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
>>> (3 + 3*sqrt(2)).as_content_primitive()
(3, 1 + sqrt(2))
Radical content is also factored out of the primitive:
>>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive()
(2, sqrt(2)*(1 + 2*sqrt(5)))
See docstring of Expr.as_content_primitive for more examples.
"""
con, prim = Add(*[_keep_coeff(*a.as_content_primitive()) for a in self.args]).primitive()
if prim.is_Add:
# look for common radicals that can be removed
args = prim.args
rads = []
common_q = None
for m in args:
term_rads = defaultdict(list)
for ai in Mul.make_args(m):
if ai.is_Pow:
b, e = ai.as_base_exp()
if e.is_Rational and b.is_Integer and b > 0:
term_rads[e.q].append(int(b)**e.p)
if not term_rads:
break
if common_q is None:
common_q = set(term_rads.keys())
else:
common_q = common_q & set(term_rads.keys())
if not common_q:
break
rads.append(term_rads)
else:
# process rads
# keep only those in common_q
for r in rads:
for q in r.keys():
if q not in common_q:
r.pop(q)
for q in r:
r[q] = prod(r[q])
# find the gcd of bases for each q
G = []
for q in common_q:
g = reduce(igcd, [r[q] for r in rads], 0)
if g != 1:
G.append(Pow(g, Rational(1, q)))
if G:
G = Mul(*G)
args = [ai/G for ai in args]
prim = G*Add(*args)
return con, prim
def as_content_primitive(self, radical=False):
"""Return the tuple (R, self/R) where R is the positive Rational
extracted from self. If radical is True (default is False) then
common radicals will be removed and included as a factor of the
primitive expression.
**Examples**
>>> from sympy import sqrt
>>> (3 + 3*sqrt(2)).as_content_primitive()
(3, 1 + sqrt(2))
Radical content can also be factored out of the primitive:
>>> (2*sqrt(2) + 4*sqrt(10)).as_content_primitive(radical=True)
(2, sqrt(2)*(1 + 2*sqrt(5)))
See docstring of Expr.as_content_primitive for more examples.
"""
con, prim = Add(*[_keep_coeff(*a.as_content_primitive(radical=radical)) for a in self.args]).primitive()
if radical and prim.is_Add:
# look for common radicals that can be removed
args = prim.args
rads = []
common_q = None
for m in args:
term_rads = defaultdict(list)
for ai in Mul.make_args(m):
if ai.is_Pow:
b, e = ai.as_base_exp()
if e.is_Rational and b.is_Integer and b > 0:
term_rads[e.q].append(int(b)**e.p)
if not term_rads:
break
if common_q is None:
common_q = set(term_rads.keys())
else:
common_q = common_q & set(term_rads.keys())
if not common_q:
break
rads.append(term_rads)
else:
# process rads
# keep only those in common_q
for r in rads:
for q in r.keys():
if q not in common_q:
r.pop(q)
for q in r:
r[q] = prod(r[q])
# find the gcd of bases for each q
G = []
for q in common_q:
g = reduce(igcd, [r[q] for r in rads], 0)
if g != 1:
G.append(Pow(g, Rational(1, q)))
if G:
G = Mul(*G)
args = [ai/G for ai in args]
prim = G*Add(*args)
return con, prim
