask(Q.complex(zoo)) is False
assert ask(Q.irrational(zoo)) is False
assert ask(Q.imaginary(zoo)) is False
assert ask(Q.positive(zoo)) is False
assert ask(Q.negative(zoo)) is False
assert ask(Q.zero(zoo)) is False
assert ask(Q.nonzero(zoo)) is False
assert ask(Q.even(zoo)) is False
assert ask(Q.odd(zoo)) is False
assert ask(Q.finite(zoo)) is False
assert ask(Q.infinite(zoo)) is True
assert ask(Q.prime(zoo)) is False
assert ask(Q.composite(zoo)) is False
assert ask(Q.hermitian(zoo)) is False
assert ask(Q.antihermitian(zoo)) is False
assert ask(Q.positive_infinite(zoo)) is False
assert ask(Q.negative_infinite(zoo)) is False
def test_nan():
nan = S.NaN
assert ask(Q.commutative(nan)) is True
assert ask(Q.integer(nan)) is None
assert ask(Q.rational(nan)) is None
assert ask(Q.algebraic(nan)) is None
assert ask(Q.real(nan)) is None
assert ask(Q.extended_real(nan)) is None
assert ask(Q.complex(nan)) is None
assert ask(Q.irrational(nan)) is None
assert ask(Q.imaginary(nan)) is None
assert ask(Q.positive(nan)) is None
assert ask(Q.nonzero(nan)) is None
assert ask(Q.zero(nan)) is None
assert ask(Q.even(nan)) is None
assert ask(Q.odd(nan)) is None
assert ask(Q.finite(nan)) is None
assert ask(Q.infinite(nan)) is None
assert ask(Q.prime(nan)) is None
assert ask(Q.composite(nan)) is None
assert ask(Q.hermitian(nan)) is None
assert ask(Q.antihermitian(nan)) is None
def test_Rational_number():
r = Rational(3, 4)
assert ask(Q.commutative(r)) is True
assert ask(Q.integer(r)) is False
assert ask(Q.rational(r)) is True
assert ask(Q.real(r)) is True
assert ask(Q.complex(r)) is True
assert ask(Q.irrational(r)) is False
assert ask(Q.imaginary(r)) is False
assert ask(Q.positive(r)) is True
assert ask(Q.negative(r)) is False
assert ask(Q.even(r)) is False
assert ask(Q.odd(r)) is False
assert ask(Q.finite(r)) is True
assert ask(Q.prime(r)) is False
assert ask(Q.composite(r)) is False
assert ask(Q.hermitian(r)) is True
assert ask(Q.antihermitian(r)) is False
r = Rational(1, 4)
assert ask(Q.positive(r)) is True
assert ask(Q.negative(r)) is False
r = Rational(5, 4)
assert ask(Q.negative(r)) is False
assert ask(Q.positive(r)) is True
r = Rational(5, 3)
assert ask(Q.positive(r)) is True
assert ask(Q.negative(r)) is False
r = Rational(-3, 4)
assert ask(Q.positive(r)) is False
assert ask(Q.negative(r)) is True
r = Rational(-1, 4)
assert ask(Q.positive(r)) is False
assert ask(Q.negative(r)) is True
r = Rational(-5, 4)
assert ask(Q.negative(r)) is True
assert ask(Q.positive(r)) is False
r = Rational(-5, 3)
assert ask(Q.positive(r)) is False
assert ask(Q.negative(r)) is True
def test_sqrt_2():
z = sqrt(2)
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_pi():
z = S.Pi
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
z = S.Pi + 1
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
z = 2*S.Pi
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
z = S.Pi ** 2
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
z = (1 + S.Pi) ** 2
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_E():
z = S.Exp1
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is False
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_GoldenRatio():
z = S.GoldenRatio
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_TribonacciConstant():
z = S.TribonacciConstant
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is True
assert ask(Q.real(z)) is True
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is True
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is True
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is True
assert ask(Q.antihermitian(z)) is False
def test_I():
z = I
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is True
assert ask(Q.real(z)) is False
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is True
assert ask(Q.positive(z)) is False
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is False
assert ask(Q.antihermitian(z)) is True
z = 1 + I
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is True
assert ask(Q.real(z)) is False
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is False
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is False
assert ask(Q.antihermitian(z)) is False
z = I*(1 + I)
assert ask(Q.commutative(z)) is True
assert ask(Q.integer(z)) is False
assert ask(Q.rational(z)) is False
assert ask(Q.algebraic(z)) is True
assert ask(Q.real(z)) is False
assert ask(Q.complex(z)) is True
assert ask(Q.irrational(z)) is False
assert ask(Q.imaginary(z)) is False
assert ask(Q.positive(z)) is False
assert ask(Q.negative(z)) is False
assert ask(Q.even(z)) is False
assert ask(Q.odd(z)) is False
assert ask(Q.finite(z)) is True
assert ask(Q.prime(z)) is False
assert ask(Q.composite(z)) is False
assert ask(Q.hermitian(z)) is False
assert ask(Q.antihermitian(z)) is False
z = I**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (-I)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (3*I)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is False
z = (1)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (-1)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (1+I)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is False
z = (I)**(I+3)
assert ask(Q.imaginary(z)) is True
assert ask(Q.real(z)) is False
z = (I)**(I+2)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (I)**(2)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
z = (I)**(3)
assert ask(Q.imaginary(z)) is True
assert ask(Q.real(z)) is False
z = (3)**(I)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is False
z = (I)**(0)
assert ask(Q.imaginary(z)) is False
assert ask(Q.real(z)) is True
def test_bounded():
x, y, z = symbols('x,y,z')
assert ask(Q.finite(x)) is None
assert ask(Q.finite(x), Q.finite(x)) is True
assert ask(Q.finite(x), Q.finite(y)) is None
assert ask(Q.finite(x), Q.complex(x)) is True
assert ask(Q.finite(x), Q.extended_real(x)) is None
assert ask(Q.finite(x + 1)) is None
assert ask(Q.finite(x + 1), Q.finite(x)) is True
a = x + y
x, y = a.args
# B + B
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True
assert ask(Q.finite(a), Q.positive(x) & Q.finite(y)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is True
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is True
assert ask(Q.finite(a), Q.positive(x) & Q.finite(y)
& ~Q.positive(y)) is True
assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
& Q.positive(y)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y) & ~Q.positive(x)
& ~Q.positive(y)) is True
# B + U
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is False
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is False
assert ask(Q.finite(a), Q.finite(x)
& Q.positive_infinite(y)) is False
assert ask(Q.finite(a), Q.positive(x)
& Q.positive_infinite(y)) is False
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
& ~Q.positive(y)) is False
assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
& Q.positive_infinite(y)) is False
assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x) & ~Q.finite(y)
& ~Q.positive(y)) is False
# B + ?
assert ask(Q.finite(a), Q.finite(x)) is None
assert ask(Q.finite(a), Q.positive(x)) is None
assert ask(Q.finite(a), Q.finite(x)
& Q.extended_positive(y)) is None
assert ask(Q.finite(a), Q.positive(x)
& Q.extended_positive(y)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.positive(y)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
& Q.extended_positive(y)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.positive(x)
& ~Q.positive(y)) is None
# U + U
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& ~Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.positive_infinite(y)) is False
assert ask(Q.finite(a), Q.positive_infinite(x) & ~Q.finite(y)
& ~Q.extended_positive(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.extended_positive(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& ~Q.extended_positive(x) & ~Q.extended_positive(y)) is False
# U + ?
assert ask(Q.finite(a), ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.extended_positive(x)
& ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.extended_positive(x)
& Q.positive_infinite(y)) is False
assert ask(Q.finite(a), Q.extended_positive(x)
& ~Q.finite(y) & ~Q.extended_positive(y)) is None
assert ask(Q.finite(a), ~Q.extended_positive(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), ~Q.extended_positive(x) & ~Q.finite(y)
