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from sympy.assumptions.ask import Q |
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from sympy.assumptions.assume import assuming |
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from sympy.core.numbers import (I, pi) |
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from sympy.core.relational import (Eq, Gt) |
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from sympy.core.singleton import S |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.complexes import Abs |
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from sympy.logic.boolalg import Implies |
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from sympy.matrices.expressions.matexpr import MatrixSymbol |
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from sympy.assumptions.cnf import CNF, Literal |
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from sympy.assumptions.satask import (satask, extract_predargs, |
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get_relevant_clsfacts) |
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from sympy.testing.pytest import raises, XFAIL |
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x, y, z = symbols('x y z') |
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def test_satask(): |
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assert satask(Q.real(x), Q.real(x)) is True |
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assert satask(Q.real(x), ~Q.real(x)) is False |
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assert satask(Q.real(x)) is None |
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assert satask(Q.real(x), Q.positive(x)) is True |
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assert satask(Q.positive(x), Q.real(x)) is None |
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assert satask(Q.real(x), ~Q.positive(x)) is None |
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assert satask(Q.positive(x), ~Q.real(x)) is False |
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raises(ValueError, lambda: satask(Q.real(x), Q.real(x) & ~Q.real(x))) |
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with assuming(Q.positive(x)): |
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assert satask(Q.real(x)) is True |
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assert satask(~Q.positive(x)) is False |
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raises(ValueError, lambda: satask(Q.real(x), ~Q.positive(x))) |
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assert satask(Q.zero(x), Q.nonzero(x)) is False |
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assert satask(Q.positive(x), Q.zero(x)) is False |
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assert satask(Q.real(x), Q.zero(x)) is True |
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assert satask(Q.zero(x), Q.zero(x*y)) is None |
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assert satask(Q.zero(x*y), Q.zero(x)) |
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def test_zero(): |
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""" |
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Everything in this test doesn't work with the ask handlers, and most |
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things would be very difficult or impossible to make work under that |
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model. |
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""" |
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assert satask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True |
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assert satask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) is True |
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assert satask(Implies(Q.zero(x), Q.zero(x*y))) is True |
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assert satask(Q.zero(x) | Q.zero(y), Q.nonzero(x*y)) is False |
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assert satask(Q.zero(x), Q.zero(x**2)) is True |
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def test_zero_positive(): |
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assert satask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False |
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assert satask(Q.positive(x) & Q.positive(y), Q.zero(x + y)) is False |
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assert satask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True |
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assert satask(Q.positive(x) & Q.positive(y), Q.nonzero(x + y)) is None |
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assert satask(Q.zero(x*(x + y)), Q.positive(x) & Q.positive(y)) is False |
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assert satask(Q.positive(pi*x*y + 1), Q.positive(x) & Q.positive(y)) is True |
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assert satask(Q.positive(pi*x*y - 5), Q.positive(x) & Q.positive(y)) is None |
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def test_zero_pow(): |
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assert satask(Q.zero(x**y), Q.zero(x) & Q.positive(y)) is True |
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assert satask(Q.zero(x**y), Q.nonzero(x) & Q.zero(y)) is False |
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assert satask(Q.zero(x), Q.zero(x**y)) is True |
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assert satask(Q.zero(x**y), Q.zero(x)) is None |
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@XFAIL |
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def test_invertible(): |
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A = MatrixSymbol('A', 5, 5) |
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B = MatrixSymbol('B', 5, 5) |
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assert satask(Q.invertible(A*B), Q.invertible(A) & Q.invertible(B)) is True |
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assert satask(Q.invertible(A), Q.invertible(A*B)) is True |
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assert satask(Q.invertible(A) & Q.invertible(B), Q.invertible(A*B)) is True |
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def test_prime(): |
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assert satask(Q.prime(5)) is True |
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assert satask(Q.prime(6)) is False |
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assert satask(Q.prime(-5)) is False |
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assert satask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None |
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assert satask(Q.prime(x*y), Q.prime(x) & Q.prime(y)) is False |
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def test_old_assump(): |
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assert satask(Q.positive(1)) is True |
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assert satask(Q.positive(-1)) is False |
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assert satask(Q.positive(0)) is False |
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assert satask(Q.positive(I)) is False |
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assert satask(Q.positive(pi)) is True |
