def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + (2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False)
arg = x*(2*x + 4*y)
garg = 2*x*(x + 2*y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue 3040-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha*x**2 + alpha + x**3 - x*(alpha + 1)
rep = (alpha, (1 + sqrt(5))/2 + alpha1*x + alpha2*x**2 + alpha3*x**3)
s = (a/(x - alpha)).subs(*rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5)/2 - S(3)/2 + O(x)
# issue 2818
assert _gcd_terms([S.Zero, S.Zero]) == (0, 0, 1)
assert _gcd_terms([2*x + 4]) == (2, x + 2, 1)
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + (2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False)
arg = x*(2*x + 4*y)
garg = 2*x*(x + 2*y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue 3040-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha*x**2 + alpha + x**3 - x*(alpha + 1)
rep = (alpha, (1 + sqrt(5))/2 + alpha1*x + alpha2*x**2 + alpha3*x**3)
s = (a/(x - alpha)).subs(*rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5)/2 - S(3)/2 + O(x)
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \
(2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((Rational(6, 5)) * ((1 + x) / (1 + x**2)), 5 + x,
1)
assert _gcd_terms(Add.make_args(f)) == \
((Rational(6, 5))*((1 + x)/(1 + x**2)), 5 + x, 1)
newf = (Rational(6, 5)) * ((1 + x) * (5 + x) / (1 + x**2))
assert gcd_terms(f) == newf
args = Add.make_args(f)
# non-Basic sequences of terms treated as terms of Add
assert gcd_terms(list(args)) == newf
assert gcd_terms(tuple(args)) == newf
assert gcd_terms(set(args)) == newf
# but a Basic sequence is treated as a container
assert gcd_terms(Tuple(*args)) != newf
assert gcd_terms(Basic(Tuple(1, 3*y + 3*x*y), Tuple(1, 3))) == \
Basic((1, 3*y*(x + 1)), (1, 3))
# but we shouldn't change keys of a dictionary or some may be lost
assert gcd_terms(Dict((x*(1 + y), 2), (x + x*y, y + x*y))) == \
Dict({x*(y + 1): 2, x + x*y: y*(1 + x)})
assert gcd_terms((2 * x + 2)**3 +
(2 * x + 2)**2) == 4 * (x + 1)**2 * (2 * x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2 * x) == Mul(2, 1 + x, evaluate=False)
arg = x * (2 * x + 4 * y)
garg = 2 * x * (x + 2 * y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue 6139-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha * x**2 + alpha + x**3 - x * (alpha + 1)
rep = (alpha,
(1 + sqrt(5)) / 2 + alpha1 * x + alpha2 * x**2 + alpha3 * x**3)
s = (a / (x - alpha)).subs(*rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5) / 2 - Rational(3, 2) + O(x)
# issue 5917
assert _gcd_terms([S.Zero, S.Zero]) == (0, 0, 1)
assert _gcd_terms([2 * x + 4]) == (2, x + 2, 1)
eq = x / (x + 1 / x)
assert gcd_terms(eq, fraction=False) == eq
eq = x / 2 / y + 1 / x / y
assert gcd_terms(eq, fraction=True, clear=True) == \
(x**2 + 2)/(2*x*y)
assert gcd_terms(eq, fraction=True, clear=False) == \
(x**2/2 + 1)/(x*y)
assert gcd_terms(eq, fraction=False, clear=True) == \
(x + 2/x)/(2*y)
assert gcd_terms(eq, fraction=False, clear=False) == \
(x/2 + 1/x)/y
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + \
(2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == \
((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
newf = (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(f) == newf
