def pushout_univariate_factors(self, other, var, Sfactors, Ofactors):
try:
return merge_overlapping(Sfactors, Ofactors, lambda f: (underlying_class(f), f._var_.var_repr))
except ValueError:
pass
cm = sage.structure.element.get_coercion_model()
try:
Z = cm.common_parent(*Sfactors + Ofactors)
return (Z,), (Z,)
except TypeError:
pass
def subfactors(F):
for f in F:
if isinstance(f, GenericProduct):
for g in subfactors(f.cartesian_factors()):
yield g
else:
yield f
try:
return merge_overlapping(
tuple(subfactors(Sfactors)),
tuple(subfactors(Ofactors)),
lambda f: (underlying_class(f), f._var_.var_repr),
)
except ValueError:
pass
from sage.structure.coerce_exceptions import CoercionException
raise CoercionException(
"Cannot construct the pushout of %s and %s: The factors "
"with variables %s are not overlapping, "
"no common parent was found, and "
"splitting the factors was unsuccessful." % (self, other, var)
)
def pushout_univariate_factors(self, other, var, Sfactors, Ofactors):
try:
return merge_overlapping(
Sfactors, Ofactors, lambda f:
(underlying_class(f), f._var_.var_repr))
except ValueError:
pass
cm = sage.structure.element.get_coercion_model()
try:
Z = cm.common_parent(*Sfactors + Ofactors)
return (Z, ), (Z, )
except TypeError:
pass
def subfactors(F):
for f in F:
if isinstance(f, GenericProduct):
for g in subfactors(f.cartesian_factors()):
yield g
else:
yield f
try:
return merge_overlapping(
tuple(subfactors(Sfactors)), tuple(subfactors(Ofactors)),
lambda f: (underlying_class(f), f._var_.var_repr))
except ValueError:
pass
from sage.structure.coerce_exceptions import CoercionException
raise CoercionException(
'Cannot construct the pushout of %s and %s: The factors '
'with variables %s are not overlapping, '
'no common parent was found, and '
'splitting the factors was unsuccessful.' % (self, other, var))
def _create_element_in_extension_(self, element):
r"""
Create an element in an extension of this Cartesian product of
growth groups which is chosen according to the input ``element``.
INPUT:
- ``element`` -- a tuple.
OUTPUT:
An element.
EXAMPLES::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: G = GrowthGroup('z^ZZ * log(z)^ZZ')
sage: z = G('z')[0]
sage: lz = G('log(z)')[1]
sage: G._create_element_in_extension_((z^3, lz)).parent()
Growth Group z^ZZ * log(z)^ZZ
sage: G._create_element_in_extension_((z^(1/2), lz)).parent()
Growth Group z^QQ * log(z)^ZZ
::
sage: G._create_element_in_extension_((3, 3, 3))
Traceback (most recent call last):
...
ValueError: Cannot create (3, 3, 3) as a Cartesian product like
Growth Group z^ZZ * log(z)^ZZ.
"""
factors = self.cartesian_factors()
if len(element) != len(factors):
raise ValueError(
'Cannot create %s as a Cartesian product like %s.' %
(element, self))
if all(n.parent() is f for n, f in zip(element, factors)):
parent = self
else:
from misc import underlying_class
parent = underlying_class(self)(tuple(n.parent() for n in element),
category=self.category())
return parent(element)
def _create_element_in_extension_(self, element):
r"""
Create an element in an extension of this Cartesian product of
growth groups which is chosen according to the input ``element``.
INPUT:
- ``element`` -- a tuple.
OUTPUT:
An element.
EXAMPLES::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: G = GrowthGroup('z^ZZ * log(z)^ZZ')
sage: z = G('z')[0]
sage: lz = G('log(z)')[1]
sage: G._create_element_in_extension_((z^3, lz)).parent()
Growth Group z^ZZ * log(z)^ZZ
sage: G._create_element_in_extension_((z^(1/2), lz)).parent()
Growth Group z^QQ * log(z)^ZZ
::
sage: G._create_element_in_extension_((3, 3, 3))
Traceback (most recent call last):
...
ValueError: Cannot create (3, 3, 3) as a Cartesian product like
Growth Group z^ZZ * log(z)^ZZ.
"""
factors = self.cartesian_factors()
if len(element) != len(factors):
raise ValueError('Cannot create %s as a Cartesian product like %s.' %
(element, self))
if all(n.parent() is f for n, f in zip(element, factors)):
parent = self
else:
from misc import underlying_class
parent = underlying_class(self)(tuple(n.parent() for n in element),
category=self.category())
return parent(element)