def test_issue_8458():
x, y = symbols('x y')
# Original issue
p1 = Piecewise((0, Eq(x, 0)), (sin(x), True))
assert p1.simplify() == sin(x)
# Slightly larger variant
p2 = Piecewise((x, Eq(x, 0)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p2.simplify() == sin(x)
# Test for problem highlighted during review
p3 = Piecewise((x+1, Eq(x, -1)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p3.simplify() == Piecewise((0, Eq(x, -1)), (sin(x), True))
def test_issue_8458():
x, y = symbols('x y')
# Original issue
p1 = Piecewise((0, Eq(x, 0)), (sin(x), True))
assert p1.simplify() == sin(x)
# Slightly larger variant
p2 = Piecewise((x, Eq(x, 0)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p2.simplify() == sin(x)
# Test for problem highlighted during review
p3 = Piecewise((x+1, Eq(x, -1)), (4*x + (y-2)**4, Eq(x, 0) & Eq(x+y, 2)), (sin(x), True))
assert p3.simplify() == Piecewise((0, Eq(x, -1)), (sin(x), True))
def test_unevaluated_CompoundDist():
# these tests need to be removed once they work with evaluation as they are currently not
# evaluated completely in sympy.
R = Rayleigh('R', 4)
X = Normal('X', 3, R)
_k = Dummy('k')
exprd = Piecewise((exp(S(3)/4 - x/4)/8, 2*Abs(arg(x - 3)) <= pi/2),
(sqrt(2)*Integral(exp(-(_k**4 + 16*(x - 3)**2)/(32*_k**2)),
(_k, 0, oo))/(32*sqrt(pi)), True))
assert (density(X)(x).simplify()).dummy_eq(exprd.simplify())
expre = Integral(_k*Integral(sqrt(2)*exp(-_k**2/32)*exp(-(_k - 3)**2/(2*_k**2)
)/(32*sqrt(pi)), (_k, 0, oo)), (_k, -oo, oo))
with ignore_warnings(UserWarning): ### TODO: Restore tests once warnings are removed
assert E(X, evaluate=False).rewrite(Integral).dummy_eq(expre)
X = Poisson('X', 1)
Y = Poisson('Y', X)
Z = Poisson('Z', Y)
exprd = exp(-1)*Sum(exp(-Y)*Y**x*Sum(exp(-X)*X**Y/(factorial(X)*factorial(Y)
), (X, 0, oo)), (Y, 0, oo))/factorial(x)
assert density(Z)(x).simplify() == exprd
N = Normal('N', 1, 2)
M = Normal('M', 3, 4)
D = Normal('D', M, N)
exprd = Integral(sqrt(2)*exp(-(_k - 1)**2/8)*Integral(exp(-(-_k + x
)**2/(2*_k**2))*exp(-(_k - 3)**2/32)/(8*pi*_k)
, (_k, -oo, oo))/(4*sqrt(pi)), (_k, -oo, oo))
assert density(D, evaluate=False)(x).dummy_eq(exprd)
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise(
(a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify(
) == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)),
Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y
+ a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify(
) == Piecewise(
(2*x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
args = (2, And(Eq(x, 2), Ge(y ,0))), (x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
args = (1, Eq(x, 0)), (sin(x)/x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
assert Piecewise((2 + y, And(Eq(x, 2), Eq(y, 0))), (x, True)
).simplify() == x
# check that x or f(x) are recognized as being Symbol-like for lhs
args = Tuple((1, Eq(x, 0)), (sin(x) + 1 + x, True))
ans = x + sin(x) + 1
f = Function('f')
assert Piecewise(*args).simplify() == ans
assert Piecewise(*args.subs(x, f(x))).simplify() == ans.subs(x, f(x))
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1) / x**2, Eq(x * (1 + x) - x**2, 0)),
