def __init__(self, sets, category, **kwds):
r"""
See :class:`GenericProduct` for details.
TESTS::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: GrowthGroup('x^ZZ * y^ZZ') # indirect doctest
Growth Group x^ZZ * y^ZZ
Check :trac:`26452`::
sage: from sage.rings.asymptotic.growth_group import MonomialGrowthGroup
sage: R = QQ.extension(x^2+1, 'i')
sage: P = MonomialGrowthGroup(R, 'w')
sage: L = MonomialGrowthGroup(ZZ, 'log(w)')
sage: cartesian_product([P, L])
Growth Group w^(Number Field in i with defining polynomial x^2 + 1) * log(w)^ZZ
"""
order = kwds.pop('order')
CartesianProductPoset.__init__(self, sets, category, order, **kwds)
vars = sum(iter(factor.variable_names()
for factor in self.cartesian_factors()),
tuple())
from itertools import groupby
from .growth_group import Variable
Vars = Variable(tuple(v for v, _ in groupby(vars)), repr=self._repr_short_())
GenericGrowthGroup.__init__(self, sets[0], Vars, self.category(), **kwds)
def _coerce_map_from_(self, S):
r"""
Return whether ``S`` coerces into this growth group.
INPUT:
- ``S`` -- a parent.
OUTPUT:
A boolean.
TESTS::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: A = GrowthGroup('QQ^x * x^QQ')
sage: B = GrowthGroup('QQ^x * x^ZZ')
sage: A.has_coerce_map_from(B) # indirect doctest
True
sage: B.has_coerce_map_from(A) # indirect doctest
False
"""
if CartesianProductPoset.has_coerce_map_from(self, S):
return True
elif isinstance(S, GenericProduct):
factors = S.cartesian_factors()
else:
factors = (S, )
if all(
any(
g.has_coerce_map_from(f) for g in self.cartesian_factors())
for f in factors):
return True
def _coerce_map_from_(self, S):
r"""
Return whether ``S`` coerces into this growth group.
INPUT:
- ``S`` -- a parent.
OUTPUT:
A boolean.
TESTS::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: A = GrowthGroup('QQ^x * x^QQ')
sage: B = GrowthGroup('QQ^x * x^ZZ')
sage: A.has_coerce_map_from(B) # indirect doctest
True
sage: B.has_coerce_map_from(A) # indirect doctest
False
"""
if CartesianProductPoset.has_coerce_map_from(self, S):
return True
elif isinstance(S, GenericProduct):
factors = S.cartesian_factors()
else:
factors = (S,)
if all(any(g.has_coerce_map_from(f) for g in self.cartesian_factors()) for f in factors):
return True
def __init__(self, sets, category, **kwds):
r"""
See :class:`GenericProduct` for details.
TESTS::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: GrowthGroup('x^ZZ * y^ZZ') # indirect doctest
Growth Group x^ZZ * y^ZZ
"""
order = kwds.pop("order")
CartesianProductPoset.__init__(self, sets, category, order, **kwds)
vars = sum(iter(factor.variable_names() for factor in self.cartesian_factors()), tuple())
from itertools import groupby
from growth_group import Variable
Vars = Variable(tuple(v for v, _ in groupby(vars)), repr=self._repr_short_())
GenericGrowthGroup.__init__(self, sets[0], Vars, self.category(), **kwds)
def __init__(self, sets, category, **kwds):
r"""
See :class:`GenericProduct` for details.
TESTS::
sage: from sage.rings.asymptotic.growth_group import GrowthGroup
sage: GrowthGroup('x^ZZ * y^ZZ') # indirect doctest
Growth Group x^ZZ * y^ZZ
"""
order = kwds.pop('order')
CartesianProductPoset.__init__(self, sets, category, order, **kwds)
vars = sum(iter(factor.variable_names()
for factor in self.cartesian_factors()),
tuple())
from itertools import groupby
from .growth_group import Variable
Vars = Variable(tuple(v for v, _ in groupby(vars)), repr=self._repr_short_())
GenericGrowthGroup.__init__(self, sets[0], Vars, self.category(), **kwds)