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test_satask.py
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test_satask.py
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from sympy.assumptions.satask import satask
from sympy import symbols, Q, assuming, Implies, MatrixSymbol, I, pi, Rational
from sympy.utilities.pytest import raises, XFAIL
x, y, z = symbols('x y z')
def test_satask():
# No relevant facts
assert satask(Q.real(x), Q.real(x)) is True
assert satask(Q.real(x), ~Q.real(x)) is False
assert satask(Q.real(x)) is None
assert satask(Q.real(x), Q.positive(x)) is True
assert satask(Q.positive(x), Q.real(x)) is None
assert satask(Q.real(x), ~Q.positive(x)) is None
assert satask(Q.positive(x), ~Q.real(x)) is False
raises(ValueError, lambda: satask(Q.real(x), Q.real(x) & ~Q.real(x)))
with assuming(Q.positive(x)):
assert satask(Q.real(x)) is True
assert satask(~Q.positive(x)) is False
raises(ValueError, lambda: satask(Q.real(x), ~Q.positive(x)))
assert satask(Q.zero(x), Q.nonzero(x)) is False
assert satask(Q.positive(x), Q.zero(x)) is False
assert satask(Q.real(x), Q.zero(x)) is True
assert satask(Q.zero(x), Q.zero(x*y)) is None
assert satask(Q.zero(x*y), Q.zero(x))
def test_zero():
"""
Everything in this test doesn't work with the ask handlers, and most
things would be very difficult or impossible to make work under that
model.
"""
assert satask(Q.zero(x) | Q.zero(y), Q.zero(x*y)) is True
assert satask(Q.zero(x*y), Q.zero(x) | Q.zero(y)) is True
assert satask(Implies(Q.zero(x), Q.zero(x*y))) is True
# This one in particular requires computing the fixed-point of the
# relevant facts, because going from Q.nonzero(x*y) -> ~Q.zero(x*y) and
# Q.zero(x*y) -> Equivalent(Q.zero(x*y), Q.zero(x) | Q.zero(y)) takes two
# steps.
assert satask(Q.zero(x) | Q.zero(y), Q.nonzero(x*y)) is False
assert satask(Q.zero(x), Q.zero(x**2)) is True
def test_zero_positive():
assert satask(Q.zero(x + y), Q.positive(x) & Q.positive(y)) is False
assert satask(Q.positive(x) & Q.positive(y), Q.zero(x + y)) is False
assert satask(Q.nonzero(x + y), Q.positive(x) & Q.positive(y)) is True
assert satask(Q.positive(x) & Q.positive(y), Q.nonzero(x + y)) is None
# This one requires several levels of forward chaining
assert satask(Q.zero(x*(x + y)), Q.positive(x) & Q.positive(y)) is False
assert satask(Q.positive(pi*x*y + 1), Q.positive(x) & Q.positive(y)) is True
assert satask(Q.positive(pi*x*y - 5), Q.positive(x) & Q.positive(y)) is None
def test_zero_pow():
assert satask(Q.zero(x**y), Q.zero(x) & Q.positive(y)) is True
assert satask(Q.zero(x**y), Q.nonzero(x) & Q.zero(y)) is False
assert satask(Q.zero(x), Q.zero(x**y)) is True
assert satask(Q.zero(x**y), Q.zero(x)) is None
@XFAIL
# Requires correct Q.square calculation first
def test_invertible():
A = MatrixSymbol('A', 5, 5)
B = MatrixSymbol('B', 5, 5)
assert satask(Q.invertible(A*B), Q.invertible(A) & Q.invertible(B)) is True
assert satask(Q.invertible(A), Q.invertible(A*B)) is True
assert satask(Q.invertible(A) & Q.invertible(B), Q.invertible(A*B)) is True
def test_prime():
assert satask(Q.prime(5)) is True
assert satask(Q.prime(6)) is False
assert satask(Q.prime(-5)) is False
assert satask(Q.prime(x*y), Q.integer(x) & Q.integer(y)) is None