((-1)**x * (-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise((a, And(Eq(a, 0), Eq(a + b, 0))),
(1, True)).simplify() == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise(
(2 * x * factorial(a) /
(factorial(y) * factorial(-y + a)), Eq(y, 0) & Eq(-y + a, 0)),
(2 * factorial(a) /
(factorial(y) * factorial(-y + a)), Eq(y, 0) & Eq(-y + a, 1)),
(0, True)).simplify() == Piecewise((2 * x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
args = (2, And(Eq(x, 2), Ge(y, 0))), (x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
args = (1, Eq(x, 0)), (sin(x) / x, True)
assert Piecewise(*args).simplify() == Piecewise(*args)
assert Piecewise((2 + y, And(Eq(x, 2), Eq(y, 0))),
(x, True)).simplify() == x
# check that x or f(x) are recognized as being Symbol-like for lhs
args = Tuple((1, Eq(x, 0)), (sin(x) + 1 + x, True))
ans = x + sin(x) + 1
f = Function('f')
assert Piecewise(*args).simplify() == ans
assert Piecewise(*args.subs(x, f(x))).simplify() == ans.subs(x, f(x))
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise(
(a, And(Eq(a, 0), Eq(a + b, 0))), (1, True)).simplify(
) == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise((2*x*factorial(a)/(factorial(y)*factorial(-y + a)),
Eq(y, 0) & Eq(-y + a, 0)), (2*factorial(a)/(factorial(y)*factorial(-y
+ a)), Eq(y, 0) & Eq(-y + a, 1)), (0, True)).simplify(
) == Piecewise(
(2*x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1) / x**2, Eq(x * (1 + x) - x**2, 0)),
((-1)**x * (-1), True))
assert p.simplify() == \
Piecewise((zoo, Eq(x, 0)), ((-1)**(x + 1), True))
# simplify when there are Eq in conditions
assert Piecewise((a, And(Eq(a, 0), Eq(a + b, 0))),
(1, True)).simplify() == Piecewise(
(0, And(Eq(a, 0), Eq(b, 0))), (1, True))
assert Piecewise(
(2 * x * factorial(a) /
(factorial(y) * factorial(-y + a)), Eq(y, 0) & Eq(-y + a, 0)),
(2 * factorial(a) /
(factorial(y) * factorial(-y + a)), Eq(y, 0) & Eq(-y + a, 1)),
(0, True)).simplify() == Piecewise((2 * x, And(Eq(a, 0), Eq(y, 0))),
(2, And(Eq(a, 1), Eq(y, 0))),
(0, True))
def test_unevaluated_CompoundDist():
# these tests need to be removed once they work with evaluation as they are currently not
# evaluated completely in sympy.
R = Rayleigh('R', 4)
X = Normal('X', 3, R)
_k = Dummy('k')
exprd = Piecewise(
(exp(S(3) / 4 - x / 4) / 8, 2 * Abs(arg(x - 3)) <= pi / 2),
(sqrt(2) * Integral(exp(-(_k**4 + 16 * (x - 3)**2) / (32 * _k**2)),
(_k, 0, oo)) / (32 * sqrt(pi)), True))
assert (density(X)(x).simplify()).dummy_eq(exprd.simplify())
expre = Integral(
Piecewise(
(_k * exp(S(3) / 4 - _k / 4) / 8, 2 * Abs(arg(_k - 3)) <= pi / 2),
(sqrt(2) * _k *
Integral(exp(-(_k**4 + 16 * (_k - 3)**2) / (32 * _k**2)),
(_k, 0, oo)) / (32 * sqrt(pi)), True)), (_k, -oo, oo))
assert (E(X, evaluate=False).simplify()).dummy_eq(expre.simplify())
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1) / x**2, Eq(x * (1 + x) - x**2, 0)),
((-1)**x * (-1), True))
assert p.simplify() == \
Piecewise((1 + 1/x**2, Eq(x, 0)), ((-1)**(x + 1), True))
def test_piecewise_simplify():
p = Piecewise(((x**2 + 1)/x**2, Eq(x*(1 + x) - x**2, 0)),
((-1)**x*(-1), True))
assert p.simplify() == \
Piecewise((1 + 1/x**2, Eq(x, 0)), ((-1)**(x + 1), True))
