def __lshift__(self, n):
r"""
Multiply this element by ``p^n``.
If ``n`` is negative and this element does not lie in a field,
digits may be truncated. See :meth:`__rshift__` for details.
EXAMPLES::
sage: R = ZpLC(5)
sage: a = R(1000); a
3*5^3 + 5^4 + O(5^23)
sage: a >> 1
3*5^2 + 5^3 + O(5^22)
sage: S = Zp(5); b = S(1000); b
3*5^3 + 5^4 + O(5^23)
"""
from sage.rings.padics.generic_nodes import pAdicRingBaseGeneric
parent = self._parent
p = parent.prime()
if isinstance(parent, pAdicRingBaseGeneric):
if self.precision_absolute() + n < 0:
return self.__class__(parent,
pRational(p, 0),
0,
dx={},
check=False)
powp = pRational(p, ZZ(1), n)
x = self._value * powp
if isinstance(parent, pAdicRingBaseGeneric):
x -= x.reduce(0)
dx = [[self, powp]]
return self.__class__(parent, x, dx=dx, check=False)
def __lshift__(self, n):
r"""
Multiply this element by ``p^n``.
If ``n`` is negative and this element does not lie in a field,
digits may be truncated. See :meth:`__rshift__` for details.
EXAMPLES::
sage: R = ZpLC(5)
sage: a = R(1000); a
3*5^3 + 5^4 + O(5^23)
sage: a >> 1
3*5^2 + 5^3 + O(5^22)
sage: S = Zp(5); b = S(1000); b
3*5^3 + 5^4 + O(5^23)
"""
from sage.rings.padics.generic_nodes import pAdicRingBaseGeneric
parent = self._parent
p = parent.prime()
if isinstance(parent, pAdicRingBaseGeneric):
if self.precision_absolute() + n < 0:
return self.__class__(parent, pRational(p, 0), 0, dx={}, check=False)
powp = pRational(p, ZZ(1), n)
x = self._value * powp
if isinstance(parent, pAdicRingBaseGeneric):
x -= x.reduce(0)
dx = [ [self, powp] ]
return self.__class__(parent, x, dx=dx, check=False)
def __init__(self, parent, x, prec=None, dx=[], dx_mode='linear_combination', valuation=None, check=True, reduce=True):
r"""
TESTS::
sage: R = ZpLC(2)
sage: x = R(1, 10) # indirect doctest
sage: x
1 + O(2^10)
"""
self._parent = parent
p = parent.prime()
pAdicGenericElement.__init__(self, parent)
self._precision = parent.precision()
if check:
if isinstance(x, pAdicGenericElement):
if parent.prime() != x.parent().prime():
raise TypeError("conversion between different p-adic rings/fields not supported")
if prec is None:
prec = x.precision_absolute()
else:
prec = min(prec, x.precision_absolute())
x = QQ(x)
if isinstance(x, pRational):
self._value = x
else:
self._value = pRational(p, QQ(x))
trunc = self._declare_new_element(dx, prec, dx_mode)
if reduce:
self._value = self._value.reduce(trunc)
def __init__(self, parent, x, prec=None, dx=[], dx_mode='linear_combination', valuation=None, check=True, reduce=True):
r"""
TESTS::
sage: R = ZpLC(2)
sage: x = R(1, 10) # indirect doctest
sage: x
1 + O(2^10)
"""
self._parent = parent
p = parent.prime()
pAdicGenericElement.__init__(self, parent)
self._precision = parent.precision()
if check:
if isinstance(x, pAdicGenericElement):
if parent.prime() != x.parent().prime():
raise TypeError("conversion between different p-adic rings/fields not supported")
if prec is None:
prec = x.precision_absolute()
else:
prec = min(prec, x.precision_absolute())
x = QQ(x)
if isinstance(x, pRational):
self._value = x
else:
self._value = pRational(p, QQ(x))
trunc = self._declare_new_element(dx, prec, dx_mode)
if reduce:
self._value = self._value.reduce(trunc)
def __init__(self, p, prec, print_mode, names, label=None):
"""
Initialization.
TESTS::
sage: R = ZpLC(17) # indirect doctest
sage: R._prec_type()
'lattice-cap'
sage: R._subtype
'cap'
sage: R = ZpLF(17) # indirect doctest
sage: R._prec_type()
'lattice-float'
sage: R._subtype
'float'
"""
from sage.rings.padics.lattice_precision import pRational
self._approx_zero = pRational(p, 0)
self._approx_one = pRational(p, 1)
self._approx_minusone = pRational(p, -1)
if label is None:
self._label = None
else:
self._label = str(label)
# We do not use the standard attribute element_class
# because we need to be careful with precision
# Instead we implement _element_constructor_ (cf below)
if self._subtype == 'cap':
(self._prec_cap_relative, self._prec_cap_absolute) = prec
self._zero_cap = None
self._precision = PrecisionLattice(p, label)
element_class = pAdicLatticeCapElement
elif self._subtype == 'float':
self._prec_cap_relative = prec
self._prec_cap_absolute = infinity
self._zero_cap = prec
self._precision = PrecisionModule(p, label, prec)
element_class = pAdicLatticeFloatElement
else:
raise ValueError("subtype must be either 'cap' or 'float'")
self._element_class = self.__make_element_class__(element_class)
pAdicGeneric.__init__(self, self, p, prec, print_mode, names, None)
def __init__(self, p, prec, print_mode, names, label=None):
"""
Initialization.
TESTS::
sage: R = ZpLC(17) # indirect doctest
sage: R._prec_type()
'lattice-cap'
sage: R._subtype
'cap'
sage: R = ZpLF(17) # indirect doctest
sage: R._prec_type()
'lattice-float'
sage: R._subtype
'float'
"""
from sage.rings.padics.lattice_precision import pRational
self._approx_zero = pRational(p, 0)
self._approx_one = pRational(p, 1)
self._approx_minusone = pRational(p, -1)
if label is None:
self._label = None
else:
self._label = str(label)
# We do not use the standard attribute element_class
# because we need to be careful with precision
# Instead we implement _element_constructor_ (cf below)
if self._subtype == 'cap':
(self._prec_cap_relative, self._prec_cap_absolute) = prec
self._zero_cap = None
self._precision = PrecisionLattice(p, label)
element_class = pAdicLatticeCapElement
elif self._subtype == 'float':
self._prec_cap_relative = prec
self._prec_cap_absolute = infinity
self._zero_cap = prec
self._precision = PrecisionModule(p, label, prec)
element_class = pAdicLatticeFloatElement
else:
raise ValueError("subtype must be either 'cap' or 'float'")
self._element_class = self.__make_element_class__(element_class)
pAdicGeneric.__init__(self, self, p, prec, print_mode, names, None)