assert satask(Q.prime(x*y), Q.prime(x) & Q.prime(y)) is False
def test_old_assump():
assert satask(Q.positive(1)) is True
assert satask(Q.positive(-1)) is False
assert satask(Q.positive(0)) is False
assert satask(Q.positive(I)) is False
assert satask(Q.positive(pi)) is True
assert satask(Q.negative(1)) is False
assert satask(Q.negative(-1)) is True
assert satask(Q.negative(0)) is False
assert satask(Q.negative(I)) is False
assert satask(Q.negative(pi)) is False
assert satask(Q.zero(1)) is False
assert satask(Q.zero(-1)) is False
assert satask(Q.zero(0)) is True
assert satask(Q.zero(I)) is False
assert satask(Q.zero(pi)) is False
assert satask(Q.nonzero(1)) is True
assert satask(Q.nonzero(-1)) is True
assert satask(Q.nonzero(0)) is False
assert satask(Q.nonzero(I)) is False
assert satask(Q.nonzero(pi)) is True
assert satask(Q.nonpositive(1)) is False
assert satask(Q.nonpositive(-1)) is True
assert satask(Q.nonpositive(0)) is True
assert satask(Q.nonpositive(I)) is False
assert satask(Q.nonpositive(pi)) is False
assert satask(Q.nonnegative(1)) is True
assert satask(Q.nonnegative(-1)) is False
assert satask(Q.nonnegative(0)) is True
assert satask(Q.nonnegative(I)) is False
assert satask(Q.nonnegative(pi)) is True
def test_rational_irrational():
assert satask(Q.irrational(2)) is False
assert satask(Q.rational(2)) is True
assert satask(Q.irrational(pi)) is True
assert satask(Q.rational(pi)) is False
assert satask(Q.irrational(I)) is False
assert satask(Q.rational(I)) is False
assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.irrational(y) &
Q.rational(z)) is None
assert satask(Q.irrational(x*y*z), Q.irrational(x) & Q.rational(y) &
Q.rational(z)) is True
assert satask(Q.irrational(pi*x*y), Q.rational(x) & Q.rational(y)) is True
assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.irrational(y) &
Q.rational(z)) is None
assert satask(Q.irrational(x + y + z), Q.irrational(x) & Q.rational(y) &
Q.rational(z)) is True
assert satask(Q.irrational(pi + x + y), Q.rational(x) & Q.rational(y)) is True
assert satask(Q.irrational(x*y*z), Q.rational(x) & Q.rational(y) &
Q.rational(z)) is False
assert satask(Q.rational(x*y*z), Q.rational(x) & Q.rational(y) &
Q.rational(z)) is True
assert satask(Q.irrational(x + y + z), Q.rational(x) & Q.rational(y) &
Q.rational(z)) is False
assert satask(Q.rational(x + y + z), Q.rational(x) & Q.rational(y) &
Q.rational(z)) is True
def test_even_satask():
assert satask(Q.even(2)) is True
assert satask(Q.even(3)) is False
assert satask(Q.even(x*y), Q.even(x) & Q.odd(y)) is True
assert satask(Q.even(x*y), Q.even(x) & Q.integer(y)) is True
assert satask(Q.even(x*y), Q.even(x) & Q.even(y)) is True
assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False
assert satask(Q.even(x*y), Q.even(x)) is None
assert satask(Q.even(x*y), Q.odd(x) & Q.integer(y)) is None
assert satask(Q.even(x*y), Q.odd(x) & Q.odd(y)) is False
assert satask(Q.even(abs(x)), Q.even(x)) is True
assert satask(Q.even(abs(x)), Q.odd(x)) is False
assert satask(Q.even(x), Q.even(abs(x))) is None # x could be complex
def test_odd_satask():
assert satask(Q.odd(2)) is False
assert satask(Q.odd(3)) is True
assert satask(Q.odd(x*y), Q.even(x) & Q.odd(y)) is False
assert satask(Q.odd(x*y), Q.even(x) & Q.integer(y)) is False