& ~Q.extended_positive(y)) is False
# ? + ?
assert ask(Q.finite(a)) is None
assert ask(Q.finite(a), Q.extended_positive(x)) is None
assert ask(Q.finite(a), Q.extended_positive(y)) is None
assert ask(Q.finite(a), Q.extended_positive(x)
& Q.extended_positive(y)) is None
assert ask(Q.finite(a), Q.extended_positive(x)
& ~Q.extended_positive(y)) is None
assert ask(Q.finite(a), ~Q.extended_positive(x)
& Q.extended_positive(y)) is None
assert ask(Q.finite(a), ~Q.extended_positive(x)
& ~Q.extended_positive(y)) is None
x, y, z = symbols('x,y,z')
a = x + y + z
x, y, z = a.args
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.negative(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.finite(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.finite(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y)
& Q.finite(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
& Q.extended_negative(z)) is False
assert ask(Q.finite(a), Q.negative(x)
& Q.negative_infinite(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.negative_infinite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.negative(x) & ~Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
& Q.negative_infinite(z)) is None
assert ask(Q.finite(a), Q.negative(x) &
Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.positive_infinite(y)
& Q.extended_positive(z)) is False
assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.extended_negative(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x)) is None
assert ask(Q.finite(a), Q.negative(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative(x) & Q.extended_positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.finite(z)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
& Q.extended_negative(z)) is False
assert ask(Q.finite(a), Q.finite(x)
& Q.negative_infinite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.negative_infinite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.finite(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.positive_infinite(y)
& Q.extended_positive(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.finite(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.extended_negative(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x)) is None
assert ask(Q.finite(a), Q.finite(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.extended_positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& Q.positive(z)) is True
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
& Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
& Q.extended_negative(z)) is False
assert ask(Q.finite(a), Q.positive(x)
& Q.negative_infinite(y)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.negative_infinite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.positive(x) & ~Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
& Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.positive_infinite(y)
& Q.extended_positive(z)) is False
assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.extended_negative(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x)) is None
assert ask(Q.finite(a), Q.positive(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive(x) & Q.extended_positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y) & Q.negative_infinite(z)) is False
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y) & ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y)& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y) & Q.extended_negative(z)) is False
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.negative_infinite(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& ~Q.finite(y) & ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& ~Q.finite(y) & Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& ~Q.finite(y) & Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& ~Q.finite(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.positive_infinite(y) & Q.positive_infinite(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.positive_infinite(y) & Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.positive_infinite(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.extended_negative(y) & Q.extended_negative(z)) is False
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.extended_negative(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.negative_infinite(x)
& Q.extended_positive(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(z)
& ~Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
& Q.positive_infinite(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), ~Q.finite(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.positive_infinite(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y)
& Q.extended_negative(z)) is None
assert ask(Q.finite(a), ~Q.finite(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_negative(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), ~Q.finite(x)) is None
assert ask(Q.finite(a), ~Q.finite(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.extended_positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.positive_infinite(y) & Q.positive_infinite(z)) is False
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.positive_infinite(y) & Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.positive_infinite(y)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.positive_infinite(y) & Q.extended_positive(z)) is False
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.extended_negative(y) & Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.extended_negative(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.positive_infinite(x)
& Q.extended_positive(y) & Q.extended_positive(z)) is False
assert ask(Q.finite(a), Q.extended_negative(x)
& Q.extended_negative(y) & Q.extended_negative(z)) is None
assert ask(Q.finite(a), Q.extended_negative(x)
& Q.extended_negative(y)) is None
assert ask(Q.finite(a), Q.extended_negative(x)
& Q.extended_negative(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.extended_negative(x)) is None
assert ask(Q.finite(a), Q.extended_negative(x)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.extended_negative(x)
& Q.extended_positive(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(a)) is None
assert ask(Q.finite(a), Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.extended_positive(y)
& Q.extended_positive(z)) is None
assert ask(Q.finite(a), Q.extended_positive(x)
& Q.extended_positive(y) & Q.extended_positive(z)) is None
assert ask(Q.finite(2*x)) is None
assert ask(Q.finite(2*x), Q.finite(x)) is True
x, y, z = symbols('x,y,z')
a = x*y
x, y = a.args
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is True
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is False
assert ask(Q.finite(a), Q.finite(x)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)) is False
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is False
assert ask(Q.finite(a), ~Q.finite(x)) is None
assert ask(Q.finite(a), Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(y)) is None
assert ask(Q.finite(a)) is None
a = x*y*z
x, y, z = a.args
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& Q.finite(z)) is True
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & Q.finite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& Q.finite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.finite(x) & Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(x) & ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(x)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)
& Q.finite(z)) is False
assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& Q.finite(z)) is False
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)
& ~Q.finite(z)) is False
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(x) & Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(x) & ~Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(x)) is None
assert ask(Q.finite(a), Q.finite(y) & Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(y) & ~Q.finite(z)) is None
assert ask(Q.finite(a), Q.finite(y)) is None
assert ask(Q.finite(a), ~Q.finite(y) & Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(y) & ~Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(y)) is None
assert ask(Q.finite(a), Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(z)) is None
assert ask(Q.finite(a), ~Q.finite(z) & Q.extended_nonzero(x)
& Q.extended_nonzero(y) & Q.extended_nonzero(z)) is None
assert ask(Q.finite(a), Q.extended_nonzero(x) & ~Q.finite(y)
& Q.extended_nonzero(y) & ~Q.finite(z)
& Q.extended_nonzero(z)) is False
x, y, z = symbols('x,y,z')
assert ask(Q.finite(x**2)) is None
assert ask(Q.finite(2**x)) is None
assert ask(Q.finite(2**x), Q.finite(x)) is True
assert ask(Q.finite(x**x)) is None
assert ask(Q.finite(S.Half ** x)) is None
assert ask(Q.finite(S.Half ** x), Q.extended_positive(x)) is True
assert ask(Q.finite(S.Half ** x), Q.extended_negative(x)) is None
assert ask(Q.finite(2**x), Q.extended_negative(x)) is True
assert ask(Q.finite(sqrt(x))) is None
assert ask(Q.finite(2**x), ~Q.finite(x)) is False
assert ask(Q.finite(x**2), ~Q.finite(x)) is False
# sign function
assert ask(Q.finite(sign(x))) is True
assert ask(Q.finite(sign(x)), ~Q.finite(x)) is True
# exponential functions
assert ask(Q.finite(log(x))) is None
assert ask(Q.finite(log(x)), Q.finite(x)) is None
