def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL'):
"""
A capped absolute representation of Zq.
INPUT:
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Zp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqCA(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring with capped absolute precision 10000 in a defined by (1 + O(3^10000))*x^3 + (O(3^10000))*x^2 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqCA(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
# Currently doesn't support polynomials with non-integral coefficients
self._shift_seed = None
self._pre_poly = prepoly
self._implementation = implementation
if implementation == 'NTL':
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()], poly.base_ring().prime()**prec)
if prec <= 30:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), prec, prec, prec, True, ntl_poly, "small", "u")
else:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), 30, prec, prec, True, ntl_poly, "big", "u")
element_class = pAdicZZpXCAElement
else:
Zpoly = _make_integral_poly(prepoly, poly.base_ring().prime(), prec)
cache_limit = min(prec, 30)
self.prime_pow = PowComputer_flint_maker(poly.base_ring().prime(), cache_limit, prec, prec, False, Zpoly, prec_type='capped-abs')
element_class = qAdicCappedAbsoluteElement
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)
if implementation != 'NTL':
from qadic_flint_CA import pAdicCoercion_ZZ_CA, pAdicConvert_QQ_CA
self.register_coercion(pAdicCoercion_ZZ_CA(self))
self.register_conversion(pAdicConvert_QQ_CA(self))
def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed, names, implementation='NTL'):
"""
A fixed modulus representation of Zq.
INPUT:
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Qp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqFM(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring of fixed modulus 3^10000 in a defined by (1 + O(3^10000))*x^3 + (O(3^10000))*x^2 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqFM(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
self._shift_seed = None
self._pre_poly = prepoly
self._implementation = implementation
if implementation == 'NTL':
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()], poly.base_ring().prime()**prec)
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), max(min(prec - 1, 30), 1), prec, prec, False, ntl_poly, "FM", "u")
element_class = pAdicZZpXFMElement
else:
Zpoly = _make_integral_poly(prepoly, poly.base_ring().prime(), prec)
cache_limit = 0 # prevents caching
self.prime_pow = PowComputer_flint_maker(poly.base_ring().prime(), cache_limit, prec, prec, False, Zpoly, prec_type='fixed-mod')
element_class = qAdicFixedModElement
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)
if implementation != 'NTL':
from qadic_flint_FM import pAdicCoercion_ZZ_FM, pAdicConvert_QQ_FM
self.register_coercion(pAdicCoercion_ZZ_FM(self))
self.register_conversion(pAdicConvert_QQ_FM(self))
def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed,
names):
"""
A capped absolute representation of Zq.
INPUTS::
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Zp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqCA(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring with capped absolute precision 10000 in a defined by (1 + O(3^10000))*x^3 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqCA(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
# Currently doesn't support polynomials with non-integral coefficients
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()],
poly.base_ring().prime()**prec)
if prec <= 30:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(),
prec, prec, prec, True,
ntl_poly, "small", "u")
else:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(),
30, prec, prec, True,
ntl_poly, "big", "u")
self._shift_seed = None
self._pre_poly = prepoly
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode,
names, pAdicZZpXCAElement)
def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed,
names):
"""
A fixed modulus representation of Zq.
INPUTS::
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Qp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqFM(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring of fixed modulus 3^10000 in a defined by (1 + O(3^10000))*x^3 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqFM(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()],
poly.base_ring().prime()**prec)
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(),
max(min(prec - 1, 30),
1), prec, prec, False,
ntl_poly, "FM", "u")
self._shift_seed = None
self._pre_poly = prepoly
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode,
names, pAdicZZpXFMElement)
def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed, names):
"""
A representation of Qq.
INPUTS::
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Qp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = Qq(27,10000); R #indirect doctest
Unramified Extension of 3-adic Field with capped relative precision 10000 in a defined by (1 + O(3^10000))*x^3 + (O(3^10000))*x^2 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = Qq(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
# Currently doesn't support polynomials with non-integral coefficients
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()], poly.base_ring().prime()**prec)
if prec <= 30:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), prec, prec, prec, True, ntl_poly, "small", "u")
else:
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), 30, prec, prec, True, ntl_poly, "big", "u")
self._shift_seed = None
self._pre_poly = prepoly
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode, names, pAdicZZpXCRElement)
def __init__(self, prepoly, poly, prec, halt, print_mode, shift_seed, names):
"""
A fixed modulus representation of Zq.