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assert satask(Q.negative(1)) is False |
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assert satask(Q.negative(-1)) is True |
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assert satask(Q.negative(0)) is False |
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assert satask(Q.negative(I)) is False |
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assert satask(Q.negative(pi)) is False |
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assert satask(Q.zero(1)) is False |
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assert satask(Q.zero(-1)) is False |
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assert satask(Q.zero(0)) is True |
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assert satask(Q.zero(I)) is False |
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assert satask(Q.zero(pi)) is False |
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assert satask(Q.nonzero(1)) is True |
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assert satask(Q.nonzero(-1)) is True |
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assert satask(Q.nonzero(0)) is False |
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assert satask(Q.nonzero(I)) is False |
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assert satask(Q.nonzero(pi)) is True |
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assert satask(Q.nonpositive(1)) is False |
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assert satask(Q.nonpositive(-1)) is True |
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assert satask(Q.nonpositive(0)) is True |
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assert satask(Q.nonpositive(I)) is False |
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assert satask(Q.nonpositive(pi)) is False |
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assert satask(Q.nonnegative(1)) is True |
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assert satask(Q.nonnegative(-1)) is False |
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assert satask(Q.nonnegative(0)) is True |
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assert satask(Q.nonnegative(I)) is False |
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assert satask(Q.nonnegative(pi)) is True |
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def test_rational_irrational(): |
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assert satask(Q.irrational(2)) is False |
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assert satask(Q.rational(2)) is True |
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assert satask(Q.irrational(pi)) is True |
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assert satask(Q.rational(pi)) is False |
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assert satask(Q.irrational(I)) is False |
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assert satask(Q.rational(I)) is False |
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assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.irrational(y) & |
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Q.rational(z)) is None |
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assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.rational(y) & |
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Q.rational(z)) is True |
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assert satask(Q.irrational(pi*x*y), Q.rational(x) & Q.rational(y)) is True |
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assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.irrational(y) & |
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Q.rational(z)) is None |
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assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.rational(y) & |
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Q.rational(z)) is True |
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assert satask(Q.irrational(pi + x + y), Q.rational(x) & Q.rational(y)) is True |
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assert satask(Q.irrational(x*y*z), Q.rational(x) & Q.rational(y) & |
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Q.rational(z)) is False |
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assert satask(Q.rational(x*y*z), Q.rational(x) & Q.rational(y) & |
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Q.rational(z)) is True |
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assert satask(Q.irrational(x + y + z), Q.rational(x) & Q.rational(y) & |
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Q.rational(z)) is False |
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assert satask(Q.rational(x + y + z), Q.rational(x) & Q.rational(y) & |
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Q.rational(z)) is True |
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def test_even_satask(): |
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assert satask(Q.even(2)) is True |
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assert satask(Q.even(3)) is False |
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assert satask(Q.even(x*y), Q.even(x) & Q.odd(y)) is True |
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assert satask(Q.even(x*y), Q.even(x) & Q.integer(y)) is True |
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assert satask(Q.even(x*y), Q.even(x) & Q.even(y)) is True |
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assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False |
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assert satask(Q.even(x*y), Q.even(x)) is None |
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assert satask(Q.even(x*y), Q.odd(x) & Q.integer(y)) is None |
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assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False |
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assert satask(Q.even(abs(x)), Q.even(x)) is True |
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assert satask(Q.even(abs(x)), Q.odd(x)) is False |
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assert satask(Q.even(x), Q.even(abs(x))) is None |
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def test_odd_satask(): |
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assert satask(Q.odd(2)) is False |
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assert satask(Q.odd(3)) is True |
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assert satask(Q.odd(x*y), Q.even(x) & Q.odd(y)) is False |
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assert satask(Q.odd(x*y), Q.even(x) & Q.integer(y)) is False |
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assert satask(Q.odd(x*y), Q.even(x) & Q.even(y)) is False |
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assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True |
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assert satask(Q.odd(x*y), Q.even(x)) is None |
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assert satask(Q.odd(x*y), Q.odd(x) & Q.integer(y)) is None |
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assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True |
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assert satask(Q.odd(abs(x)), Q.even(x)) is False |
