295 lines
11 KiB
Python
295 lines
11 KiB
Python
|
from sympy.core.expr import unchanged
|
||
|
|
from sympy.sets import (ConditionSet, Intersection, FiniteSet,
|
||
|
|
EmptySet, Union, Contains, ImageSet)
|
||
|
|
from sympy.sets.sets import SetKind
|
||
|
|
from sympy.core.function import (Function, Lambda)
|
||
|
|
from sympy.core.mod import Mod
|
||
|
|
from sympy.core.kind import NumberKind
|
||
|
|
from sympy.core.numbers import (oo, pi)
|
||
|
|
from sympy.core.relational import (Eq, Ne)
|
||
|
|
from sympy.core.singleton import S
|
||
|
|
from sympy.core.symbol import (Symbol, symbols)
|
||
|
|
from sympy.functions.elementary.complexes import Abs
|
||
|
|
from sympy.functions.elementary.trigonometric import (asin, sin)
|
||
|
|
from sympy.logic.boolalg import And
|
||
|
|
from sympy.matrices.dense import Matrix
|
||
|
|
from sympy.matrices.expressions.matexpr import MatrixSymbol
|
||
|
|
from sympy.sets.sets import Interval
|
||
|
|
from sympy.testing.pytest import raises, warns_deprecated_sympy
|
||
|
|
|
||
|
|
|
||
|
|
w = Symbol('w')
|
||
|
|
x = Symbol('x')
|
||
|
|
y = Symbol('y')
|
||
|
|
z = Symbol('z')
|
||
|
|
f = Function('f')
|
||
|
|
|
||
|
|
|
||
|
|
def test_CondSet():
|
||
|
|
sin_sols_principal = ConditionSet(x, Eq(sin(x), 0),
|
||
|
|
Interval(0, 2*pi, False, True))
|
||
|
|
assert pi in sin_sols_principal
|
||
|
|
assert pi/2 not in sin_sols_principal
|
||
|
|
assert 3*pi not in sin_sols_principal
|
||
|
|
assert oo not in sin_sols_principal
|
||
|
|
assert 5 in ConditionSet(x, x**2 > 4, S.Reals)
|
||
|
|
assert 1 not in ConditionSet(x, x**2 > 4, S.Reals)
|
||
|
|
# in this case, 0 is not part of the base set so
|
||
|
|
# it can't be in any subset selected by the condition
|
||
|
|
assert 0 not in ConditionSet(x, y > 5, Interval(1, 7))