assert ask(Q.finite(log(x)), ~Q.zero(x)) is True
assert ask(Q.finite(log(x)), Q.infinite(x)) is False
assert ask(Q.finite(log(x)), Q.zero(x)) is False
assert ask(Q.finite(exp(x))) is None
assert ask(Q.finite(exp(x)), Q.finite(x)) is True
assert ask(Q.finite(exp(2))) is True
# trigonometric functions
assert ask(Q.finite(sin(x))) is True
assert ask(Q.finite(sin(x)), ~Q.finite(x)) is True
assert ask(Q.finite(cos(x))) is True
assert ask(Q.finite(cos(x)), ~Q.finite(x)) is True
assert ask(Q.finite(2*sin(x))) is True
assert ask(Q.finite(sin(x)**2)) is True
assert ask(Q.finite(cos(x)**2)) is True
assert ask(Q.finite(cos(x) + sin(x))) is True
@XFAIL
def test_bounded_xfail():
"""We need to support relations in ask for this to work"""
assert ask(Q.finite(sin(x)**x)) is True
assert ask(Q.finite(cos(x)**x)) is True
def test_commutative():
"""By default objects are Q.commutative that is why it returns True
for both key=True and key=False"""
assert ask(Q.commutative(x)) is True
assert ask(Q.commutative(x), ~Q.commutative(x)) is False
assert ask(Q.commutative(x), Q.complex(x)) is True
assert ask(Q.commutative(x), Q.imaginary(x)) is True
assert ask(Q.commutative(x), Q.real(x)) is True
assert ask(Q.commutative(x), Q.positive(x)) is True
assert ask(Q.commutative(x), ~Q.commutative(y)) is True
assert ask(Q.commutative(2*x)) is True
assert ask(Q.commutative(2*x), ~Q.commutative(x)) is False
assert ask(Q.commutative(x + 1)) is True
assert ask(Q.commutative(x + 1), ~Q.commutative(x)) is False
assert ask(Q.commutative(x**2)) is True
assert ask(Q.commutative(x**2), ~Q.commutative(x)) is False
assert ask(Q.commutative(log(x))) is True
@_both_exp_pow
def test_complex():
assert ask(Q.complex(x)) is None
assert ask(Q.complex(x), Q.complex(x)) is True
assert ask(Q.complex(x), Q.complex(y)) is None
assert ask(Q.complex(x), ~Q.complex(x)) is False
assert ask(Q.complex(x), Q.real(x)) is True
assert ask(Q.complex(x), ~Q.real(x)) is None
assert ask(Q.complex(x), Q.rational(x)) is True
assert ask(Q.complex(x), Q.irrational(x)) is True
assert ask(Q.complex(x), Q.positive(x)) is True
assert ask(Q.complex(x), Q.imaginary(x)) is True
assert ask(Q.complex(x), Q.algebraic(x)) is True
# a+b
assert ask(Q.complex(x + 1), Q.complex(x)) is True
assert ask(Q.complex(x + 1), Q.real(x)) is True
assert ask(Q.complex(x + 1), Q.rational(x)) is True
assert ask(Q.complex(x + 1), Q.irrational(x)) is True
assert ask(Q.complex(x + 1), Q.imaginary(x)) is True
assert ask(Q.complex(x + 1), Q.integer(x)) is True
assert ask(Q.complex(x + 1), Q.even(x)) is True
assert ask(Q.complex(x + 1), Q.odd(x)) is True
assert ask(Q.complex(x + y), Q.complex(x) & Q.complex(y)) is True
assert ask(Q.complex(x + y), Q.real(x) & Q.imaginary(y)) is True
# a*x +b
assert ask(Q.complex(2*x + 1), Q.complex(x)) is True
assert ask(Q.complex(2*x + 1), Q.real(x)) is True
assert ask(Q.complex(2*x + 1), Q.positive(x)) is True
assert ask(Q.complex(2*x + 1), Q.rational(x)) is True
assert ask(Q.complex(2*x + 1), Q.irrational(x)) is True
assert ask(Q.complex(2*x + 1), Q.imaginary(x)) is True
assert ask(Q.complex(2*x + 1), Q.integer(x)) is True
assert ask(Q.complex(2*x + 1), Q.even(x)) is True
assert ask(Q.complex(2*x + 1), Q.odd(x)) is True
# x**2
assert ask(Q.complex(x**2), Q.complex(x)) is True
assert ask(Q.complex(x**2), Q.real(x)) is True
assert ask(Q.complex(x**2), Q.positive(x)) is True
assert ask(Q.complex(x**2), Q.rational(x)) is True
assert ask(Q.complex(x**2), Q.irrational(x)) is True
assert ask(Q.complex(x**2), Q.imaginary(x)) is True
assert ask(Q.complex(x**2), Q.integer(x)) is True
assert ask(Q.complex(x**2), Q.even(x)) is True
assert ask(Q.complex(x**2), Q.odd(x)) is True
# 2**x
assert ask(Q.complex(2**x), Q.complex(x)) is True
assert ask(Q.complex(2**x), Q.real(x)) is True
assert ask(Q.complex(2**x), Q.positive(x)) is True
assert ask(Q.complex(2**x), Q.rational(x)) is True
assert ask(Q.complex(2**x), Q.irrational(x)) is True
assert ask(Q.complex(2**x), Q.imaginary(x)) is True
assert ask(Q.complex(2**x), Q.integer(x)) is True
assert ask(Q.complex(2**x), Q.even(x)) is True
assert ask(Q.complex(2**x), Q.odd(x)) is True
assert ask(Q.complex(x**y), Q.complex(x) & Q.complex(y)) is True
# trigonometric expressions
assert ask(Q.complex(sin(x))) is True
assert ask(Q.complex(sin(2*x + 1))) is True
assert ask(Q.complex(cos(x))) is True
assert ask(Q.complex(cos(2*x + 1))) is True
# exponential
assert ask(Q.complex(exp(x))) is True
assert ask(Q.complex(exp(x))) is True
# Q.complexes
assert ask(Q.complex(Abs(x))) is True
assert ask(Q.complex(re(x))) is True
assert ask(Q.complex(im(x))) is True
def test_even_query():
assert ask(Q.even(x)) is None
assert ask(Q.even(x), Q.integer(x)) is None
assert ask(Q.even(x), ~Q.integer(x)) is False
assert ask(Q.even(x), Q.rational(x)) is None
assert ask(Q.even(x), Q.positive(x)) is None
assert ask(Q.even(2*x)) is None
assert ask(Q.even(2*x), Q.integer(x)) is True
assert ask(Q.even(2*x), Q.even(x)) is True
assert ask(Q.even(2*x), Q.irrational(x)) is False
assert ask(Q.even(2*x), Q.odd(x)) is True
assert ask(Q.even(2*x), ~Q.integer(x)) is None
assert ask(Q.even(3*x), Q.integer(x)) is None
assert ask(Q.even(3*x), Q.even(x)) is True
assert ask(Q.even(3*x), Q.odd(x)) is False
assert ask(Q.even(x + 1), Q.odd(x)) is True
assert ask(Q.even(x + 1), Q.even(x)) is False
assert ask(Q.even(x + 2), Q.odd(x)) is False
assert ask(Q.even(x + 2), Q.even(x)) is True
assert ask(Q.even(7 - x), Q.odd(x)) is True
assert ask(Q.even(7 + x), Q.odd(x)) is True
assert ask(Q.even(x + y), Q.odd(x) & Q.odd(y)) is True
assert ask(Q.even(x + y), Q.odd(x) & Q.even(y)) is False
assert ask(Q.even(x + y), Q.even(x) & Q.even(y)) is True
assert ask(Q.even(2*x + 1), Q.integer(x)) is False
assert ask(Q.even(2*x*y), Q.rational(x) & Q.rational(x)) is None
assert ask(Q.even(2*x*y), Q.irrational(x) & Q.irrational(x)) is None
assert ask(Q.even(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is True
assert ask(Q.even(x + y + z + t),
Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None
assert ask(Q.even(Abs(x)), Q.even(x)) is True
assert ask(Q.even(Abs(x)), ~Q.even(x)) is None
assert ask(Q.even(re(x)), Q.even(x)) is True
assert ask(Q.even(re(x)), ~Q.even(x)) is None
assert ask(Q.even(im(x)), Q.even(x)) is True
assert ask(Q.even(im(x)), Q.real(x)) is True
assert ask(Q.even((-1)**n), Q.integer(n)) is False
assert ask(Q.even(k**2), Q.even(k)) is True
assert ask(Q.even(n**2), Q.odd(n)) is False
assert ask(Q.even(2**k), Q.even(k)) is None
assert ask(Q.even(x**2)) is None
assert ask(Q.even(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.even(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is False
assert ask(Q.even(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is True
assert ask(Q.even(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is False
assert ask(Q.even(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.even(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None
assert ask(Q.even(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.even(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None
assert ask(Q.even(k**x), Q.even(k)) is None
assert ask(Q.even(n**x), Q.odd(n)) is None
assert ask(Q.even(x*y), Q.integer(x) & Q.integer(y)) is None
assert ask(Q.even(x*x), Q.integer(x)) is None
assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.odd(y)) is True
assert ask(Q.even(x*(x + y)), Q.integer(x) & Q.even(y)) is None
@XFAIL
def test_evenness_in_ternary_integer_product_with_odd():
# Tests that oddness inference is independent of term ordering.
# Term ordering at the point of testing depends on SymPy's symbol order, so
# we try to force a different order by modifying symbol names.
assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True
assert ask(Q.even(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is True
def test_evenness_in_ternary_integer_product_with_even():
assert ask(Q.even(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None
def test_extended_real():
assert ask(Q.extended_real(x), Q.positive_infinite(x)) is True
assert ask(Q.extended_real(x), Q.positive(x)) is True
assert ask(Q.extended_real(x), Q.zero(x)) is True
assert ask(Q.extended_real(x), Q.negative(x)) is True
assert ask(Q.extended_real(x), Q.negative_infinite(x)) is True
assert ask(Q.extended_real(-x), Q.positive(x)) is True
assert ask(Q.extended_real(-x), Q.negative(x)) is True
assert ask(Q.extended_real(x + S.Infinity), Q.real(x)) is True
assert ask(Q.extended_real(x), Q.infinite(x)) is None
@_both_exp_pow
def test_rational():
assert ask(Q.rational(x), Q.integer(x)) is True
assert ask(Q.rational(x), Q.irrational(x)) is False
assert ask(Q.rational(x), Q.real(x)) is None
assert ask(Q.rational(x), Q.positive(x)) is None
assert ask(Q.rational(x), Q.negative(x)) is None
assert ask(Q.rational(x), Q.nonzero(x)) is None
assert ask(Q.rational(x), ~Q.algebraic(x)) is False
assert ask(Q.rational(2*x), Q.rational(x)) is True
assert ask(Q.rational(2*x), Q.integer(x)) is True
assert ask(Q.rational(2*x), Q.even(x)) is True
assert ask(Q.rational(2*x), Q.odd(x)) is True
assert ask(Q.rational(2*x), Q.irrational(x)) is False
assert ask(Q.rational(x/2), Q.rational(x)) is True
assert ask(Q.rational(x/2), Q.integer(x)) is True
assert ask(Q.rational(x/2), Q.even(x)) is True