args = Add.make_args(f)
# non-Basic sequences of terms treated as terms of Add
assert gcd_terms(list(args)) == newf
assert gcd_terms(tuple(args)) == newf
assert gcd_terms(set(args)) == newf
# but a Basic sequence is treated as a container
assert gcd_terms(Tuple(*args)) != newf
assert gcd_terms(Basic(Tuple(1, 3*y + 3*x*y), Tuple(1, 3))) == \
Basic((1, 3*y*(x + 1)), (1, 3))
# but we shouldn't change keys of a dictionary or some may be lost
assert gcd_terms(Dict((x*(1 + y), 2), (x + x*y, y + x*y))) == \
Dict({x*(y + 1): 2, x + x*y: y*(1 + x)})
assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False)
arg = x*(2*x + 4*y)
garg = 2*x*(x + 2*y)
assert gcd_terms(arg) == garg
assert gcd_terms(sin(arg)) == sin(garg)
# issue 6139-like
alpha, alpha1, alpha2, alpha3 = symbols('alpha:4')
a = alpha**2 - alpha*x**2 + alpha + x**3 - x*(alpha + 1)
rep = (alpha, (1 + sqrt(5))/2 + alpha1*x + alpha2*x**2 + alpha3*x**3)
s = (a/(x - alpha)).subs(*rep).series(x, 0, 1)
assert simplify(collect(s, x)) == -sqrt(5)/2 - S(3)/2 + O(x)
# issue 5917
assert _gcd_terms([S.Zero, S.Zero]) == (0, 0, 1)
assert _gcd_terms([2*x + 4]) == (2, x + 2, 1)
eq = x/(x + 1/x)
assert gcd_terms(eq, fraction=False) == eq
eq = x/2/y + 1/x/y
assert gcd_terms(eq, fraction=True, clear=True) == \
(x**2 + 2)/(2*x*y)
assert gcd_terms(eq, fraction=True, clear=False) == \
(x**2/2 + 1)/(x*y)
assert gcd_terms(eq, fraction=False, clear=True) == \
(x + 2/x)/(2*y)
assert gcd_terms(eq, fraction=False, clear=False) == \
(x/2 + 1/x)/y
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + (2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
def test_gcd_terms():
f = 2 * (x + 1) * (x + 4) / (5 * x**2 + 5) + (2 * x + 2) * (x + 5) / (
x**2 + 1) / 5 + (2 * x + 2) * (x + 6) / (5 * x**2 + 5)
assert _gcd_terms(f) == ((S(6) / 5) * ((1 + x) / (1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6) / 5) *
((1 + x) / (1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6) / 5) * ((1 + x) * (5 + x) / (1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6) / 5) * ((1 + x) * (5 + x) /
(1 + x**2))
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
def test_gcd_terms():
f = 2*(x + 1)*(x + 4)/(5*x**2 + 5) + (2*x + 2)*(x + 5)/(x**2 + 1)/5 + (2*x + 2)*(x + 6)/(5*x**2 + 5)
assert _gcd_terms(f) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6)/5)*((1 + x)/(1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6)/5)*((1 + x)*(5 + x)/(1 + x**2))
assert gcd_terms((2*x + 2)**3 + (2*x + 2)**2) == 4*(x + 1)**2*(2*x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2*x) == Mul(2, 1 + x, evaluate=False)
def test_gcd_terms():
f = 2 * (x + 1) * (x + 4) / (5 * x**2 + 5) + (2 * x + 2) * (x + 5) / (
x**2 + 1) / 5 + (2 * x + 2) * (x + 6) / (5 * x**2 + 5)
assert _gcd_terms(f) == ((S(6) / 5) * ((1 + x) / (1 + x**2)), 5 + x, 1)
assert _gcd_terms(Add.make_args(f)) == ((S(6) / 5) *
((1 + x) / (1 + x**2)), 5 + x, 1)
assert gcd_terms(f) == (S(6) / 5) * ((1 + x) * (5 + x) / (1 + x**2))
assert gcd_terms(Add.make_args(f)) == (S(6) / 5) * ((1 + x) * (5 + x) /
(1 + x**2))
assert gcd_terms((2 * x + 2)**3 +
(2 * x + 2)**2) == 4 * (x + 1)**2 * (2 * x + 3)
assert gcd_terms(0) == 0
assert gcd_terms(1) == 1
assert gcd_terms(x) == x
assert gcd_terms(2 + 2 * x) == Mul(2, 1 + x, evaluate=False)