INPUTS::
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Qp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqFM(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring of fixed modulus 3^10000 in a defined by (1 + O(3^10000))*x^3 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqFM(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()], poly.base_ring().prime()**prec)
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(), max(min(prec - 1, 30), 1), prec, prec, False, ntl_poly, "FM", "u")
self._shift_seed = None
self._pre_poly = prepoly
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode, names, pAdicZZpXFMElement)
def __init__(self,
prepoly,
poly,
prec,
halt,
print_mode,
shift_seed,
names,
implementation='NTL'):
"""
A fixed modulus representation of Zq.
INPUT:
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Qp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqFM(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring of fixed modulus 3^10000 in a defined by (1 + O(3^10000))*x^3 + (O(3^10000))*x^2 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqFM(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
self._shift_seed = None
self._pre_poly = prepoly
self._implementation = implementation
if implementation == 'NTL':
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()],
poly.base_ring().prime()**prec)
self.prime_pow = PowComputer_ext_maker(poly.base_ring().prime(),
max(min(prec - 1, 30),
1), prec, prec, False,
ntl_poly, "FM", "u")
element_class = pAdicZZpXFMElement
else:
Zpoly = _make_integral_poly(prepoly,
poly.base_ring().prime(), prec)
cache_limit = 0 # prevents caching
self.prime_pow = PowComputer_flint_maker(poly.base_ring().prime(),
cache_limit,
prec,
prec,
False,
Zpoly,
prec_type='fixed-mod')
element_class = qAdicFixedModElement
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode,
names, element_class)
if implementation != 'NTL':
from qadic_flint_FM import pAdicCoercion_ZZ_FM, pAdicConvert_QQ_FM
self.register_coercion(pAdicCoercion_ZZ_FM(self))
self.register_conversion(pAdicConvert_QQ_FM(self))
def __init__(self,
prepoly,
poly,
prec,
halt,
print_mode,
shift_seed,
names,
implementation='NTL'):
"""
A capped absolute representation of Zq.
INPUT:
- prepoly -- The original polynomial defining the
extension. This could be a polynomial with integer
coefficients, for example, while poly has coefficients
in Zp.
- poly -- The polynomial with coefficients in
self.base_ring() defining this extension.
- prec -- The precision cap of this ring.
- halt -- unused
- print_mode -- A dictionary of print options.
- shift_seed -- unused
- names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name)
EXAMPLES::
sage: R.<a> = ZqCA(27,10000); R #indirect doctest
Unramified Extension of 3-adic Ring with capped absolute precision 10000 in a defined by (1 + O(3^10000))*x^3 + (O(3^10000))*x^2 + (2 + O(3^10000))*x + (1 + O(3^10000))
sage: R.<a> = ZqCA(next_prime(10^30)^3, 3); R.prime()
1000000000000000000000000000057
"""
# Currently doesn't support polynomials with non-integral coefficients
self._shift_seed = None
self._pre_poly = prepoly
self._implementation = implementation
if implementation == 'NTL':
ntl_poly = ntl_ZZ_pX([a.lift() for a in poly.list()],
poly.base_ring().prime()**prec)
if prec <= 30:
self.prime_pow = PowComputer_ext_maker(
poly.base_ring().prime(), prec, prec, prec, True, ntl_poly,
"small", "u")
else:
self.prime_pow = PowComputer_ext_maker(
poly.base_ring().prime(), 30, prec, prec, True, ntl_poly,
"big", "u")
element_class = pAdicZZpXCAElement
else:
Zpoly = _make_integral_poly(prepoly,
poly.base_ring().prime(), prec)
cache_limit = min(prec, 30)
self.prime_pow = PowComputer_flint_maker(poly.base_ring().prime(),
cache_limit,
prec,
prec,
False,
Zpoly,
prec_type='capped-abs')
element_class = qAdicCappedAbsoluteElement
UnramifiedExtensionGeneric.__init__(self, poly, prec, print_mode,
names, element_class)
if implementation != 'NTL':
from qadic_flint_CA import pAdicCoercion_ZZ_CA, pAdicConvert_QQ_CA
self.register_coercion(pAdicCoercion_ZZ_CA(self))
self.register_conversion(pAdicConvert_QQ_CA(self))