assert ask(Q.rational(x/2), Q.odd(x)) is True
assert ask(Q.rational(x/2), Q.irrational(x)) is False
assert ask(Q.rational(1/x), Q.rational(x)) is True
assert ask(Q.rational(1/x), Q.integer(x)) is True
assert ask(Q.rational(1/x), Q.even(x)) is True
assert ask(Q.rational(1/x), Q.odd(x)) is True
assert ask(Q.rational(1/x), Q.irrational(x)) is False
assert ask(Q.rational(2/x), Q.rational(x)) is True
assert ask(Q.rational(2/x), Q.integer(x)) is True
assert ask(Q.rational(2/x), Q.even(x)) is True
assert ask(Q.rational(2/x), Q.odd(x)) is True
assert ask(Q.rational(2/x), Q.irrational(x)) is False
assert ask(Q.rational(x), ~Q.algebraic(x)) is False
# with multiple symbols
assert ask(Q.rational(x*y), Q.irrational(x) & Q.irrational(y)) is None
assert ask(Q.rational(y/x), Q.rational(x) & Q.rational(y)) is True
assert ask(Q.rational(y/x), Q.integer(x) & Q.rational(y)) is True
assert ask(Q.rational(y/x), Q.even(x) & Q.rational(y)) is True
assert ask(Q.rational(y/x), Q.odd(x) & Q.rational(y)) is True
assert ask(Q.rational(y/x), Q.irrational(x) & Q.rational(y)) is False
for f in [exp, sin, tan, asin, atan, cos]:
assert ask(Q.rational(f(7))) is False
assert ask(Q.rational(f(7, evaluate=False))) is False
assert ask(Q.rational(f(0, evaluate=False))) is True
assert ask(Q.rational(f(x)), Q.rational(x)) is None
assert ask(Q.rational(f(x)), Q.rational(x) & Q.nonzero(x)) is False
for g in [log, acos]:
assert ask(Q.rational(g(7))) is False
assert ask(Q.rational(g(7, evaluate=False))) is False
assert ask(Q.rational(g(1, evaluate=False))) is True
assert ask(Q.rational(g(x)), Q.rational(x)) is None
assert ask(Q.rational(g(x)), Q.rational(x) & Q.nonzero(x - 1)) is False
for h in [cot, acot]:
assert ask(Q.rational(h(7))) is False
assert ask(Q.rational(h(7, evaluate=False))) is False
assert ask(Q.rational(h(x)), Q.rational(x)) is False
def test_hermitian():
assert ask(Q.hermitian(x)) is None
assert ask(Q.hermitian(x), Q.antihermitian(x)) is None
assert ask(Q.hermitian(x), Q.imaginary(x)) is False
assert ask(Q.hermitian(x), Q.prime(x)) is True
assert ask(Q.hermitian(x), Q.real(x)) is True
assert ask(Q.hermitian(x), Q.zero(x)) is True
assert ask(Q.hermitian(x + 1), Q.antihermitian(x)) is None
assert ask(Q.hermitian(x + 1), Q.complex(x)) is None
assert ask(Q.hermitian(x + 1), Q.hermitian(x)) is True
assert ask(Q.hermitian(x + 1), Q.imaginary(x)) is False
assert ask(Q.hermitian(x + 1), Q.real(x)) is True
assert ask(Q.hermitian(x + I), Q.antihermitian(x)) is None
assert ask(Q.hermitian(x + I), Q.complex(x)) is None
assert ask(Q.hermitian(x + I), Q.hermitian(x)) is False
assert ask(Q.hermitian(x + I), Q.imaginary(x)) is None
assert ask(Q.hermitian(x + I), Q.real(x)) is False
assert ask(
Q.hermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y)) is None
assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None
assert ask(
Q.hermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None
assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is None
assert ask(Q.hermitian(x + y), Q.antihermitian(x) & Q.real(y)) is None
assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None
assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.hermitian(y)) is True
assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is False
assert ask(Q.hermitian(x + y), Q.hermitian(x) & Q.real(y)) is True
assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None
assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is None
assert ask(Q.hermitian(x + y), Q.imaginary(x) & Q.real(y)) is False
assert ask(Q.hermitian(x + y), Q.real(x) & Q.complex(y)) is None
assert ask(Q.hermitian(x + y), Q.real(x) & Q.real(y)) is True
assert ask(Q.hermitian(I*x), Q.antihermitian(x)) is True
assert ask(Q.hermitian(I*x), Q.complex(x)) is None
assert ask(Q.hermitian(I*x), Q.hermitian(x)) is False
assert ask(Q.hermitian(I*x), Q.imaginary(x)) is True
assert ask(Q.hermitian(I*x), Q.real(x)) is False
assert ask(Q.hermitian(x*y), Q.hermitian(x) & Q.real(y)) is True
assert ask(
Q.hermitian(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True
assert ask(Q.hermitian(x + y + z),
Q.real(x) & Q.real(y) & Q.imaginary(z)) is False
assert ask(Q.hermitian(x + y + z),
Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is None
assert ask(Q.hermitian(x + y + z),
Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is None
assert ask(Q.antihermitian(x)) is None
assert ask(Q.antihermitian(x), Q.real(x)) is False
assert ask(Q.antihermitian(x), Q.prime(x)) is False
assert ask(Q.antihermitian(x + 1), Q.antihermitian(x)) is False
assert ask(Q.antihermitian(x + 1), Q.complex(x)) is None
assert ask(Q.antihermitian(x + 1), Q.hermitian(x)) is None
assert ask(Q.antihermitian(x + 1), Q.imaginary(x)) is False
assert ask(Q.antihermitian(x + 1), Q.real(x)) is None
assert ask(Q.antihermitian(x + I), Q.antihermitian(x)) is True
assert ask(Q.antihermitian(x + I), Q.complex(x)) is None
assert ask(Q.antihermitian(x + I), Q.hermitian(x)) is None
assert ask(Q.antihermitian(x + I), Q.imaginary(x)) is True
assert ask(Q.antihermitian(x + I), Q.real(x)) is False
assert ask(Q.antihermitian(x), Q.zero(x)) is True
assert ask(
Q.antihermitian(x + y), Q.antihermitian(x) & Q.antihermitian(y)
) is True
assert ask(
Q.antihermitian(x + y), Q.antihermitian(x) & Q.complex(y)) is None
assert ask(
Q.antihermitian(x + y), Q.antihermitian(x) & Q.hermitian(y)) is None
assert ask(
Q.antihermitian(x + y), Q.antihermitian(x) & Q.imaginary(y)) is True
assert ask(Q.antihermitian(x + y), Q.antihermitian(x) & Q.real(y)
) is False
assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.complex(y)) is None
assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.hermitian(y)
) is None
assert ask(
Q.antihermitian(x + y), Q.hermitian(x) & Q.imaginary(y)) is None
assert ask(Q.antihermitian(x + y), Q.hermitian(x) & Q.real(y)) is None
assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.complex(y)) is None
assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.imaginary(y)) is True
assert ask(Q.antihermitian(x + y), Q.imaginary(x) & Q.real(y)) is False
assert ask(Q.antihermitian(x + y), Q.real(x) & Q.complex(y)) is None
assert ask(Q.antihermitian(x + y), Q.real(x) & Q.real(y)) is None
assert ask(Q.antihermitian(I*x), Q.real(x)) is True
assert ask(Q.antihermitian(I*x), Q.antihermitian(x)) is False
assert ask(Q.antihermitian(I*x), Q.complex(x)) is None
assert ask(Q.antihermitian(x*y), Q.antihermitian(x) & Q.real(y)) is True
assert ask(Q.antihermitian(x + y + z),
Q.real(x) & Q.real(y) & Q.real(z)) is None
assert ask(Q.antihermitian(x + y + z),
Q.real(x) & Q.real(y) & Q.imaginary(z)) is None
assert ask(Q.antihermitian(x + y + z),
Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False
assert ask(Q.antihermitian(x + y + z),
Q.imaginary(x) & Q.imaginary(y) & Q.imaginary(z)) is True
@_both_exp_pow
def test_imaginary():
assert ask(Q.imaginary(x)) is None
assert ask(Q.imaginary(x), Q.real(x)) is False
assert ask(Q.imaginary(x), Q.prime(x)) is False
assert ask(Q.imaginary(x + 1), Q.real(x)) is False
assert ask(Q.imaginary(x + 1), Q.imaginary(x)) is False
assert ask(Q.imaginary(x + I), Q.real(x)) is False
assert ask(Q.imaginary(x + I), Q.imaginary(x)) is True
assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.imaginary(y)) is True
assert ask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False
assert ask(Q.imaginary(x + y), Q.imaginary(x) & Q.real(y)) is False
assert ask(Q.imaginary(x + y), Q.complex(x) & Q.real(y)) is None
assert ask(
Q.imaginary(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is False
assert ask(Q.imaginary(x + y + z),
Q.real(x) & Q.real(y) & Q.imaginary(z)) is None
assert ask(Q.imaginary(x + y + z),
Q.real(x) & Q.imaginary(y) & Q.imaginary(z)) is False
assert ask(Q.imaginary(I*x), Q.real(x)) is True
assert ask(Q.imaginary(I*x), Q.imaginary(x)) is False
assert ask(Q.imaginary(I*x), Q.complex(x)) is None
assert ask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True
assert ask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False
assert ask(Q.imaginary(I**x), Q.negative(x)) is None
assert ask(Q.imaginary(I**x), Q.positive(x)) is None
assert ask(Q.imaginary(I**x), Q.even(x)) is False
assert ask(Q.imaginary(I**x), Q.odd(x)) is True
assert ask(Q.imaginary(I**x), Q.imaginary(x)) is False
assert ask(Q.imaginary((2*I)**x), Q.imaginary(x)) is False
assert ask(Q.imaginary(x**0), Q.imaginary(x)) is False
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.imaginary(y)) is None
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.real(y)) is None
assert ask(Q.imaginary(x**y), Q.real(x) & Q.imaginary(y)) is None
assert ask(Q.imaginary(x**y), Q.real(x) & Q.real(y)) is None
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.integer(y)) is None
assert ask(Q.imaginary(x**y), Q.imaginary(y) & Q.integer(x)) is None
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.odd(y)) is True
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.rational(y)) is None
assert ask(Q.imaginary(x**y), Q.imaginary(x) & Q.even(y)) is False
assert ask(Q.imaginary(x**y), Q.real(x) & Q.integer(y)) is False
assert ask(Q.imaginary(x**y), Q.positive(x) & Q.real(y)) is False
assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y)) is None
assert ask(Q.imaginary(x**y), Q.negative(x) & Q.real(y) & ~Q.rational(y)) is False