|
||
|
|
# since 'in' requires a true/false, the following raises
|
||
|
|
# an error because the given value provides no information
|
||
|
|
# for the condition to evaluate (since the condition does
|
||
|
|
# not depend on the dummy symbol): the result is `y > 5`.
|
||
|
|
# In this case, ConditionSet is just acting like
|
||
|
|
# Piecewise((Interval(1, 7), y > 5), (S.EmptySet, True)).
|
||
|
|
raises(TypeError, lambda: 6 in ConditionSet(x, y > 5,
|
||
|
|
Interval(1, 7)))
|
||
|
|
|
||
|
|
X = MatrixSymbol('X', 2, 2)
|
||
|
|
matrix_set = ConditionSet(X, Eq(X*Matrix([[1, 1], [1, 1]]), X))
|
||
|
|
Y = Matrix([[0, 0], [0, 0]])
|
||
|
|
assert matrix_set.contains(Y).doit() is S.true
|
||
|
|
Z = Matrix([[1, 2], [3, 4]])
|
||
|
|
assert matrix_set.contains(Z).doit() is S.false
|
||
|
|
|
||
|
|
assert isinstance(ConditionSet(x, x < 1, {x, y}).base_set,
|
||
|
|
FiniteSet)
|
||
|
|
raises(TypeError, lambda: ConditionSet(x, x + 1, {x, y}))
|
||
|
|
raises(TypeError, lambda: ConditionSet(x, x, 1))
|
||
|
|
|
||
|
|
I = S.Integers
|
||
|
|
U = S.UniversalSet
|
||
|
|
C = ConditionSet
|
||
|
|
assert C(x, False, I) is S.EmptySet
|
||
|
|
assert C(x, True, I) is I
|
||
|
|
assert C(x, x < 1, C(x, x < 2, I)
|
||
|
|
) == C(x, (x < 1) & (x < 2), I)
|
||
|
|
assert C(y, y < 1, C(x, y < 2, I)
|
||
|
|
) == C(x, (x < 1) & (y < 2), I), C(y, y < 1, C(x, y < 2, I))
|
||
|
|
assert C(y, y < 1, C(x, x < 2, I)
|
||
|
|
) == C(y, (y < 1) & (y < 2), I)
|
||
|
|
assert C(y, y < 1, C(x, y < x, I)
|
||
|
|
) == C(x, (x < 1) & (y < x), I)
|
||
|
|
assert unchanged(C, y, x < 1, C(x, y < x, I))
|
||
|
|
assert ConditionSet(x, x < 1).base_set is U
|
||
|
|
# arg checking is not done at instantiation but this
|
||
|
|
# will raise an error when containment is tested
|
||
|
|
assert ConditionSet((x,), x < 1).base_set is U
|
||
|
|
|
||
|
|
c = ConditionSet((x, y), x < y, I**2)
|
||
|
|
assert (1, 2) in c
|
||
|
|
assert (1, pi) not in c
|
||
|
|
|
||
|
|
raises(TypeError, lambda: C(x, x > 1, C((x, y), x > 1, I**2)))
|
||
|
|
# signature mismatch since only 3 args are accepted
|
||
|
|
raises(TypeError, lambda: C((x, y), x + y < 2, U, U))
|
||
|
|
|
||
|
|
|
||
|
|
def test_CondSet_intersect():
|
||
|
|
input_conditionset = ConditionSet(x, x**2 > 4, Interval(1, 4, False,
|
||
|
|
False))
|
||
|
|
other_domain = Interval(0, 3, False, False)
|
||
|
|
output_conditionset = ConditionSet(x, x**2 > 4, Interval(
|
||
|
|
1, 3, False, False))
|
||
|
|
assert Intersection(input_conditionset, other_domain
|
||
|
|
) == output_conditionset
|
||
|
|
|
||
|
|
|
||
|
|
def test_issue_9849():
|
||
|
|
assert ConditionSet(x, Eq(x, x), S.Naturals
|
||
|
|
) is S.Naturals
|
||
|
|
assert ConditionSet(x, Eq(Abs(sin(x)), -1), S.Naturals
|
||
|
|
) == S.EmptySet
|
||
|
|
|
||
|
|
|
||
|
|
def test_simplified_FiniteSet_in_CondSet():
|
||
|
|
assert ConditionSet(x, And(x < 1, x > -3), FiniteSet(0, 1, 2)
|
||
|
|
) == FiniteSet(0)
|
||
|
|
