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