def gcd_terms(terms):
"""
Compute the GCD of ``terms`` and put them together.
**Example**
>>> from sympy.core import gcd_terms
>>> from sympy.abc import x, y
>>> gcd_terms((x + 1)**2*y + (x + 1)*y**2)
y*(x + 1)*(x + y + 1)
"""
from sympy.polys.polytools import _keep_coeff
cont, numer, denom = _gcd_terms(sympify(terms))
coeff, factors = cont.as_coeff_Mul()
return _keep_coeff(coeff, factors*numer/denom)
def as_content_primitive(self):
"""Return the tuple (R, self/R) where R is the positive Rational
extracted from self.
**Examples**
>>> from sympy import sqrt
>>> sqrt(4 + 4*sqrt(2)).as_content_primitive()
(2, sqrt(1 + sqrt(2)))
>>> sqrt(3 + 3*sqrt(2)).as_content_primitive()
(1, sqrt(3)*sqrt(1 + sqrt(2)))
>>> from sympy import separate, powsimp, Mul
>>> from sympy.abc import x, y
>>> ((2*x + 2)**2).as_content_primitive()
(4, (x + 1)**2)
>>> (4**((1 + y)/2)).as_content_primitive()
(2, 4**(y/2))
>>> (3**((1 + y)/2)).as_content_primitive()
(1, 3**((y + 1)/2))
>>> (3**((5 + y)/2)).as_content_primitive()
(9, 3**((y + 1)/2))
>>> eq = 3**(2 + 2*x)
>>> powsimp(eq) == eq
True
>>> eq.as_content_primitive()
(9, 3**(2*x))
>>> powsimp(Mul(*_))
9*9**x
>>> eq = (2 + 2*x)**y
>>> s = separate(eq); s.is_Mul, s
(False, (2*x + 2)**y)
>>> eq.as_content_primitive()
(1, (2*(x + 1))**y)
>>> s = separate(_[1]); s.is_Mul, s
(True, 2**y*(x + 1)**y)
See docstring of Expr.as_content_primitive for more examples.
"""
from sympy.polys.polytools import _keep_coeff
b, e = self.as_base_exp()
b = _keep_coeff(*b.as_content_primitive())
ce, pe = e.as_content_primitive()
if b.is_Rational:
#e
#= ce*pe
#= ce*(h + t)
#= ce*h + ce*t
#=> self
#= b**(ce*h)*b**(ce*t)
#= b**(cehp/cehq)*b**(ce*t)
#= b**(iceh+r/cehq)*b**(ce*t)
#= b**(iceh)*b**(r/cehq)*b**(ce*t)
#= b**(iceh)*b**(ce*t + r/cehq)
h, t = pe.as_coeff_Add()
if h.is_Rational:
ceh = ce*h
c = Pow(b, ceh)
r = S.Zero
if not c.is_Rational:
iceh, r = divmod(ceh.p, ceh.q)
c = Pow(b, iceh)
return c, Pow(b, _keep_coeff(ce, t + r/ce/ceh.q))
e = _keep_coeff(ce, pe)
# b**e = (h*t)**e = h**e*t**e = c*m*t**e
if e.is_Rational and b.is_Mul:
h, t = b.as_content_primitive() # h is positive
c, m = Pow(h, e).as_coeff_Mul() # so c is positive
m, me = m.as_base_exp()
if m is S.One or me == e: # probably always true
# return the following, not return c, m*Pow(t, e)
# which would change Pow into Mul; we let sympy
# decide what to do by using the unevaluated Mul
return c, Pow(_keep_coeff(m, t), e)
return S.One, Pow(b, e)