def __init__(self, base, ideal=None):
"""
The Python constructor.
EXAMPLES::
sage: Berkovich_Cp_Affine(3)
Affine Berkovich line over Cp(3) of precision 20
"""
if base in ZZ:
if base.is_prime():
base = Qp(base) # change to Qpbar
else:
raise ValueError("non-prime passed into Berkovich space")
if is_AffineSpace(base):
base = base.base_ring()
if base in NumberFields():
if ideal is None:
raise ValueError('passed a number field but not an ideal')
if base is not QQ:
if not isinstance(ideal, NumberFieldFractionalIdeal):
raise ValueError(
'ideal was not an ideal of a number field')
if ideal.number_field() != base:
raise ValueError('passed number field ' + \
'%s but ideal was an ideal of %s' %(base, ideal.number_field()))
prime = ideal.smallest_integer()
else:
if ideal not in QQ:
raise ValueError('ideal was not an element of QQ')
prime = ideal
if not ideal.is_prime():
raise ValueError('passed non prime ideal')
self._base_type = 'number field'
elif isinstance(base,
sage.rings.abc.pAdicField): # change base to Qpbar
prime = base.prime()
ideal = None
self._base_type = 'padic field'
else:
raise ValueError("base of Berkovich Space must be a padic field " + \
"or a number field")
self._ideal = ideal
self._p = prime
Parent.__init__(self, base=base, category=TopologicalSpaces())