assert satask(Q.odd(x*y), Q.even(x) & Q.even(y)) is False
assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
assert satask(Q.odd(x*y), Q.even(x)) is None
assert satask(Q.odd(x*y), Q.odd(x) & Q.integer(y)) is None
assert satask(Q.odd(x*y), Q.odd(x) & Q.odd(y)) is True
assert satask(Q.odd(abs(x)), Q.even(x)) is False
assert satask(Q.odd(abs(x)), Q.odd(x)) is True
assert satask(Q.odd(x), Q.odd(abs(x))) is None # x could be complex
def test_integer():
assert satask(Q.integer(1)) is True
assert satask(Q.integer(Rational(1, 2))) is False
assert satask(Q.integer(x + y), Q.integer(x) & Q.integer(y)) is True
assert satask(Q.integer(x + y), Q.integer(x)) is None
assert satask(Q.integer(x + y), Q.integer(x) & ~Q.integer(y)) is False
assert satask(Q.integer(x + y + z), Q.integer(x) & Q.integer(y) &
~Q.integer(z)) is False
assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y) &
~Q.integer(z)) is None
assert satask(Q.integer(x + y + z), Q.integer(x) & ~Q.integer(y)) is None
assert satask(Q.integer(x + y), Q.integer(x) & Q.irrational(y)) is False
assert satask(Q.integer(x*y), Q.integer(x) & Q.integer(y)) is True
assert satask(Q.integer(x*y), Q.integer(x)) is None
assert satask(Q.integer(x*y), Q.integer(x) & ~Q.integer(y)) is None
assert satask(Q.integer(x*y), Q.integer(x) & ~Q.rational(y)) is False
assert satask(Q.integer(x*y*z), Q.integer(x) & Q.integer(y) &
~Q.rational(z)) is False
assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y) &
~Q.rational(z)) is None
assert satask(Q.integer(x*y*z), Q.integer(x) & ~Q.rational(y)) is None
assert satask(Q.integer(x*y), Q.integer(x) & Q.irrational(y)) is False
def test_abs():
assert satask(Q.nonnegative(abs(x))) is True
assert satask(Q.positive(abs(x)), ~Q.zero(x)) is True
assert satask(Q.zero(x), ~Q.zero(abs(x))) is False
assert satask(Q.zero(x), Q.zero(abs(x))) is True
assert satask(Q.nonzero(x), ~Q.zero(abs(x))) is None # x could be complex
assert satask(Q.zero(abs(x)), Q.zero(x)) is True
def test_imaginary():
assert satask(Q.imaginary(2*I)) is True
assert satask(Q.imaginary(x*y), Q.imaginary(x)) is None
assert satask(Q.imaginary(x*y), Q.imaginary(x) & Q.real(y)) is True
assert satask(Q.imaginary(x), Q.real(x)) is False
assert satask(Q.imaginary(1)) is False
assert satask(Q.imaginary(x*y), Q.real(x) & Q.real(y)) is False
assert satask(Q.imaginary(x + y), Q.real(x) & Q.real(y)) is False
def test_real():
assert satask(Q.real(x*y), Q.real(x) & Q.real(y)) is True
assert satask(Q.real(x + y), Q.real(x) & Q.real(y)) is True
assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.real(z)) is True
assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y)) is None
assert satask(Q.real(x*y*z), Q.real(x) & Q.real(y) & Q.imaginary(z)) is False
assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y) & Q.real(z)) is True
assert satask(Q.real(x + y + z), Q.real(x) & Q.real(y)) is None
def test_pos_neg():
assert satask(~Q.positive(x), Q.negative(x)) is True
assert satask(~Q.negative(x), Q.positive(x)) is True
assert satask(Q.positive(x + y), Q.positive(x) & Q.positive(y)) is True
assert satask(Q.negative(x + y), Q.negative(x) & Q.negative(y)) is True
assert satask(Q.positive(x + y), Q.negative(x) & Q.negative(y)) is False
assert satask(Q.negative(x + y), Q.positive(x) & Q.positive(y)) is False
