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2409 lines
96 KiB
2409 lines
96 KiB
from sympy.abc import t, w, x, y, z, n, k, m, p, i
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from sympy.assumptions import (ask, AssumptionsContext, Q, register_handler,
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remove_handler)
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from sympy.assumptions.assume import assuming, global_assumptions, Predicate
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from sympy.assumptions.cnf import CNF, Literal
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from sympy.assumptions.facts import (single_fact_lookup,
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get_known_facts, generate_known_facts_dict, get_known_facts_keys)
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from sympy.assumptions.handlers import AskHandler
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from sympy.assumptions.ask_generated import (get_all_known_facts,
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get_known_facts_dict)
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from sympy.core.add import Add
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from sympy.core.numbers import (I, Integer, Rational, oo, zoo, pi)
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from sympy.core.singleton import S
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from sympy.core.power import Pow
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from sympy.core.symbol import Str, symbols, Symbol
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from sympy.functions.combinatorial.factorials import factorial
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from sympy.functions.elementary.complexes import (Abs, im, re, sign)
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from sympy.functions.elementary.exponential import (exp, log)
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from sympy.functions.elementary.miscellaneous import sqrt
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from sympy.functions.elementary.trigonometric import (
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acos, acot, asin, atan, cos, cot, sin, tan)
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from sympy.logic.boolalg import Equivalent, Implies, Xor, And, to_cnf
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from sympy.matrices import Matrix, SparseMatrix
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from sympy.testing.pytest import (XFAIL, slow, raises, warns_deprecated_sympy,
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_both_exp_pow)
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import math
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def test_int_1():
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z = 1
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is True
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assert ask(Q.rational(z)) is True
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is False
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is True
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_int_11():
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z = 11
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is True
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assert ask(Q.rational(z)) is True
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is False
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is True
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is True
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_int_12():
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z = 12
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is True
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assert ask(Q.rational(z)) is True
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is False
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is True
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is True
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_float_1():
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z = 1.0
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is None
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is None
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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z = 7.2123
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is None
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is None
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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# test for issue #12168
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assert ask(Q.rational(math.pi)) is None
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def test_zero_0():
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z = Integer(0)
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assert ask(Q.nonzero(z)) is False
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assert ask(Q.zero(z)) is True
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is True
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assert ask(Q.rational(z)) is True
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is False
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is True
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is True
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def test_negativeone():
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z = Integer(-1)
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assert ask(Q.nonzero(z)) is True
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assert ask(Q.zero(z)) is False
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is True
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assert ask(Q.rational(z)) is True
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is False
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is False
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assert ask(Q.negative(z)) is True
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is True
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_infinity():
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assert ask(Q.commutative(oo)) is True
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assert ask(Q.integer(oo)) is False
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assert ask(Q.rational(oo)) is False
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assert ask(Q.algebraic(oo)) is False
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assert ask(Q.real(oo)) is False
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assert ask(Q.extended_real(oo)) is True
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assert ask(Q.complex(oo)) is False
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assert ask(Q.irrational(oo)) is False
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assert ask(Q.imaginary(oo)) is False
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assert ask(Q.positive(oo)) is False
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assert ask(Q.extended_positive(oo)) is True
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assert ask(Q.negative(oo)) is False
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assert ask(Q.even(oo)) is False
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assert ask(Q.odd(oo)) is False
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assert ask(Q.finite(oo)) is False
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assert ask(Q.infinite(oo)) is True
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assert ask(Q.prime(oo)) is False
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assert ask(Q.composite(oo)) is False
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assert ask(Q.hermitian(oo)) is False
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assert ask(Q.antihermitian(oo)) is False
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assert ask(Q.positive_infinite(oo)) is True
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assert ask(Q.negative_infinite(oo)) is False
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def test_neg_infinity():
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mm = S.NegativeInfinity
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assert ask(Q.commutative(mm)) is True
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assert ask(Q.integer(mm)) is False
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assert ask(Q.rational(mm)) is False
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assert ask(Q.algebraic(mm)) is False
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assert ask(Q.real(mm)) is False
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assert ask(Q.extended_real(mm)) is True
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assert ask(Q.complex(mm)) is False
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assert ask(Q.irrational(mm)) is False
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assert ask(Q.imaginary(mm)) is False
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assert ask(Q.positive(mm)) is False
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assert ask(Q.negative(mm)) is False
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assert ask(Q.extended_negative(mm)) is True
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assert ask(Q.even(mm)) is False
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assert ask(Q.odd(mm)) is False
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assert ask(Q.finite(mm)) is False
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assert ask(Q.infinite(oo)) is True
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assert ask(Q.prime(mm)) is False
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assert ask(Q.composite(mm)) is False
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assert ask(Q.hermitian(mm)) is False
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assert ask(Q.antihermitian(mm)) is False
