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 __divmod__(self, other):
if not isinstance(other, Polynomial):
dm_list = [(exp, divmod(coeff, other)) for exp, coeff in self.Data]
return (
Polynomial(self.Base, [(exp, quot) for (exp, (quot, rem)) in dm_list]),
Polynomial(self.Base, [(exp, rem) for (exp, (quot, rem)) in dm_list]),
)
if other.Base != self.Base:
assert self.VarLess == other.VarLess
if self.VarLess(self.Base, other.Base):
dm_list = [(exp, divmod(coeff, other)) for exp, coeff in self.Data]
return (
Polynomial(self.Base, [(exp, quot) for (exp, (quot, rem)) in dm_list]),
Polynomial(self.Base, [(exp, rem) for (exp, (quot, rem)) in dm_list]),
)
else:
other_unit = Polynomial(other.Base, ((0, other.unit),), self.VarLess)
quot, rem = divmod(other_unit, other)
return quot * self, rem * self
if other.degree == -1:
raise DivisionByZeroError
quot = Polynomial(self.Base, ())
rem = self
other_lead_coeff = other.Data[-1][1]
other_lead_exp = other.Data[-1][0]
coeffs_are_field = isinstance(traits(self.Unit), FieldTraits)
from pymbolic.primitives import quotient
while rem.degree >= other.degree:
if coeffs_are_field:
coeff_factor = quotient(rem.Data[-1][1], other_lead_coeff)
else:
coeff_factor, lead_rem = divmod(rem.Data[-1][1], other_lead_coeff)
if lead_rem:
return quot, rem
deg_diff = rem.Data[-1][0] - other_lead_exp
this_fac = Polynomial(self.Base, ((deg_diff, coeff_factor),))
quot += this_fac
rem -= this_fac * other
return quot, rem
def __divmod__(self, other):
if not isinstance(other, Polynomial):
dm_list = [(exp, divmod(coeff, other)) for exp, coeff in self.Data]
return Polynomial(self.Base, [(exp, quot) for (exp, (quot, rem)) in dm_list]),\
Polynomial(self.Base, [(exp, rem) for (exp, (quot, rem)) in dm_list])
if other.Base != self.Base:
assert self.VarLess == other.VarLess
if self.VarLess(self.Base, other.Base):
dm_list = [(exp, divmod(coeff, other))
for exp, coeff in self.Data]
return Polynomial(self.Base, [(exp, quot) for (exp, (quot, rem)) in dm_list]),\
Polynomial(self.Base, [(exp, rem) for (exp, (quot, rem)) in dm_list])
else:
other_unit = Polynomial(other.Base, ((0, other.unit), ),
self.VarLess)
quot, rem = divmod(other_unit, other)
return quot * self, rem * self
if other.degree == -1:
raise DivisionByZeroError
quot = Polynomial(self.Base, ())
rem = self
other_lead_coeff = other.Data[-1][1]
other_lead_exp = other.Data[-1][0]
coeffs_are_field = isinstance(traits(self.Unit), FieldTraits)
from pymbolic.primitives import quotient
while rem.degree >= other.degree:
if coeffs_are_field:
coeff_factor = quotient(rem.Data[-1][1], other_lead_coeff)
else:
coeff_factor, lead_rem = divmod(rem.Data[-1][1],
other_lead_coeff)
if lead_rem:
return quot, rem
deg_diff = rem.Data[-1][0] - other_lead_exp
this_fac = Polynomial(self.Base, ((deg_diff, coeff_factor), ))
quot += this_fac
rem -= this_fac * other
return quot, rem
def map_math_functions_by_name(i, func, pars):
try:
f = pymbolic.evaluate(func, {"math": math, "cmath": cmath})
except pymbolic.mapper.evaluator.UnknownVariableError:
raise RuntimeError("No derivative of non-constant function "+str(func))
def make_f(name):
return primitives.Lookup(primitives.Variable("math"), name)
if f is math.sin and len(pars) == 1:
return make_f("cos")(*pars)
elif f is math.cos and len(pars) == 1:
return -make_f("sin")(*pars)
elif f is math.tan and len(pars) == 1:
return make_f("tan")(*pars)**2+1
elif f is math.log and len(pars) == 1:
return primitives.quotient(1, pars[0])
elif f is math.exp and len(pars) == 1:
return make_f("exp")(*pars)
else:
raise RuntimeError("unrecognized function, cannot differentiate")
def map_math_functions_by_name(i, func, pars, allowed_nonsmoothness="none"):
def make_f(name):
return primitives.Lookup(primitives.Variable("math"), name)
if func == make_f("sin") and len(pars) == 1:
return make_f("cos")(*pars)
elif func == make_f("cos") and len(pars) == 1:
return -make_f("sin")(*pars)
elif func == make_f("tan") and len(pars) == 1:
return make_f("tan")(*pars)**2 + 1
elif func == make_f("log") and len(pars) == 1:
return primitives.quotient(1, pars[0])
elif func == make_f("exp") and len(pars) == 1:
return make_f("exp")(*pars)
elif func == make_f("sinh") and len(pars) == 1:
return make_f("cosh")(*pars)
elif func == make_f("cosh") and len(pars) == 1:
return make_f("sinh")(*pars)
elif func == make_f("tanh") and len(pars) == 1:
return 1 - make_f("tanh")(*pars)**2
elif func == make_f("expm1") and len(pars) == 1:
return make_f("exp")(*pars)
elif func == make_f("fabs") and len(pars) == 1:
if allowed_nonsmoothness in ["continuous", "discontinuous"]:
from pymbolic.functions import sign
return sign(*pars)
else:
raise ValueError("fabs is not smooth"
", pass allowed_nonsmoothness='continuous' "
"to return sign")
elif func == make_f("copysign") and len(pars) == 2:
if allowed_nonsmoothness == "discontinuous":
return 0
else:
raise ValueError("sign is discontinuous"
", pass allowed_nonsmoothness='discontinuous' "
"to return 0")
else:
raise RuntimeError("unrecognized function, cannot differentiate")