assert ask(Q.imaginary(x**y), Q.integer(x) & Q.imaginary(y)) is None
assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & Q.integer(2*y)) is True
assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y) & ~Q.integer(2*y)) is False
assert ask(Q.imaginary(x**y), Q.negative(x) & Q.rational(y)) is None
assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & ~Q.integer(2*y)) is False
assert ask(Q.imaginary(x**y), Q.real(x) & Q.rational(y) & Q.integer(2*y)) is None
# logarithm
assert ask(Q.imaginary(log(I))) is True
assert ask(Q.imaginary(log(2*I))) is False
assert ask(Q.imaginary(log(I + 1))) is False
assert ask(Q.imaginary(log(x)), Q.complex(x)) is None
assert ask(Q.imaginary(log(x)), Q.imaginary(x)) is None
assert ask(Q.imaginary(log(x)), Q.positive(x)) is False
assert ask(Q.imaginary(log(exp(x))), Q.complex(x)) is None
assert ask(Q.imaginary(log(exp(x))), Q.imaginary(x)) is None # zoo/I/a+I*b
assert ask(Q.imaginary(log(exp(I)))) is True
# exponential
assert ask(Q.imaginary(exp(x)**x), Q.imaginary(x)) is False
eq = Pow(exp(pi*I*x, evaluate=False), x, evaluate=False)
assert ask(Q.imaginary(eq), Q.even(x)) is False
eq = Pow(exp(pi*I*x/2, evaluate=False), x, evaluate=False)
assert ask(Q.imaginary(eq), Q.odd(x)) is True
assert ask(Q.imaginary(exp(3*I*pi*x)**x), Q.integer(x)) is False
assert ask(Q.imaginary(exp(2*pi*I, evaluate=False))) is False
assert ask(Q.imaginary(exp(pi*I/2, evaluate=False))) is True
# issue 7886
assert ask(Q.imaginary(Pow(x, Rational(1, 4))), Q.real(x) & Q.negative(x)) is False
def test_integer():
assert ask(Q.integer(x)) is None
assert ask(Q.integer(x), Q.integer(x)) is True
assert ask(Q.integer(x), ~Q.integer(x)) is False
assert ask(Q.integer(x), ~Q.real(x)) is False
assert ask(Q.integer(x), ~Q.positive(x)) is None
assert ask(Q.integer(x), Q.even(x) | Q.odd(x)) is True
assert ask(Q.integer(2*x), Q.integer(x)) is True
assert ask(Q.integer(2*x), Q.even(x)) is True
assert ask(Q.integer(2*x), Q.prime(x)) is True
assert ask(Q.integer(2*x), Q.rational(x)) is None
assert ask(Q.integer(2*x), Q.real(x)) is None
assert ask(Q.integer(sqrt(2)*x), Q.integer(x)) is False
assert ask(Q.integer(sqrt(2)*x), Q.irrational(x)) is None
assert ask(Q.integer(x/2), Q.odd(x)) is False
assert ask(Q.integer(x/2), Q.even(x)) is True
assert ask(Q.integer(x/3), Q.odd(x)) is None
assert ask(Q.integer(x/3), Q.even(x)) is None
def test_negative():
assert ask(Q.negative(x), Q.negative(x)) is True
assert ask(Q.negative(x), Q.positive(x)) is False
assert ask(Q.negative(x), ~Q.real(x)) is False
assert ask(Q.negative(x), Q.prime(x)) is False
assert ask(Q.negative(x), ~Q.prime(x)) is None
assert ask(Q.negative(-x), Q.positive(x)) is True
assert ask(Q.negative(-x), ~Q.positive(x)) is None
assert ask(Q.negative(-x), Q.negative(x)) is False
assert ask(Q.negative(-x), Q.positive(x)) is True
assert ask(Q.negative(x - 1), Q.negative(x)) is True
assert ask(Q.negative(x + y)) is None
assert ask(Q.negative(x + y), Q.negative(x)) is None
assert ask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True
assert ask(Q.negative(x + y), Q.negative(x) & Q.nonpositive(y)) is True
assert ask(Q.negative(2 + I)) is False
# although this could be False, it is representative of expressions
# that don't evaluate to a zero with precision
assert ask(Q.negative(cos(I)**2 + sin(I)**2 - 1)) is None
assert ask(Q.negative(-I + I*(cos(2)**2 + sin(2)**2))) is None
assert ask(Q.negative(x**2)) is None
assert ask(Q.negative(x**2), Q.real(x)) is False
assert ask(Q.negative(x**1.4), Q.real(x)) is None
assert ask(Q.negative(x**I), Q.positive(x)) is None
assert ask(Q.negative(x*y)) is None
assert ask(Q.negative(x*y), Q.positive(x) & Q.positive(y)) is False
assert ask(Q.negative(x*y), Q.positive(x) & Q.negative(y)) is True
assert ask(Q.negative(x*y), Q.complex(x) & Q.complex(y)) is None
assert ask(Q.negative(x**y)) is None
assert ask(Q.negative(x**y), Q.negative(x) & Q.even(y)) is False
assert ask(Q.negative(x**y), Q.negative(x) & Q.odd(y)) is True
assert ask(Q.negative(x**y), Q.positive(x) & Q.integer(y)) is False
assert ask(Q.negative(Abs(x))) is False
def test_nonzero():
assert ask(Q.nonzero(x)) is None
assert ask(Q.nonzero(x), Q.real(x)) is None
assert ask(Q.nonzero(x), Q.positive(x)) is True
assert ask(Q.nonzero(x), Q.negative(x)) is True
assert ask(Q.nonzero(x), Q.negative(x) | Q.positive(x)) is True
assert ask(Q.nonzero(x + y)) is None
assert ask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True
assert ask(Q.nonzero(x + y), Q.positive(x) & Q.negative(y)) is None
assert ask(Q.nonzero(x + y), Q.negative(x) & Q.negative(y)) is True
assert ask(Q.nonzero(2*x)) is None
assert ask(Q.nonzero(2*x), Q.positive(x)) is True
assert ask(Q.nonzero(2*x), Q.negative(x)) is True
assert ask(Q.nonzero(x*y), Q.nonzero(x)) is None
assert ask(Q.nonzero(x*y), Q.nonzero(x) & Q.nonzero(y)) is True
assert ask(Q.nonzero(x**y), Q.nonzero(x)) is True
assert ask(Q.nonzero(Abs(x))) is None
assert ask(Q.nonzero(Abs(x)), Q.nonzero(x)) is True
assert ask(Q.nonzero(log(exp(2*I)))) is False
# although this could be False, it is representative of expressions
# that don't evaluate to a zero with precision
assert ask(Q.nonzero(cos(1)**2 + sin(1)**2 - 1)) is None
def test_zero():
assert ask(Q.zero(x)) is None
assert ask(Q.zero(x), Q.real(x)) is None
assert ask(Q.zero(x), Q.positive(x)) is False
assert ask(Q.zero(x), Q.negative(x)) is False
assert ask(Q.zero(x), Q.negative(x) | Q.positive(x)) is False
assert ask(Q.zero(x), Q.nonnegative(x) & Q.nonpositive(x)) is True
assert ask(Q.zero(x + y)) is None
assert ask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False
assert ask(Q.zero(x + y), Q.positive(x) & Q.negative(y)) is None
assert ask(Q.zero(x + y), Q.negative(x) & Q.negative(y)) is False
assert ask(Q.zero(2*x)) is None
assert ask(Q.zero(2*x), Q.positive(x)) is False
assert ask(Q.zero(2*x), Q.negative(x)) is False
assert ask(Q.zero(x*y), Q.nonzero(x)) is None
assert ask(Q.zero(Abs(x))) is None
assert ask(Q.zero(Abs(x)), Q.zero(x)) is True
assert ask(Q.integer(x), Q.zero(x)) is True
assert ask(Q.even(x), Q.zero(x)) is True
assert ask(Q.odd(x), Q.zero(x)) is False
assert ask(Q.zero(x), Q.even(x)) is None
assert ask(Q.zero(x), Q.odd(x)) is False
assert ask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True
def test_odd_query():
assert ask(Q.odd(x)) is None
assert ask(Q.odd(x), Q.odd(x)) is True
assert ask(Q.odd(x), Q.integer(x)) is None
assert ask(Q.odd(x), ~Q.integer(x)) is False
assert ask(Q.odd(x), Q.rational(x)) is None
assert ask(Q.odd(x), Q.positive(x)) is None
assert ask(Q.odd(-x), Q.odd(x)) is True
assert ask(Q.odd(2*x)) is None
assert ask(Q.odd(2*x), Q.integer(x)) is False
assert ask(Q.odd(2*x), Q.odd(x)) is False
assert ask(Q.odd(2*x), Q.irrational(x)) is False
assert ask(Q.odd(2*x), ~Q.integer(x)) is None
assert ask(Q.odd(3*x), Q.integer(x)) is None
assert ask(Q.odd(x/3), Q.odd(x)) is None
assert ask(Q.odd(x/3), Q.even(x)) is None
assert ask(Q.odd(x + 1), Q.even(x)) is True
assert ask(Q.odd(x + 2), Q.even(x)) is False
assert ask(Q.odd(x + 2), Q.odd(x)) is True
assert ask(Q.odd(3 - x), Q.odd(x)) is False
assert ask(Q.odd(3 - x), Q.even(x)) is True
assert ask(Q.odd(3 + x), Q.odd(x)) is False
assert ask(Q.odd(3 + x), Q.even(x)) is True
assert ask(Q.odd(x + y), Q.odd(x) & Q.odd(y)) is False
assert ask(Q.odd(x + y), Q.odd(x) & Q.even(y)) is True
assert ask(Q.odd(x - y), Q.even(x) & Q.odd(y)) is True
assert ask(Q.odd(x - y), Q.odd(x) & Q.odd(y)) is False
assert ask(Q.odd(x + y + z), Q.odd(x) & Q.odd(y) & Q.even(z)) is False
assert ask(Q.odd(x + y + z + t),
Q.odd(x) & Q.odd(y) & Q.even(z) & Q.integer(t)) is None
assert ask(Q.odd(2*x + 1), Q.integer(x)) is True
assert ask(Q.odd(2*x + y), Q.integer(x) & Q.odd(y)) is True
assert ask(Q.odd(2*x + y), Q.integer(x) & Q.even(y)) is False
assert ask(Q.odd(2*x + y), Q.integer(x) & Q.integer(y)) is None
assert ask(Q.odd(x*y), Q.odd(x) & Q.even(y)) is False
assert ask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
assert ask(Q.odd(2*x*y), Q.rational(x) & Q.rational(x)) is None
assert ask(Q.odd(2*x*y), Q.irrational(x) & Q.irrational(x)) is None
assert ask(Q.odd(Abs(x)), Q.odd(x)) is True
assert ask(Q.odd((-1)**n), Q.integer(n)) is True
assert ask(Q.odd(k**2), Q.even(k)) is False
assert ask(Q.odd(n**2), Q.odd(n)) is True
assert ask(Q.odd(3**k), Q.even(k)) is None
assert ask(Q.odd(k**m), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.odd(n**m), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is True
assert ask(Q.odd(k**p), Q.even(k) & Q.integer(p) & Q.positive(p)) is False
assert ask(Q.odd(n**p), Q.odd(n) & Q.integer(p) & Q.positive(p)) is True
assert ask(Q.odd(m**k), Q.even(k) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.odd(p**k), Q.even(k) & Q.integer(p) & Q.positive(p)) is None
assert ask(Q.odd(m**n), Q.odd(n) & Q.integer(m) & ~Q.negative(m)) is None
assert ask(Q.odd(p**n), Q.odd(n) & Q.integer(p) & Q.positive(p)) is None
assert ask(Q.odd(k**x), Q.even(k)) is None
assert ask(Q.odd(n**x), Q.odd(n)) is None
assert ask(Q.odd(x*y), Q.integer(x) & Q.integer(y)) is None
assert ask(Q.odd(x*x), Q.integer(x)) is None
assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.odd(y)) is False
assert ask(Q.odd(x*(x + y)), Q.integer(x) & Q.even(y)) is None
@XFAIL
def test_oddness_in_ternary_integer_product_with_odd():