assert ConditionSet(x, x < 0, FiniteSet(0, 1, 2)) == EmptySet
|
||
|
|
assert ConditionSet(x, And(x < -3), EmptySet) == EmptySet
|
||
|
|
y = Symbol('y')
|
||
|
|
assert (ConditionSet(x, And(x > 0), FiniteSet(-1, 0, 1, y)) ==
|
||
|
|
Union(FiniteSet(1), ConditionSet(x, And(x > 0), FiniteSet(y))))
|
||
|
|
assert (ConditionSet(x, Eq(Mod(x, 3), 1), FiniteSet(1, 4, 2, y)) ==
|
||
|
|
Union(FiniteSet(1, 4), ConditionSet(x, Eq(Mod(x, 3), 1),
|
||
|
|
FiniteSet(y))))
|
||
|
|
|
||
|
|
|
||
|
|
def test_free_symbols():
|
||
|
|
assert ConditionSet(x, Eq(y, 0), FiniteSet(z)
|
||
|
|
).free_symbols == {y, z}
|
||
|
|
assert ConditionSet(x, Eq(x, 0), FiniteSet(z)
|
||
|
|
).free_symbols == {z}
|
||
|
|
assert ConditionSet(x, Eq(x, 0), FiniteSet(x, z)
|
||
|
|
).free_symbols == {x, z}
|
||
|
|
assert ConditionSet(x, Eq(x, 0), ImageSet(Lambda(y, y**2),
|
||
|
|
S.Integers)).free_symbols == set()
|
||
|
|
|
||
|
|
|
||
|
|
def test_bound_symbols():
|
||
|
|
assert ConditionSet(x, Eq(y, 0), FiniteSet(z)
|
||
|
|
).bound_symbols == [x]
|
||
|
|
assert ConditionSet(x, Eq(x, 0), FiniteSet(x, y)
|
||
|
|
).bound_symbols == [x]
|
||
|
|
assert ConditionSet(x, x < 10, ImageSet(Lambda(y, y**2), S.Integers)
|
||
|
|
).bound_symbols == [x]
|
||
|
|
assert ConditionSet(x, x < 10, ConditionSet(y, y > 1, S.Integers)
|
||
|
|
).bound_symbols == [x]
|
||
|
|
|
||
|
|
|
||
|
|
def test_as_dummy():
|
||
|
|
_0, _1 = symbols('_0 _1')
|
||
|
|
assert ConditionSet(x, x < 1, Interval(y, oo)
|
||
|
|
).as_dummy() == ConditionSet(_0, _0 < 1, Interval(y, oo))
|
||
|
|
assert ConditionSet(x, x < 1, Interval(x, oo)
|
||
|
|
).as_dummy() == ConditionSet(_0, _0 < 1, Interval(x, oo))
|
||
|
|
assert ConditionSet(x, x < 1, ImageSet(Lambda(y, y**2), S.Integers)
|
||
|
|
).as_dummy() == ConditionSet(
|
||
|
|
_0, _0 < 1, ImageSet(Lambda(_0, _0**2), S.Integers))
|
||
|
|
e = ConditionSet((x, y), x <= y, S.Reals**2)
|
||
|
|
assert e.bound_symbols == [x, y]
|
||
|
|
assert e.as_dummy() == ConditionSet((_0, _1), _0 <= _1, S.Reals**2)
|
||
|
|
assert e.as_dummy() == ConditionSet((y, x), y <= x, S.Reals**2
|
||
|
|
).as_dummy()
|
||
|
|
|
||
|
|
|
||
|
|
def test_subs_CondSet():
|
||
|
|
s = FiniteSet(z, y)
|
||
|
|
c = ConditionSet(x, x < 2, s)
|
||
|
|
assert c.subs(x, y) == c
|
||
|
|
assert c.subs(z, y) == ConditionSet(x, x < 2, FiniteSet(y))
|
||
|
|
assert c.xreplace({x: y}) == ConditionSet(y, y < 2, s)
|
||
|
|
|
||
|
|
assert ConditionSet(x, x < y, s
|
||
|
|
).subs(y, w) == ConditionSet(x, x < w, s.subs(y, w))
|
||
|
|
# if the user uses assumptions that cause the condition
|
||
|
|
# to evaluate, that can't be helped from SymPy's end
|
||
|
|
n = Symbol('n', negative=True)
|
||
|
|
assert ConditionSet(n, 0 < n, S.Integers) is S.EmptySet
|
||
|
|
p = Symbol('p', positive=True)
|
||
|
|
assert ConditionSet(n, n < y, S.Integers
|
||
|
|
).subs(n, x) == ConditionSet(n, n < y, S.Integers)
|
||
|
|
raises(ValueError, lambda: ConditionSet(
|
||
|
|
x + 1, x < 1, S.Integers))
|
||