def test_pow_pos_neg():
assert satask(Q.nonnegative(x**2), Q.positive(x)) is True
assert satask(Q.nonpositive(x**2), Q.positive(x)) is False
assert satask(Q.positive(x**2), Q.positive(x)) is True
assert satask(Q.negative(x**2), Q.positive(x)) is False
assert satask(Q.real(x**2), Q.positive(x)) is True
assert satask(Q.nonnegative(x**2), Q.negative(x)) is True
assert satask(Q.nonpositive(x**2), Q.negative(x)) is False
assert satask(Q.positive(x**2), Q.negative(x)) is True
assert satask(Q.negative(x**2), Q.negative(x)) is False
assert satask(Q.real(x**2), Q.negative(x)) is True
assert satask(Q.nonnegative(x**2), Q.nonnegative(x)) is True
assert satask(Q.nonpositive(x**2), Q.nonnegative(x)) is None
assert satask(Q.positive(x**2), Q.nonnegative(x)) is None
assert satask(Q.negative(x**2), Q.nonnegative(x)) is False
assert satask(Q.real(x**2), Q.nonnegative(x)) is True
assert satask(Q.nonnegative(x**2), Q.nonpositive(x)) is True
assert satask(Q.nonpositive(x**2), Q.nonpositive(x)) is None
assert satask(Q.positive(x**2), Q.nonpositive(x)) is None
assert satask(Q.negative(x**2), Q.nonpositive(x)) is False
assert satask(Q.real(x**2), Q.nonpositive(x)) is True
assert satask(Q.nonnegative(x**3), Q.positive(x)) is True
assert satask(Q.nonpositive(x**3), Q.positive(x)) is False
assert satask(Q.positive(x**3), Q.positive(x)) is True
assert satask(Q.negative(x**3), Q.positive(x)) is False
assert satask(Q.real(x**3), Q.positive(x)) is True
assert satask(Q.nonnegative(x**3), Q.negative(x)) is False
assert satask(Q.nonpositive(x**3), Q.negative(x)) is True
assert satask(Q.positive(x**3), Q.negative(x)) is False
assert satask(Q.negative(x**3), Q.negative(x)) is True
assert satask(Q.real(x**3), Q.negative(x)) is True
assert satask(Q.nonnegative(x**3), Q.nonnegative(x)) is True
assert satask(Q.nonpositive(x**3), Q.nonnegative(x)) is None
assert satask(Q.positive(x**3), Q.nonnegative(x)) is None
assert satask(Q.negative(x**3), Q.nonnegative(x)) is False
assert satask(Q.real(x**3), Q.nonnegative(x)) is True
assert satask(Q.nonnegative(x**3), Q.nonpositive(x)) is None
assert satask(Q.nonpositive(x**3), Q.nonpositive(x)) is True
assert satask(Q.positive(x**3), Q.nonpositive(x)) is False
assert satask(Q.negative(x**3), Q.nonpositive(x)) is None
assert satask(Q.real(x**3), Q.nonpositive(x)) is True
# If x is zero, x**negative is not real.
assert satask(Q.nonnegative(x**-2), Q.nonpositive(x)) is None
assert satask(Q.nonpositive(x**-2), Q.nonpositive(x)) is None
assert satask(Q.positive(x**-2), Q.nonpositive(x)) is None
assert satask(Q.negative(x**-2), Q.nonpositive(x)) is None
assert satask(Q.real(x**-2), Q.nonpositive(x)) is None
# We could deduce things for negative powers if x is nonzero, but it
# isn't implemented yet.
def test_prime_composite():
assert satask(Q.prime(x), Q.composite(x)) is False
assert satask(Q.composite(x), Q.prime(x)) is False
assert satask(Q.composite(x), ~Q.prime(x)) is None
assert satask(Q.prime(x), ~Q.composite(x)) is None
# since 1 is neither prime nor composite the following should hold
assert satask(Q.prime(x), Q.integer(x) & Q.positive(x) & ~Q.composite(x)) is None
assert satask(Q.prime(2)) is True
assert satask(Q.prime(4)) is False
assert satask(Q.prime(1)) is False
assert satask(Q.composite(1)) is False