# Tests that oddness inference is independent of term ordering.
# Term ordering at the point of testing depends on SymPy's symbol order, so
# we try to force a different order by modifying symbol names.
assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False
assert ask(Q.odd(y*x*(x + z)), Q.integer(x) & Q.integer(y) & Q.odd(z)) is False
def test_oddness_in_ternary_integer_product_with_even():
assert ask(Q.odd(x*y*(y + z)), Q.integer(x) & Q.integer(y) & Q.even(z)) is None
def test_prime():
assert ask(Q.prime(x), Q.prime(x)) is True
assert ask(Q.prime(x), ~Q.prime(x)) is False
assert ask(Q.prime(x), Q.integer(x)) is None
assert ask(Q.prime(x), ~Q.integer(x)) is False
assert ask(Q.prime(2*x), Q.integer(x)) is None
assert ask(Q.prime(x*y)) is None
assert ask(Q.prime(x*y), Q.prime(x)) is None
assert ask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None
assert ask(Q.prime(4*x), Q.integer(x)) is False
assert ask(Q.prime(4*x)) is None
assert ask(Q.prime(x**2), Q.integer(x)) is False
assert ask(Q.prime(x**2), Q.prime(x)) is False
assert ask(Q.prime(x**y), Q.integer(x) & Q.integer(y)) is False
@_both_exp_pow
def test_positive():
assert ask(Q.positive(x), Q.positive(x)) is True
assert ask(Q.positive(x), Q.negative(x)) is False
assert ask(Q.positive(x), Q.nonzero(x)) is None
assert ask(Q.positive(-x), Q.positive(x)) is False
assert ask(Q.positive(-x), Q.negative(x)) is True
assert ask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True
assert ask(Q.positive(x + y), Q.positive(x) & Q.nonnegative(y)) is True
assert ask(Q.positive(x + y), Q.positive(x) & Q.negative(y)) is None
assert ask(Q.positive(x + y), Q.positive(x) & Q.imaginary(y)) is False
assert ask(Q.positive(2*x), Q.positive(x)) is True
assumptions = Q.positive(x) & Q.negative(y) & Q.negative(z) & Q.positive(w)
assert ask(Q.positive(x*y*z)) is None
assert ask(Q.positive(x*y*z), assumptions) is True
assert ask(Q.positive(-x*y*z), assumptions) is False
assert ask(Q.positive(x**I), Q.positive(x)) is None
assert ask(Q.positive(x**2), Q.positive(x)) is True
assert ask(Q.positive(x**2), Q.negative(x)) is True
assert ask(Q.positive(x**3), Q.negative(x)) is False
assert ask(Q.positive(1/(1 + x**2)), Q.real(x)) is True
assert ask(Q.positive(2**I)) is False
assert ask(Q.positive(2 + I)) is False
# although this could be False, it is representative of expressions
# that don't evaluate to a zero with precision
assert ask(Q.positive(cos(I)**2 + sin(I)**2 - 1)) is None
assert ask(Q.positive(-I + I*(cos(2)**2 + sin(2)**2))) is None
#exponential
assert ask(Q.positive(exp(x)), Q.real(x)) is True
assert ask(~Q.negative(exp(x)), Q.real(x)) is True
assert ask(Q.positive(x + exp(x)), Q.real(x)) is None
assert ask(Q.positive(exp(x)), Q.imaginary(x)) is None
assert ask(Q.positive(exp(2*pi*I, evaluate=False)), Q.imaginary(x)) is True
assert ask(Q.negative(exp(pi*I, evaluate=False)), Q.imaginary(x)) is True
assert ask(Q.positive(exp(x*pi*I)), Q.even(x)) is True
assert ask(Q.positive(exp(x*pi*I)), Q.odd(x)) is False
assert ask(Q.positive(exp(x*pi*I)), Q.real(x)) is None
# logarithm
assert ask(Q.positive(log(x)), Q.imaginary(x)) is False
assert ask(Q.positive(log(x)), Q.negative(x)) is False
assert ask(Q.positive(log(x)), Q.positive(x)) is None
assert ask(Q.positive(log(x + 2)), Q.positive(x)) is True
# factorial
assert ask(Q.positive(factorial(x)), Q.integer(x) & Q.positive(x))
assert ask(Q.positive(factorial(x)), Q.integer(x)) is None
#absolute value
assert ask(Q.positive(Abs(x))) is None # Abs(0) = 0
assert ask(Q.positive(Abs(x)), Q.positive(x)) is True
def test_nonpositive():
assert ask(Q.nonpositive(-1))
assert ask(Q.nonpositive(0))
assert ask(Q.nonpositive(1)) is False
assert ask(~Q.positive(x), Q.nonpositive(x))
assert ask(Q.nonpositive(x), Q.positive(x)) is False
assert ask(Q.nonpositive(sqrt(-1))) is False
assert ask(Q.nonpositive(x), Q.imaginary(x)) is False
def test_nonnegative():
assert ask(Q.nonnegative(-1)) is False
assert ask(Q.nonnegative(0))
assert ask(Q.nonnegative(1))
assert ask(~Q.negative(x), Q.nonnegative(x))
assert ask(Q.nonnegative(x), Q.negative(x)) is False
assert ask(Q.nonnegative(sqrt(-1))) is False
assert ask(Q.nonnegative(x), Q.imaginary(x)) is False
def test_real_basic():
assert ask(Q.real(x)) is None
assert ask(Q.real(x), Q.real(x)) is True
assert ask(Q.real(x), Q.nonzero(x)) is True
assert ask(Q.real(x), Q.positive(x)) is True
assert ask(Q.real(x), Q.negative(x)) is True
assert ask(Q.real(x), Q.integer(x)) is True
assert ask(Q.real(x), Q.even(x)) is True
assert ask(Q.real(x), Q.prime(x)) is True
assert ask(Q.real(x/sqrt(2)), Q.real(x)) is True
assert ask(Q.real(x/sqrt(-2)), Q.real(x)) is False
assert ask(Q.real(x + 1), Q.real(x)) is True
assert ask(Q.real(x + I), Q.real(x)) is False
assert ask(Q.real(x + I), Q.complex(x)) is None
assert ask(Q.real(2*x), Q.real(x)) is True
assert ask(Q.real(I*x), Q.real(x)) is False
assert ask(Q.real(I*x), Q.imaginary(x)) is True
assert ask(Q.real(I*x), Q.complex(x)) is None
def test_real_pow():
assert ask(Q.real(x**2), Q.real(x)) is True
assert ask(Q.real(sqrt(x)), Q.negative(x)) is False
assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) is True
assert ask(Q.real(x**y), Q.real(x) & Q.real(y)) is None
assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True
assert ask(Q.real(x**y), Q.imaginary(x) & Q.imaginary(y)) is None # I**I or (2*I)**I
assert ask(Q.real(x**y), Q.imaginary(x) & Q.real(y)) is None # I**1 or I**0
assert ask(Q.real(x**y), Q.real(x) & Q.imaginary(y)) is None # could be exp(2*pi*I) or 2**I
assert ask(Q.real(x**0), Q.imaginary(x)) is True
assert ask(Q.real(x**y), Q.real(x) & Q.integer(y)) is True
assert ask(Q.real(x**y), Q.positive(x) & Q.real(y)) is True
assert ask(Q.real(x**y), Q.real(x) & Q.rational(y)) is None
assert ask(Q.real(x**y), Q.imaginary(x) & Q.integer(y)) is None
assert ask(Q.real(x**y), Q.imaginary(x) & Q.odd(y)) is False
assert ask(Q.real(x**y), Q.imaginary(x) & Q.even(y)) is True
assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.rational(y/z) & Q.even(z) & Q.positive(x)) is True
assert ask(Q.real(x**(y/z)), Q.real(x) & Q.rational(y/z) & Q.even(z) & Q.negative(x)) is False
assert ask(Q.real(x**(y/z)), Q.real(x) & Q.integer(y/z)) is True
assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.positive(x)) is True
assert ask(Q.real(x**(y/z)), Q.real(x) & Q.real(y/z) & Q.negative(x)) is False
assert ask(Q.real((-I)**i), Q.imaginary(i)) is True
assert ask(Q.real(I**i), Q.imaginary(i)) is True
assert ask(Q.real(i**i), Q.imaginary(i)) is None # i might be 2*I
assert ask(Q.real(x**i), Q.imaginary(i)) is None # x could be 0
assert ask(Q.real(x**(I*pi/log(x))), Q.real(x)) is True
@_both_exp_pow
def test_real_functions():
# trigonometric functions
assert ask(Q.real(sin(x))) is None
assert ask(Q.real(cos(x))) is None
assert ask(Q.real(sin(x)), Q.real(x)) is True
assert ask(Q.real(cos(x)), Q.real(x)) is True
# exponential function
assert ask(Q.real(exp(x))) is None
assert ask(Q.real(exp(x)), Q.real(x)) is True
assert ask(Q.real(x + exp(x)), Q.real(x)) is True
assert ask(Q.real(exp(2*pi*I, evaluate=False))) is True
assert ask(Q.real(exp(pi*I, evaluate=False))) is True