|
|
assert ConditionSet(
|
||
|
|
p, n < x, Interval(-5, 5)).subs(x, p) == Interval(-5, 5), ConditionSet(
|
||
|
|
p, n < x, Interval(-5, 5)).subs(x, p)
|
||
|
|
assert ConditionSet(
|
||
|
|
n, n < x, Interval(-oo, 0)).subs(x, p
|
||
|
|
) == Interval(-oo, 0)
|
||
|
|
|
||
|
|
assert ConditionSet(f(x), f(x) < 1, {w, z}
|
||
|
|
).subs(f(x), y) == ConditionSet(f(x), f(x) < 1, {w, z})
|
||
|
|
|
||
|
|
# issue 17341
|
||
|
|
k = Symbol('k')
|
||
|
|
img1 = ImageSet(Lambda(k, 2*k*pi + asin(y)), S.Integers)
|
||
|
|
img2 = ImageSet(Lambda(k, 2*k*pi + asin(S.One/3)), S.Integers)
|
||
|
|
assert ConditionSet(x, Contains(
|
||
|
|
y, Interval(-1,1)), img1).subs(y, S.One/3).dummy_eq(img2)
|
||
|
|
|
||
|
|
assert (0, 1) in ConditionSet((x, y), x + y < 3, S.Integers**2)
|
||
|
|
|
||
|
|
raises(TypeError, lambda: ConditionSet(n, n < -10, Interval(0, 10)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_subs_CondSet_tebr():
|
||
|
|
with warns_deprecated_sympy():
|
||
|
|
assert ConditionSet((x, y), {x + 1, x + y}, S.Reals**2) == \
|
||
|
|
ConditionSet((x, y), Eq(x + 1, 0) & Eq(x + y, 0), S.Reals**2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_dummy_eq():
|
||
|
|
C = ConditionSet
|
||
|
|
I = S.Integers
|
||
|
|
c = C(x, x < 1, I)
|
||
|
|
assert c.dummy_eq(C(y, y < 1, I))
|
||
|
|
assert c.dummy_eq(1) == False
|
||
|
|
assert c.dummy_eq(C(x, x < 1, S.Reals)) == False
|
||
|
|
|
||
|
|
c1 = ConditionSet((x, y), Eq(x + 1, 0) & Eq(x + y, 0), S.Reals**2)
|
||
|
|
c2 = ConditionSet((x, y), Eq(x + 1, 0) & Eq(x + y, 0), S.Reals**2)
|
||
|
|
c3 = ConditionSet((x, y), Eq(x + 1, 0) & Eq(x + y, 0), S.Complexes**2)
|
||
|
|
assert c1.dummy_eq(c2)
|
||
|
|
assert c1.dummy_eq(c3) is False
|
||
|
|
assert c.dummy_eq(c1) is False
|
||
|
|
assert c1.dummy_eq(c) is False
|
||
|
|
|
||
|
|
# issue 19496
|
||
|
|
m = Symbol('m')
|
||
|
|
n = Symbol('n')
|
||
|
|
a = Symbol('a')
|
||
|
|
d1 = ImageSet(Lambda(m, m*pi), S.Integers)
|
||
|
|
d2 = ImageSet(Lambda(n, n*pi), S.Integers)
|
||
|
|
c1 = ConditionSet(x, Ne(a, 0), d1)
|
||
|
|
c2 = ConditionSet(x, Ne(a, 0), d2)
|
||
|
|
assert c1.dummy_eq(c2)
|
||
|
|
|
||
|
|
|
||
|
|
def test_contains():
|
||
|
|
assert 6 in ConditionSet(x, x > 5, Interval(1, 7))
|
||
|
|
assert (8 in ConditionSet(x, y > 5, Interval(1, 7))) is False
|
||
|
|
# `in` should give True or False; in this case there is not
|
||
|
|
# enough information for that result
|
||
|
|
raises(TypeError,
|
||
|
|
lambda: 6 in ConditionSet(x, y > 5, Interval(1, 7)))
|
||
|
|
# here, there is enough information but the comparison is
|
||
|
|
# not defined
|
||
|
|
raises(TypeError, lambda: 0 in ConditionSet(x, 1/x >= 0, S.Reals))
|
||
|
|
assert ConditionSet(x, y > 5, Interval(1, 7)
|
||
|
|
).contains(6) == (y > 5)
|
||
|
|
assert ConditionSet(x, y > 5, Interval(1, 7)
|
||
|
|
).contains(8) is S.false
|
||
|
|
assert ConditionSet(x, y > 5, Interval(1, 7)
|
||
|
|
).contains(w) == And(Contains(w, Interval(1, 7)), y > 5)
