Coverage for local/lib/python2.7/site-packages/sage/rings/padics/pow_computer_flint.pyx : 76%
Hot-keys on this page
r m x p toggle line displays
j k next/prev highlighted chunk
0 (zero) top of page
1 (one) first highlighted chunk
|
from __future__ import absolute_import
from cysignals.memory cimport sig_malloc, sig_free from cysignals.signals cimport sig_on, sig_off
from sage.libs.gmp.mpz cimport mpz_init, mpz_clear, mpz_pow_ui from sage.libs.flint.padic cimport * from sage.libs.flint.fmpz_poly cimport * from sage.libs.flint.nmod_vec cimport * from sage.libs.flint.fmpz_vec cimport * from sage.libs.flint.fmpz cimport fmpz_init, fmpz_one, fmpz_mul, fmpz_set, fmpz_get_mpz, fmpz_clear, fmpz_pow_ui, fmpz_set_mpz, fmpz_fdiv_q_2exp
from cpython.object cimport Py_EQ, Py_NE from sage.structure.richcmp cimport richcmp_not_equal from sage.rings.integer cimport Integer from sage.rings.all import ZZ from sage.rings.polynomial.polynomial_integer_dense_flint cimport Polynomial_integer_dense_flint
cdef class PowComputer_flint(PowComputer_class): """ A PowComputer for use in `p`-adics implemented via FLINT.
For a description of inputs see :func:`PowComputer_flint_maker`.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint sage: PowComputer_flint(5, 20, 20, 20, False) FLINT PowComputer for 5 """ def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None, shift_seed = None): """ Memory initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint sage: type(PowComputer_flint(5, 20, 20, 20, False)) <type 'sage.rings.padics.pow_computer_flint.PowComputer_flint'>
""" # fmpz_init does not allocate memory
finally:
def __init__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None, shift_seed=None): """ Initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_maker sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_maker(5, 20, 20, 20, False, f, 'capped-rel') # indirect doctest sage: TestSuite(A).run()
"""
def __dealloc__(self): """ Deallocation.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint sage: A = PowComputer_flint(5, 20, 20, 20, False) sage: del A """
def __reduce__(self): """ Pickling.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_maker sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_maker(5, 20, 20, 20, False, f, 'capped-rel') # indirect doctest sage: A._test_pickling() # indirect doctest
"""
def _repr_(self): """ String representation of this powcomputer.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint sage: A = PowComputer_flint(5, 20, 20, 20, False); A FLINT PowComputer for 5 """
cdef fmpz_t* pow_fmpz_t_tmp(self, unsigned long n) except NULL: """ Returns a pointer to a FLINT ``fmpz_t`` holding `p^n`.
Analogous to :meth:`sage.rings.padics.pow_computer.PowComputer_class.pow_mpz_t_tmp` but with FLINT ``fmpz_t`` rather than GMP ``mpz_t``. The same important warnings apply. """ else:
cdef mpz_srcptr pow_mpz_t_tmp(self, long n) except NULL: """ Returns a pointer to an ``mpz_t`` holding `p^n`.
See :meth:`sage.rings.padics.pow_computer.PowComputer_class.pow_mpz_t_tmp` for important warnings. """
cdef mpz_srcptr pow_mpz_t_top(self): """ Returns a pointer to an ``mpz_t`` holding `p^N`, where `N` is the precision cap. """ return self.top_power
cdef unsigned long capdiv(self, unsigned long n): """ Returns ceil(n / e). """ if self.e == 1: return n if n == 0: return 0 return (n-1) / self.e + 1
def polynomial(self, n=None, var='x'): """ Returns ``None``.
For consistency with subclasses.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint sage: A = PowComputer_flint(5, 20, 20, 20, False, None) sage: A.polynomial() is None True
"""
cdef class PowComputer_flint_1step(PowComputer_flint): """ A PowComputer for a `p`-adic extension defined by a single polynomial.
For a description of inputs see :func:`PowComputer_flint_maker`.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f); A FLINT PowComputer for 5 with polynomial x^3 - 8*x - 2
""" def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, _poly): """ Memory initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f) sage: type(A) <type 'sage.rings.padics.pow_computer_flint.PowComputer_flint_1step'>
"""
cdef Py_ssize_t i
# fmpz_init does not allocate memory
raise MemoryError except BaseException: i-=1 while i: fmpz_poly_clear(self._moduli[i]) i-=1 raise except BaseException: fmpz_poly_clear(self.modulus) raise except BaseException: sig_free(self._moduli) raise finally:
def __init__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, _poly, shift_seed=None): """ Initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_maker sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_maker(5, 20, 20, 20, False, f, 'capped-rel') sage: TestSuite(A).run()
"""
cdef Py_ssize_t i
def __dealloc__(self): """ Deallocation.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f) sage: del A """ cdef Py_ssize_t i
def _repr_(self): """ String representation of this powcomputer.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f); A FLINT PowComputer for 5 with polynomial x^3 - 8*x - 2 """
def __richcmp__(self, other, int op): """ Comparison.