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assert satask(Q.odd(abs(x)), Q.odd(x)) is True |
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assert satask(Q.odd(x), Q.odd(abs(x))) is None |
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def test_integer(): |
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assert satask(Q.integer(1)) is True |
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assert satask(Q.integer(S.Half)) is False |
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assert satask(Q.integer(x + y), Q.integer(x) & Q.integer(y)) is True |
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assert satask(Q.integer(x + y), Q.integer(x)) is None |
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assert satask(Q.integer(x + y), Q.integer(x) & ~Q.integer(y)) is False |
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assert satask(Q.integer(x + y + z), Q.integer(x) & Q.integer(y) & |
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~Q.integer(z)) is False |
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assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y) & |
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~Q.integer(z)) is None |
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assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y)) is None |
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assert satask(Q.integer(x + y), Q.integer(x) & Q.irrational(y)) is False |
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assert satask(Q.integer(x*y), Q.integer(x) & Q.integer(y)) is True |
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assert satask(Q.integer(x*y), Q.integer(x)) is None |
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assert satask(Q.integer(x*y), Q.integer(x) & ~Q.integer(y)) is None |
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assert satask(Q.integer(x*y), Q.integer(x) & ~Q.rational(y)) is False |
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assert satask(Q.integer(x*y*z), Q.integer(x) & Q.integer(y) & |
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~Q.rational(z)) is False |
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assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y) & |
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~Q.rational(z)) is None |
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assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y)) is None |
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assert satask(Q.integer(x*y), Q.integer(x) & Q.irrational(y)) is False |
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def test_abs(): |
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assert satask(Q.nonnegative(abs(x))) is True |
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assert satask(Q.positive(abs(x)), ~Q.zero(x)) is True |
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assert satask(Q.zero(x), ~Q.zero(abs(x))) is False |
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assert satask(Q.zero(x), Q.zero(abs(x))) is True |
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assert satask(Q.nonzero(x), ~Q.zero(abs(x))) is None |
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assert satask(Q.zero(abs(x)), Q.zero(x)) is True |
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def test_imaginary(): |
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assert satask(Q.imaginary(2*I)) is True |
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assert satask(Q.imaginary(x*y), Q.imaginary(x)) is None |
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assert satask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True |
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assert satask(Q.imaginary(x), Q.real(x)) is False |
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assert satask(Q.imaginary(1)) is False |
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assert satask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False |
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assert satask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False |
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def test_real(): |
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assert satask(Q.real(x*y), Q.real(x) & Q.real(y)) is True |
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assert satask(Q.real(x + y), Q.real(x) & Q.real(y)) is True |
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assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) is True |
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assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y)) is None |
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assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.imaginary(z)) is False |
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assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True |
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assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y)) is None |
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def test_pos_neg(): |
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assert satask(~Q.positive(x), Q.negative(x)) is True |
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assert satask(~Q.negative(x), Q.positive(x)) is True |
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assert satask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True |
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assert satask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True |
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assert satask(Q.positive(x + y), Q.negative(x) & Q.negative(y)) is False |
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assert satask(Q.negative(x + y), Q.positive(x) & Q.positive(y)) is False |
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def test_pow_pos_neg(): |
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assert satask(Q.nonnegative(x**2), Q.positive(x)) is True |
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assert satask(Q.nonpositive(x**2), Q.positive(x)) is False |
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assert satask(Q.positive(x**2), Q.positive(x)) is True |
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assert satask(Q.negative(x**2), Q.positive(x)) is False |
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assert satask(Q.real(x**2), Q.positive(x)) is True |
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assert satask(Q.nonnegative(x**2), Q.negative(x)) is True |
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assert satask(Q.nonpositive(x**2), Q.negative(x)) is False |
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assert satask(Q.positive(x**2), Q.negative(x)) is True |
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assert satask(Q.negative(x**2), Q.negative(x)) is False |
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assert satask(Q.real(x**2), Q.negative(x)) is True |
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assert satask(Q.nonnegative(x**2), Q.nonnegative(x)) is True |
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assert satask(Q.nonpositive(x**2), Q.nonnegative(x)) is None |
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assert satask(Q.positive(x**2), Q.nonnegative(x)) is None |