assert ask(Q.real(exp(pi*I/2, evaluate=False))) is False
# logarithm
assert ask(Q.real(log(I))) is False
assert ask(Q.real(log(2*I))) is False
assert ask(Q.real(log(I + 1))) is False
assert ask(Q.real(log(x)), Q.complex(x)) is None
assert ask(Q.real(log(x)), Q.imaginary(x)) is False
assert ask(Q.real(log(exp(x))), Q.imaginary(x)) is None # exp(2*pi*I) is 1, log(exp(pi*I)) is pi*I (disregarding periodicity)
assert ask(Q.real(log(exp(x))), Q.complex(x)) is None
eq = Pow(exp(2*pi*I*x, evaluate=False), x, evaluate=False)
assert ask(Q.real(eq), Q.integer(x)) is True
assert ask(Q.real(exp(x)**x), Q.imaginary(x)) is True
assert ask(Q.real(exp(x)**x), Q.complex(x)) is None
# Q.complexes
assert ask(Q.real(re(x))) is True
assert ask(Q.real(im(x))) is True
def test_matrix():
# hermitian
assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 - I, 3, I], [4, -I, 1]]))) == True
assert ask(Q.hermitian(Matrix([[2, 2 + I, 4], [2 + I, 3, I], [4, -I, 1]]))) == False
z = symbols('z', complex=True)
assert ask(Q.hermitian(Matrix([[2, 2 + I, z], [2 - I, 3, I], [4, -I, 1]]))) == None
assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, 18, 0), (-5, 0, 11))))) == True
assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, I, 0), (-5, 0, 11))))) == False
assert ask(Q.hermitian(SparseMatrix(((25, 15, -5), (15, z, 0), (-5, 0, 11))))) == None
# antihermitian
A = Matrix([[0, -2 - I, 0], [2 - I, 0, -I], [0, -I, 0]])
B = Matrix([[-I, 2 + I, 0], [-2 + I, 0, 2 + I], [0, -2 + I, -I]])
assert ask(Q.antihermitian(A)) is True
assert ask(Q.antihermitian(B)) is True
assert ask(Q.antihermitian(A**2)) is False
C = (B**3)
C.simplify()
assert ask(Q.antihermitian(C)) is True
_A = Matrix([[0, -2 - I, 0], [z, 0, -I], [0, -I, 0]])
assert ask(Q.antihermitian(_A)) is None
@_both_exp_pow
def test_algebraic():
assert ask(Q.algebraic(x)) is None
assert ask(Q.algebraic(I)) is True
assert ask(Q.algebraic(2*I)) is True
assert ask(Q.algebraic(I/3)) is True
assert ask(Q.algebraic(sqrt(7))) is True
assert ask(Q.algebraic(2*sqrt(7))) is True
assert ask(Q.algebraic(sqrt(7)/3)) is True
assert ask(Q.algebraic(I*sqrt(3))) is True
assert ask(Q.algebraic(sqrt(1 + I*sqrt(3)))) is True
assert ask(Q.algebraic(1 + I*sqrt(3)**Rational(17, 31))) is True
assert ask(Q.algebraic(1 + I*sqrt(3)**(17/pi))) is False
for f in [exp, sin, tan, asin, atan, cos]:
assert ask(Q.algebraic(f(7))) is False
assert ask(Q.algebraic(f(7, evaluate=False))) is False
assert ask(Q.algebraic(f(0, evaluate=False))) is True
assert ask(Q.algebraic(f(x)), Q.algebraic(x)) is None
assert ask(Q.algebraic(f(x)), Q.algebraic(x) & Q.nonzero(x)) is False
for g in [log, acos]:
assert ask(Q.algebraic(g(7))) is False
assert ask(Q.algebraic(g(7, evaluate=False))) is False
assert ask(Q.algebraic(g(1, evaluate=False))) is True
assert ask(Q.algebraic(g(x)), Q.algebraic(x)) is None
assert ask(Q.algebraic(g(x)), Q.algebraic(x) & Q.nonzero(x - 1)) is False
for h in [cot, acot]:
assert ask(Q.algebraic(h(7))) is False
assert ask(Q.algebraic(h(7, evaluate=False))) is False
assert ask(Q.algebraic(h(x)), Q.algebraic(x)) is False
assert ask(Q.algebraic(sqrt(sin(7)))) is False
assert ask(Q.algebraic(sqrt(y + I*sqrt(7)))) is None
assert ask(Q.algebraic(2.47)) is True
assert ask(Q.algebraic(x), Q.transcendental(x)) is False
assert ask(Q.transcendental(x), Q.algebraic(x)) is False
def test_global():
"""Test ask with global assumptions"""
assert ask(Q.integer(x)) is None
global_assumptions.add(Q.integer(x))
assert ask(Q.integer(x)) is True
global_assumptions.clear()
assert ask(Q.integer(x)) is None
def test_custom_context():
"""Test ask with custom assumptions context"""
assert ask(Q.integer(x)) is None
local_context = AssumptionsContext()
local_context.add(Q.integer(x))
assert ask(Q.integer(x), context=local_context) is True
assert ask(Q.integer(x)) is None
def test_functions_in_assumptions():
assert ask(Q.negative(x), Q.real(x) >> Q.positive(x)) is False
assert ask(Q.negative(x), Equivalent(Q.real(x), Q.positive(x))) is False
assert ask(Q.negative(x), Xor(Q.real(x), Q.negative(x))) is False
def test_composite_ask():
assert ask(Q.negative(x) & Q.integer(x),
assumptions=Q.real(x) >> Q.positive(x)) is False
def test_composite_proposition():
assert ask(True) is True
assert ask(False) is False
assert ask(~Q.negative(x), Q.positive(x)) is True
assert ask(~Q.real(x), Q.commutative(x)) is None
assert ask(Q.negative(x) & Q.integer(x), Q.positive(x)) is False
assert ask(Q.negative(x) & Q.integer(x)) is None
assert ask(Q.real(x) | Q.integer(x), Q.positive(x)) is True
assert ask(Q.real(x) | Q.integer(x)) is None
assert ask(Q.real(x) >> Q.positive(x), Q.negative(x)) is False
assert ask(Implies(
Q.real(x), Q.positive(x), evaluate=False), Q.negative(x)) is False
assert ask(Implies(Q.real(x), Q.positive(x), evaluate=False)) is None
assert ask(Equivalent(Q.integer(x), Q.even(x)), Q.even(x)) is True
assert ask(Equivalent(Q.integer(x), Q.even(x))) is None
assert ask(Equivalent(Q.positive(x), Q.integer(x)), Q.integer(x)) is None
assert ask(Q.real(x) | Q.integer(x), Q.real(x) | Q.integer(x)) is True
def test_tautology():
assert ask(Q.real(x) | ~Q.real(x)) is True
assert ask(Q.real(x) & ~Q.real(x)) is False
def test_composite_assumptions():
assert ask(Q.real(x), Q.real(x) & Q.real(y)) is True
assert ask(Q.positive(x), Q.positive(x) | Q.positive(y)) is None
assert ask(Q.positive(x), Q.real(x) >> Q.positive(y)) is None
assert ask(Q.real(x), ~(Q.real(x) >> Q.real(y))) is True
def test_key_extensibility():
"""test that you can add keys to the ask system at runtime"""
# make sure the key is not defined
raises(AttributeError, lambda: ask(Q.my_key(x)))
# Old handler system
class MyAskHandler(AskHandler):
@staticmethod
def Symbol(expr, assumptions):
return True
try:
with warns_deprecated_sympy():
register_handler('my_key', MyAskHandler)
with warns_deprecated_sympy():
assert ask(Q.my_key(x)) is True
with warns_deprecated_sympy():
assert ask(Q.my_key(x + 1)) is None
finally:
# We have to disable the stacklevel testing here because this raises
# the warning twice from two different places
with warns_deprecated_sympy():
remove_handler('my_key', MyAskHandler)
del Q.my_key
raises(AttributeError, lambda: ask(Q.my_key(x)))
# New handler system
class MyPredicate(Predicate):
pass
try:
Q.my_key = MyPredicate()
@Q.my_key.register(Symbol)
def _(expr, assumptions):
return True
assert ask(Q.my_key(x)) is True
assert ask(Q.my_key(x+1)) is None
finally:
del Q.my_key
raises(AttributeError, lambda: ask(Q.my_key(x)))
def test_type_extensibility():
"""test that new types can be added to the ask system at runtime
"""
from sympy.core import Basic
class MyType(Basic):
pass
@Q.prime.register(MyType)
def _(expr, assumptions):
return True
assert ask(Q.prime(MyType())) is True
def test_single_fact_lookup():
known_facts = And(Implies(Q.integer, Q.rational),
Implies(Q.rational, Q.real),
Implies(Q.real, Q.complex))
known_facts_keys = {Q.integer, Q.rational, Q.real, Q.complex}
known_facts_cnf = to_cnf(known_facts)
mapping = single_fact_lookup(known_facts_keys, known_facts_cnf)
assert mapping[Q.rational] == {Q.real, Q.rational, Q.complex}
def test_generate_known_facts_dict():
known_facts = And(Implies(Q.integer(x), Q.rational(x)),
