def extended_euclidean(q, r):
"""Return a tuple *(p, a, b)* such that :math:`p = aq + br`,
where *p* is the greatest common divisor of *q* and *r*.
See also the
`Wikipedia article on the Euclidean algorithm
<https://en.wikipedia.org/wiki/Euclidean_algorithm>`_.
"""
import pymbolic.traits as traits
# see [Davenport], Appendix, p. 214
t = traits.common_traits(q, r)
if t.norm(q) < t.norm(r):
p, a, b = extended_euclidean(r, q)
return p, b, a
Q = 1, 0 # noqa
R = 0, 1 # noqa
while r:
quot, t = divmod(q, r)
T = Q[0] - quot * R[0], Q[1] - quot * R[1] # noqa
q, r = r, t
Q, R = R, T
return q, Q[0], Q[1]
def extended_euclidean(q, r):
"""Return a tuple *(p, a, b)* such that :math:`p = aq + br`,
where *p* is the greatest common divisor of *q* and *r*.
See also the
`Wikipedia article on the Euclidean algorithm
<https://en.wikipedia.org/wiki/Euclidean_algorithm>`_.
"""
import pymbolic.traits as traits
# see [Davenport], Appendix, p. 214
t = traits.common_traits(q, r)
if t.norm(q) < t.norm(r):
p, a, b = extended_euclidean(r, q)
return p, b, a
Q = 1, 0 # noqa
R = 0, 1 # noqa
while r:
quot, t = divmod(q, r)
T = Q[0] - quot*R[0], Q[1] - quot*R[1] # noqa
q, r = r, t
Q, R = R, T
return q, Q[0], Q[1]
def __add__(self, other):
if not isinstance(other, Rational):
newother = Rational(other)
else:
newother = other
try:
t = traits.common_traits(self.Denominator, newother.Denominator)
newden = t.lcm(self.Denominator, newother.Denominator)
newnum = self.Numerator * newden/self.Denominator + \
newother.Numerator * newden/newother.Denominator
gcd = t.gcd(newden, newnum)
return primitives.quotient(newnum/gcd, newden/gcd)
except traits.NoTraitsError:
return primitives.Expression.__add__(self, other)
except traits.NoCommonTraitsError:
return primitives.Expression.__add__(self, other)
def __add__(self, other):
if not isinstance(other, Rational):
newother = Rational(other)
else:
newother = other
try:
t = traits.common_traits(self.Denominator, newother.Denominator)
newden = t.lcm(self.Denominator, newother.Denominator)
newnum = self.Numerator * newden/self.Denominator + \
newother.Numerator * newden/newother.Denominator
gcd = t.gcd(newden, newnum)
return primitives.quotient(newnum/gcd, newden/gcd)
except traits.NoTraitsError:
return primitives.Expression.__add__(self, other)
except traits.NoCommonTraitsError:
return primitives.Expression.__add__(self, other)
def quotient(numerator, denominator):
if not (denominator - 1):
return numerator
import pymbolic.rational as rat
if isinstance(numerator, rat.Rational) and \
isinstance(denominator, rat.Rational):
return numerator * denominator.reciprocal()
try:
c_traits = traits.common_traits(numerator, denominator)
if isinstance(c_traits, traits.EuclideanRingTraits):
return rat.Rational(numerator, denominator)
except traits.NoCommonTraitsError:
pass
except traits.NoTraitsError:
pass
return Quotient(numerator, denominator)
def quotient(numerator, denominator):
if not (denominator-1):
return numerator
import pymbolic.rational as rat
if isinstance(numerator, rat.Rational) and \
isinstance(denominator, rat.Rational):
return numerator * denominator.reciprocal()
try:
c_traits = traits.common_traits(numerator, denominator)
if isinstance(c_traits, traits.EuclideanRingTraits):
return rat.Rational(numerator, denominator)
except traits.NoCommonTraitsError:
pass
except traits.NoTraitsError:
pass
return Quotient(numerator, denominator)
def __mul__(self, other):
if not isinstance(other, Rational):
newother = Rational(other)
try:
t = traits.common_traits(self.Numerator, newother.Numerator,
self.Denominator, newother. Denominator)
gcd_1 = t.gcd(self.Numerator, newother.Denominator)
gcd_2 = t.gcd(newother.Numerator, self.Denominator)
new_num = self.Numerator/gcd_1 * newother.Numerator/gcd_2
new_denom = self.Denominator/gcd_2 * newother.Denominator/gcd_1
if not (new_denom-1):
return new_num
return Rational(new_num, new_denom)
except traits.NoTraitsError:
return primitives.Expression.__mul__(self, other)
except traits.NoCommonTraitsError:
return primitives.Expression.__mul__(self, other)
def __mul__(self, other):
if not isinstance(other, Rational):
newother = Rational(other)
try:
t = traits.common_traits(self.Numerator, newother.Numerator,
self.Denominator, newother. Denominator)
gcd_1 = t.gcd(self.Numerator, newother.Denominator)
gcd_2 = t.gcd(newother.Numerator, self.Denominator)
new_num = self.Numerator/gcd_1 * newother.Numerator/gcd_2
new_denom = self.Denominator/gcd_2 * newother.Denominator/gcd_1
if not (new_denom-1):
return new_num
return Rational(new_num, new_denom)
except traits.NoTraitsError:
return primitives.Expression.__mul__(self, other)
except traits.NoCommonTraitsError:
return primitives.Expression.__mul__(self, other)
def extended_euclidean(q, r):
"""Return a tuple (p, a, b) such that p = aq + br,
where p is the greatest common divisor.
"""
import pymbolic.traits as traits
# see [Davenport], Appendix, p. 214
t = traits.common_traits(q, r)
if t.norm(q) < t.norm(r):
p, a, b = extended_euclidean(r, q)
return p, b, a
Q = 1, 0
R = 0, 1
while r:
quot, t = divmod(q, r)
T = Q[0] - quot * R[0], Q[1] - quot * R[1]
q, r = r, t
Q, R = R, T
return q, Q[0], Q[1]
def extended_euclidean(q, r):
"""Return a tuple (p, a, b) such that p = aq + br,
where p is the greatest common divisor.
"""
import pymbolic.traits as traits
# see [Davenport], Appendix, p. 214
t = traits.common_traits(q, r)
if t.norm(q) < t.norm(r):
p, a, b = extended_euclidean(r, q)
return p, b, a
Q = 1, 0
R = 0, 1
while r:
quot, t = divmod(q, r)
T = Q[0] - quot*R[0], Q[1] - quot*R[1]
q, r = r, t
Q, R = R, T
return q, Q[0], Q[1]
