def __init__(self, k, p=None, prec_cap=None, base=None, character=None,
adjuster=None, act_on_left=False, dettwist=None,
act_padic=False, implementation=None):
"""
See ``OverconvergentDistributions_abstract`` for full documentation.
EXAMPLES::
sage: from sage.modular.pollack_stevens.distributions import OverconvergentDistributions
sage: D = OverconvergentDistributions(2, 3, 5); D
Space of 3-adic distributions with k=2 action and precision cap 5
sage: type(D)
<class 'sage.modular.pollack_stevens.distributions.OverconvergentDistributions_class_with_category'>
`p` must be a prime, but `p=6` below, which is not prime::
sage: OverconvergentDistributions(k=0, p=6, prec_cap=10)
Traceback (most recent call last):
...
ValueError: p must be prime
"""
if not isinstance(base, ring.Ring):
raise TypeError("base must be a ring")
from sage.rings.padics.pow_computer import PowComputer
# should eventually be the PowComputer on ZpCA once that uses longs.
Dist, WeightKAction = get_dist_classes(p, prec_cap, base,
self.is_symk(), implementation)
self.Element = Dist
# if Dist is Dist_long:
# self.prime_pow = PowComputer(p, prec_cap, prec_cap, prec_cap)
Parent.__init__(self, base, category=Modules(base))
self._k = k
self._p = p
self._prec_cap = prec_cap
self._character = character
self._adjuster = adjuster
self._dettwist = dettwist
if self.is_symk() or character is not None:
self._act = WeightKAction(self, character, adjuster, act_on_left,
dettwist, padic=act_padic)
else:
self._act = WeightKAction(self, character, adjuster, act_on_left,
dettwist, padic=True)
self._populate_coercion_lists_(action_list=[self._act])