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assert satask(Q.negative(x**2), Q.nonnegative(x)) is False |
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assert satask(Q.real(x**2), Q.nonnegative(x)) is True |
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assert satask(Q.nonnegative(x**2), Q.nonpositive(x)) is True |
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assert satask(Q.nonpositive(x**2), Q.nonpositive(x)) is None |
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assert satask(Q.positive(x**2), Q.nonpositive(x)) is None |
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assert satask(Q.negative(x**2), Q.nonpositive(x)) is False |
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assert satask(Q.real(x**2), Q.nonpositive(x)) is True |
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assert satask(Q.nonnegative(x**3), Q.positive(x)) is True |
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assert satask(Q.nonpositive(x**3), Q.positive(x)) is False |
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assert satask(Q.positive(x**3), Q.positive(x)) is True |
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assert satask(Q.negative(x**3), Q.positive(x)) is False |
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assert satask(Q.real(x**3), Q.positive(x)) is True |
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assert satask(Q.nonnegative(x**3), Q.negative(x)) is False |
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assert satask(Q.nonpositive(x**3), Q.negative(x)) is True |
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assert satask(Q.positive(x**3), Q.negative(x)) is False |
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assert satask(Q.negative(x**3), Q.negative(x)) is True |
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assert satask(Q.real(x**3), Q.negative(x)) is True |
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assert satask(Q.nonnegative(x**3), Q.nonnegative(x)) is True |
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assert satask(Q.nonpositive(x**3), Q.nonnegative(x)) is None |
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assert satask(Q.positive(x**3), Q.nonnegative(x)) is None |
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assert satask(Q.negative(x**3), Q.nonnegative(x)) is False |
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assert satask(Q.real(x**3), Q.nonnegative(x)) is True |
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assert satask(Q.nonnegative(x**3), Q.nonpositive(x)) is None |
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assert satask(Q.nonpositive(x**3), Q.nonpositive(x)) is True |
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assert satask(Q.positive(x**3), Q.nonpositive(x)) is False |
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assert satask(Q.negative(x**3), Q.nonpositive(x)) is None |
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assert satask(Q.real(x**3), Q.nonpositive(x)) is True |
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assert satask(Q.nonnegative(x**-2), Q.nonpositive(x)) is None |
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assert satask(Q.nonpositive(x**-2), Q.nonpositive(x)) is None |
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assert satask(Q.positive(x**-2), Q.nonpositive(x)) is None |
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assert satask(Q.negative(x**-2), Q.nonpositive(x)) is None |
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assert satask(Q.real(x**-2), Q.nonpositive(x)) is None |
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def test_prime_composite(): |
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assert satask(Q.prime(x), Q.composite(x)) is False |
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assert satask(Q.composite(x), Q.prime(x)) is False |
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assert satask(Q.composite(x), ~Q.prime(x)) is None |
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assert satask(Q.prime(x), ~Q.composite(x)) is None |
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assert satask(Q.prime(x), Q.integer(x) & Q.positive(x) & ~Q.composite(x)) is None |
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assert satask(Q.prime(2)) is True |
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assert satask(Q.prime(4)) is False |
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assert satask(Q.prime(1)) is False |
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assert satask(Q.composite(1)) is False |
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def test_extract_predargs(): |
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props = CNF.from_prop(Q.zero(Abs(x*y)) & Q.zero(x*y)) |
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assump = CNF.from_prop(Q.zero(x)) |
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context = CNF.from_prop(Q.zero(y)) |
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assert extract_predargs(props) == {Abs(x*y), x*y} |
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assert extract_predargs(props, assump) == {Abs(x*y), x*y, x} |
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assert extract_predargs(props, assump, context) == {Abs(x*y), x*y, x, y} |
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props = CNF.from_prop(Eq(x, y)) |
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assump = CNF.from_prop(Gt(y, z)) |
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assert extract_predargs(props, assump) == {x, y, z} |
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def test_get_relevant_clsfacts(): |
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exprs = {Abs(x*y)} |
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exprs, facts = get_relevant_clsfacts(exprs) |
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assert exprs == {x*y} |
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assert facts.clauses == \ |
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{frozenset({Literal(Q.odd(Abs(x*y)), False), Literal(Q.odd(x*y), True)}), |
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frozenset({Literal(Q.zero(Abs(x*y)), False), Literal(Q.zero(x*y), True)}), |
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frozenset({Literal(Q.even(Abs(x*y)), False), Literal(Q.even(x*y), True)}), |
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frozenset({Literal(Q.zero(Abs(x*y)), True), Literal(Q.zero(x*y), False)}), |
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frozenset({Literal(Q.even(Abs(x*y)), False), |
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Literal(Q.odd(Abs(x*y)), False), |
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Literal(Q.odd(x*y), True)}), |
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frozenset({Literal(Q.even(Abs(x*y)), False), |
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Literal(Q.even(x*y), True), |
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Literal(Q.odd(Abs(x*y)), False)}), |
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frozenset({Literal(Q.positive(Abs(x*y)), False), |
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Literal(Q.zero(Abs(x*y)), False)})} |
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