Implies(Q.rational(x), Q.real(x)),
Implies(Q.real(x), Q.complex(x)))
known_facts_keys = {Q.integer(x), Q.rational(x), Q.real(x), Q.complex(x)}
assert generate_known_facts_dict(known_facts_keys, known_facts) == \
{Q.complex: ({Q.complex}, set()),
Q.integer: ({Q.complex, Q.integer, Q.rational, Q.real}, set()),
Q.rational: ({Q.complex, Q.rational, Q.real}, set()),
Q.real: ({Q.complex, Q.real}, set())}
@slow
def test_known_facts_consistent():
""""Test that ask_generated.py is up-to-date"""
x = Symbol('x')
fact = get_known_facts(x)
# test cnf clauses of fact between unary predicates
cnf = CNF.to_CNF(fact)
clauses = set()
for cl in cnf.clauses:
clauses.add(frozenset(Literal(lit.arg.function, lit.is_Not) for lit in sorted(cl, key=str)))
assert get_all_known_facts() == clauses
# test dictionary of fact between unary predicates
keys = [pred(x) for pred in get_known_facts_keys()]
mapping = generate_known_facts_dict(keys, fact)
assert get_known_facts_dict() == mapping
def test_Add_queries():
assert ask(Q.prime(12345678901234567890 + (cos(1)**2 + sin(1)**2))) is True
assert ask(Q.even(Add(S(2), S(2), evaluate=0))) is True
assert ask(Q.prime(Add(S(2), S(2), evaluate=0))) is False
assert ask(Q.integer(Add(S(2), S(2), evaluate=0))) is True
def test_positive_assuming():
with assuming(Q.positive(x + 1)):
assert not ask(Q.positive(x))
def test_issue_5421():
raises(TypeError, lambda: ask(pi/log(x), Q.real))
def test_issue_3906():
raises(TypeError, lambda: ask(Q.positive))
def test_issue_5833():
assert ask(Q.positive(log(x)**2), Q.positive(x)) is None
assert ask(~Q.negative(log(x)**2), Q.positive(x)) is True
def test_issue_6732():
raises(ValueError, lambda: ask(Q.positive(x), Q.positive(x) & Q.negative(x)))
raises(ValueError, lambda: ask(Q.negative(x), Q.positive(x) & Q.negative(x)))
def test_issue_7246():
assert ask(Q.positive(atan(p)), Q.positive(p)) is True
assert ask(Q.positive(atan(p)), Q.negative(p)) is False
assert ask(Q.positive(atan(p)), Q.zero(p)) is False
assert ask(Q.positive(atan(x))) is None
assert ask(Q.positive(asin(p)), Q.positive(p)) is None
assert ask(Q.positive(asin(p)), Q.zero(p)) is None
assert ask(Q.positive(asin(Rational(1, 7)))) is True
assert ask(Q.positive(asin(x)), Q.positive(x) & Q.nonpositive(x - 1)) is True
assert ask(Q.positive(asin(x)), Q.negative(x) & Q.nonnegative(x + 1)) is False
assert ask(Q.positive(acos(p)), Q.positive(p)) is None
assert ask(Q.positive(acos(Rational(1, 7)))) is True
assert ask(Q.positive(acos(x)), Q.nonnegative(x + 1) & Q.nonpositive(x - 1)) is True
assert ask(Q.positive(acos(x)), Q.nonnegative(x - 1)) is None
assert ask(Q.positive(acot(x)), Q.positive(x)) is True
assert ask(Q.positive(acot(x)), Q.real(x)) is True
assert ask(Q.positive(acot(x)), Q.imaginary(x)) is False
assert ask(Q.positive(acot(x))) is None
@XFAIL
def test_issue_7246_failing():
#Move this test to test_issue_7246 once
#the new assumptions module is improved.
assert ask(Q.positive(acos(x)), Q.zero(x)) is True
def test_check_old_assumption():
x = symbols('x', real=True)
assert ask(Q.real(x)) is True
assert ask(Q.imaginary(x)) is False
assert ask(Q.complex(x)) is True
x = symbols('x', imaginary=True)
assert ask(Q.real(x)) is False
assert ask(Q.imaginary(x)) is True
assert ask(Q.complex(x)) is True
x = symbols('x', complex=True)
assert ask(Q.real(x)) is None
assert ask(Q.complex(x)) is True
x = symbols('x', positive=True)
assert ask(Q.positive(x)) is True
assert ask(Q.negative(x)) is False
assert ask(Q.real(x)) is True
x = symbols('x', commutative=False)
assert ask(Q.commutative(x)) is False
x = symbols('x', negative=True)
assert ask(Q.positive(x)) is False
assert ask(Q.negative(x)) is True
x = symbols('x', nonnegative=True)
assert ask(Q.negative(x)) is False
assert ask(Q.positive(x)) is None
assert ask(Q.zero(x)) is None
x = symbols('x', finite=True)
assert ask(Q.finite(x)) is True
x = symbols('x', prime=True)
assert ask(Q.prime(x)) is True
assert ask(Q.composite(x)) is False
x = symbols('x', composite=True)
assert ask(Q.prime(x)) is False
assert ask(Q.composite(x)) is True
x = symbols('x', even=True)
assert ask(Q.even(x)) is True
assert ask(Q.odd(x)) is False
x = symbols('x', odd=True)
assert ask(Q.even(x)) is False
assert ask(Q.odd(x)) is True
x = symbols('x', nonzero=True)
assert ask(Q.nonzero(x)) is True
assert ask(Q.zero(x)) is False
x = symbols('x', zero=True)
assert ask(Q.zero(x)) is True
x = symbols('x', integer=True)
assert ask(Q.integer(x)) is True
x = symbols('x', rational=True)
assert ask(Q.rational(x)) is True
assert ask(Q.irrational(x)) is False
x = symbols('x', irrational=True)
assert ask(Q.irrational(x)) is True
assert ask(Q.rational(x)) is False
def test_issue_9636():
assert ask(Q.integer(1.0)) is False
assert ask(Q.prime(3.0)) is False
assert ask(Q.composite(4.0)) is False
assert ask(Q.even(2.0)) is False
assert ask(Q.odd(3.0)) is False
def test_autosimp_used_to_fail():
# See issue #9807
assert ask(Q.imaginary(0**I)) is None
assert ask(Q.imaginary(0**(-I))) is None
assert ask(Q.real(0**I)) is None
assert ask(Q.real(0**(-I))) is None
def test_custom_AskHandler():
from sympy.logic.boolalg import conjuncts
# Old handler system
class MersenneHandler(AskHandler):
@staticmethod
def Integer(expr, assumptions):
if ask(Q.integer(log(expr + 1, 2))):
return True
@staticmethod
def Symbol(expr, assumptions):
if expr in conjuncts(assumptions):
return True
try:
with warns_deprecated_sympy():
register_handler('mersenne', MersenneHandler)
n = Symbol('n', integer=True)
with warns_deprecated_sympy():
assert ask(Q.mersenne(7))
with warns_deprecated_sympy():
assert ask(Q.mersenne(n), Q.mersenne(n))
finally:
del Q.mersenne
# New handler system
class MersennePredicate(Predicate):
pass
try:
Q.mersenne = MersennePredicate()
@Q.mersenne.register(Integer)
def _(expr, assumptions):
if ask(Q.integer(log(expr + 1, 2))):
return True
@Q.mersenne.register(Symbol)
def _(expr, assumptions):
if expr in conjuncts(assumptions):
return True
assert ask(Q.mersenne(7))
assert ask(Q.mersenne(n), Q.mersenne(n))
finally:
del Q.mersenne
def test_polyadic_predicate():
class SexyPredicate(Predicate):
pass
try:
Q.sexyprime = SexyPredicate()
@Q.sexyprime.register(Integer, Integer)
def _(int1, int2, assumptions):
args = sorted([int1, int2])
if not all(ask(Q.prime(a), assumptions) for a in args):
return False
return args[1] - args[0] == 6
@Q.sexyprime.register(Integer, Integer, Integer)
def _(int1, int2, int3, assumptions):
args = sorted([int1, int2, int3])
if not all(ask(Q.prime(a), assumptions) for a in args):
return False
return args[2] - args[1] == 6 and args[1] - args[0] == 6
assert ask(Q.sexyprime(5, 11))
assert ask(Q.sexyprime(7, 13, 19))
finally:
del Q.sexyprime
def test_Predicate_handler_is_unique():
# Undefined predicate does not have a handler
assert Predicate('mypredicate').handler is None
# Handler of defined predicate is unique to the class
class MyPredicate(Predicate):
pass
mp1 = MyPredicate(Str('mp1'))
mp2 = MyPredicate(Str('mp2'))
assert mp1.handler is mp2.handler
def test_relational():
assert ask(Q.eq(x, 0), Q.zero(x))
assert not ask(Q.eq(x, 0), Q.nonzero(x))
assert not ask(Q.ne(x, 0), Q.zero(x))
assert ask(Q.ne(x, 0), Q.nonzero(x))