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assert ask(Q.positive_infinite(-oo)) is False
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assert ask(Q.negative_infinite(-oo)) is True
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def test_complex_infinity():
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assert ask(Q.commutative(zoo)) is True
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assert ask(Q.integer(zoo)) is False
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assert ask(Q.rational(zoo)) is False
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assert ask(Q.algebraic(zoo)) is False
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assert ask(Q.real(zoo)) is False
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assert ask(Q.extended_real(zoo)) is False
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assert ask(Q.complex(zoo)) is False
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assert ask(Q.irrational(zoo)) is False
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assert ask(Q.imaginary(zoo)) is False
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assert ask(Q.positive(zoo)) is False
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assert ask(Q.negative(zoo)) is False
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assert ask(Q.zero(zoo)) is False
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assert ask(Q.nonzero(zoo)) is False
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assert ask(Q.even(zoo)) is False
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assert ask(Q.odd(zoo)) is False
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assert ask(Q.finite(zoo)) is False
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assert ask(Q.infinite(zoo)) is True
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assert ask(Q.prime(zoo)) is False
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assert ask(Q.composite(zoo)) is False
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assert ask(Q.hermitian(zoo)) is False
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assert ask(Q.antihermitian(zoo)) is False
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assert ask(Q.positive_infinite(zoo)) is False
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assert ask(Q.negative_infinite(zoo)) is False
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def test_nan():
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nan = S.NaN
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assert ask(Q.commutative(nan)) is True
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assert ask(Q.integer(nan)) is None
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assert ask(Q.rational(nan)) is None
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assert ask(Q.algebraic(nan)) is None
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assert ask(Q.real(nan)) is None
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assert ask(Q.extended_real(nan)) is None
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assert ask(Q.complex(nan)) is None
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assert ask(Q.irrational(nan)) is None
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assert ask(Q.imaginary(nan)) is None
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assert ask(Q.positive(nan)) is None
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assert ask(Q.nonzero(nan)) is None
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assert ask(Q.zero(nan)) is None
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assert ask(Q.even(nan)) is None
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assert ask(Q.odd(nan)) is None
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assert ask(Q.finite(nan)) is None
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assert ask(Q.infinite(nan)) is None
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assert ask(Q.prime(nan)) is None
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assert ask(Q.composite(nan)) is None
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assert ask(Q.hermitian(nan)) is None
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assert ask(Q.antihermitian(nan)) is None
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def test_Rational_number():
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r = Rational(3, 4)
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assert ask(Q.commutative(r)) is True
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assert ask(Q.integer(r)) is False
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assert ask(Q.rational(r)) is True
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assert ask(Q.real(r)) is True
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assert ask(Q.complex(r)) is True
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assert ask(Q.irrational(r)) is False
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assert ask(Q.imaginary(r)) is False
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assert ask(Q.positive(r)) is True
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assert ask(Q.negative(r)) is False
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assert ask(Q.even(r)) is False
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assert ask(Q.odd(r)) is False
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assert ask(Q.finite(r)) is True
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assert ask(Q.prime(r)) is False
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assert ask(Q.composite(r)) is False
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assert ask(Q.hermitian(r)) is True
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assert ask(Q.antihermitian(r)) is False
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r = Rational(1, 4)
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assert ask(Q.positive(r)) is True
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assert ask(Q.negative(r)) is False
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r = Rational(5, 4)
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assert ask(Q.negative(r)) is False
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assert ask(Q.positive(r)) is True
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r = Rational(5, 3)
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assert ask(Q.positive(r)) is True
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assert ask(Q.negative(r)) is False
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r = Rational(-3, 4)
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assert ask(Q.positive(r)) is False
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assert ask(Q.negative(r)) is True
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r = Rational(-1, 4)
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assert ask(Q.positive(r)) is False
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assert ask(Q.negative(r)) is True
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r = Rational(-5, 4)
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assert ask(Q.negative(r)) is True
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assert ask(Q.positive(r)) is False
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r = Rational(-5, 3)
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assert ask(Q.positive(r)) is False
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assert ask(Q.negative(r)) is True
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def test_sqrt_2():
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z = sqrt(2)
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_pi():
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z = S.Pi
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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z = S.Pi + 1
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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z = 2*S.Pi
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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z = S.Pi ** 2
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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z = (1 + S.Pi) ** 2
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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assert ask(Q.irrational(z)) is True
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assert ask(Q.imaginary(z)) is False
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assert ask(Q.positive(z)) is True
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assert ask(Q.negative(z)) is False
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assert ask(Q.even(z)) is False
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assert ask(Q.odd(z)) is False
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assert ask(Q.finite(z)) is True
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assert ask(Q.prime(z)) is False
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assert ask(Q.composite(z)) is False
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assert ask(Q.hermitian(z)) is True
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assert ask(Q.antihermitian(z)) is False
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def test_E():
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z = S.Exp1
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assert ask(Q.commutative(z)) is True
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assert ask(Q.integer(z)) is False
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assert ask(Q.rational(z)) is False
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assert ask(Q.algebraic(z)) is False
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assert ask(Q.real(z)) is True
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assert ask(Q.complex(z)) is True
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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))
|