|
||
|
|
# This returns an unevaluated Contains object
|
||
|
|
# because 1/0 should not be defined for 1 and 0 in the context of
|
||
|
|
# reals.
|
||
|
|
assert ConditionSet(x, 1/x >= 0, S.Reals).contains(0) == \
|
||
|
|
Contains(0, ConditionSet(x, 1/x >= 0, S.Reals), evaluate=False)
|
||
|
|
c = ConditionSet((x, y), x + y > 1, S.Integers**2)
|
||
|
|
assert not c.contains(1)
|
||
|
|
assert c.contains((2, 1))
|
||
|
|
assert not c.contains((0, 1))
|
||
|
|
c = ConditionSet((w, (x, y)), w + x + y > 1, S.Integers*S.Integers**2)
|
||
|
|
assert not c.contains(1)
|
||
|
|
assert not c.contains((1, 2))
|
||
|
|
assert not c.contains(((1, 2), 3))
|
||
|
|
assert not c.contains(((1, 2), (3, 4)))
|
||
|
|
assert c.contains((1, (3, 4)))
|
||
|
|
|
||
|
|
|
||
|
|
def test_as_relational():
|
||
|
|
assert ConditionSet((x, y), x > 1, S.Integers**2).as_relational((x, y)
|
||
|
|
) == (x > 1) & Contains((x, y), S.Integers**2)
|
||
|
|
assert ConditionSet(x, x > 1, S.Integers).as_relational(x
|
||
|
|
) == Contains(x, S.Integers) & (x > 1)
|
||
|
|
|
||
|
|
|
||
|
|
def test_flatten():
|
||
|
|
"""Tests whether there is basic denesting functionality"""
|
||
|
|
inner = ConditionSet(x, sin(x) + x > 0)
|
||
|
|
outer = ConditionSet(x, Contains(x, inner), S.Reals)
|
||
|
|
assert outer == ConditionSet(x, sin(x) + x > 0, S.Reals)
|
||
|
|
|
||
|
|
inner = ConditionSet(y, sin(y) + y > 0)
|
||
|
|
outer = ConditionSet(x, Contains(y, inner), S.Reals)
|
||
|
|
assert outer != ConditionSet(x, sin(x) + x > 0, S.Reals)
|
||
|
|
|
||
|
|
inner = ConditionSet(x, sin(x) + x > 0).intersect(Interval(-1, 1))
|
||
|
|
outer = ConditionSet(x, Contains(x, inner), S.Reals)
|
||
|
|
assert outer == ConditionSet(x, sin(x) + x > 0, Interval(-1, 1))
|
||
|
|
|
||
|
|
|
||
|
|
def test_duplicate():
|
||
|
|
from sympy.core.function import BadSignatureError
|
||
|
|
# test coverage for line 95 in conditionset.py, check for duplicates in symbols
|
||
|
|
dup = symbols('a,a')
|
||
|
|
raises(BadSignatureError, lambda: ConditionSet(dup, x < 0))
|
||
|
|
|
||
|
|
|
||
|
|
def test_SetKind_ConditionSet():
|
||
|
|
assert ConditionSet(x, Eq(sin(x), 0), Interval(0, 2*pi)).kind is SetKind(NumberKind)
|
||
|
|
assert ConditionSet(x, x < 0).kind is SetKind(NumberKind)
|