Lexicographic on class, prime, precision cap, cache_limit and polynomial.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2; g = x^3 - (8 + 5^22)*x - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f) sage: B = PowComputer_flint_1step(5, 20, 20, 20, False, g) sage: A == B False """ if op in [Py_EQ, Py_NE]: return (op == Py_NE) return NotImplemented
return richcmp_not_equal(lx, rx, op)
return richcmp_not_equal(lx, rx, op)
return richcmp_not_equal(lx, rx, op)
return richcmp_not_equal(lx, rx, op)
# return cmp(self.polynomial(), other.polynomial()) return False
cdef fmpz_poly_t* get_modulus(self, unsigned long k): """ Returns the defining polynomial reduced modulo `p^k`.
The same warnings apply as for :meth:`sage.rings.padics.pow_computer.PowComputer_class.pow_mpz_t_tmp`. """ cdef long c else: (<fmpz_poly_struct*>self.modulus)[0].coeffs, self.deg + 1,
cdef fmpz_poly_t* get_modulus_capdiv(self, unsigned long k): """ Returns the defining polynomial reduced modulo `p^a`, where `a` is the ceiling of `k/e`.
The same warnings apply as for :meth:`sage.rings.padics.pow_computer.PowComputer_class.pow_mpz_t_tmp`. """ return self.get_modulus(self.capdiv(k))
def polynomial(self, _n=None, var='x'): """ Returns the polynomial attached to this ``PowComputer``, possibly reduced modulo a power of `p`.
INPUT:
- ``_n`` -- (default ``None``) an integer, the power of `p` modulo which to reduce.
- ``var`` -- (default ``'x'``) the variable for the returned polynomial
.. NOTE::
From Cython you should use :meth:`get_modulus` instead for speed.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_1step sage: R.<y> = ZZ[]; f = y^3 - 8*y - 2 sage: A = PowComputer_flint_1step(5, 20, 20, 20, False, f) sage: A.polynomial() x^3 - 8*x - 2 sage: A.polynomial(var='y') y^3 - 8*y - 2 sage: A.polynomial(2) x^3 + 17*x + 23 """ else:
cdef _new_fmpz_poly(self, fmpz_poly_t value, var='x'): """ Returns a polynomial with the value stored in ``value`` and variable name ``var``. """
cdef class PowComputer_flint_unram(PowComputer_flint_1step): """ A PowComputer for a `p`-adic extension defined by an unramified polynomial.
For a description of inputs see :func:`PowComputer_flint_maker`.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_unram sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_unram(5, 20, 20, 20, False, f); A FLINT PowComputer for 5 with polynomial x^3 - 8*x - 2
""" def __cinit__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, _poly, shift_seed=None): """ Memory initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_unram sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_unram(5, 20, 20, 20, False, f) sage: type(A) <type 'sage.rings.padics.pow_computer_flint.PowComputer_flint_unram'>
""" # fmpz_init does not allocate memory
# While the following allocations have the potential to leak # small amounts of memory when interrupted or when one of the # init methods raises a MemoryError, the only leak-free # solution we could devise used 11-nested try blocks. We # choose readable code in this case.
def __dealloc__(self): """ Deallocation.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_unram sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_unram(5, 20, 20, 20, False, f) sage: del A
"""
def __init__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None): """ Initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_maker sage: R.<x> = ZZ[]; f = x^3 - 8*x - 2 sage: A = PowComputer_flint_maker(5, 20, 20, 20, False, f, 'capped-rel') sage: TestSuite(A).run()
"""
cdef class PowComputer_flint_eis(PowComputer_flint_1step): """ A PowComputer for a `p`-adic extension defined by an Eisenstein polynomial.
For a description of inputs see :func:`PowComputer_flint_maker`.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_eis sage: R.<x> = ZZ[]; f = x^3 - 25*x + 5 sage: A = PowComputer_flint_eis(5, 20, 20, 60, False, f); A FLINT PowComputer for 5 with polynomial x^3 - 25*x + 5 """ def __init__(self, Integer prime, long cache_limit, long prec_cap, long ram_prec_cap, bint in_field, poly=None): """ Initialization.
TESTS::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_eis sage: R.<x> = ZZ[]; f = x^3 - 25*x + 5 sage: A = PowComputer_flint_eis(5, 20, 20, 60, False, f) sage: type(A) <type 'sage.rings.padics.pow_computer_flint.PowComputer_flint_eis'>
"""
def PowComputer_flint_maker(prime, cache_limit, prec_cap, ram_prec_cap, in_field, poly, prec_type): """ Return an appropriate FLINT PowComputer for the given input.
INPUT:
- ``prime`` -- an integral prime
- ``cache_limit`` -- a non-negative integer, controlling the caching. Powers of ``prime``, reductions of ``poly`` modulo different powers of ``prime`` and inverses of the leading coefficient modulo different powers of ``prime`` are cached. Additional data is cached for ramified extensions.
- ``prec_cap`` -- the power of `p` modulo which elements of largest precision are defined.
- ``ram_prec_cap`` -- Approximately ``e*prec_cap``, where ``e`` is the ramification degree of the extension. For a ramified extension this is what Sage calls the precision cap of the ring. In fact, it's possible to have rings with precision cap not a multiple of `e`, in which case the actual relationship between ``ram_prec_cap`` and ``prec_cap`` is that ``prec_cap = ceil(n/e)``
- ``in_field`` -- (boolean) whether the associated ring is actually a field.
- ``poly`` -- the polynomial defining the extension.
- `prec_type`` -- one of ``"capped-rel"``, ``"capped-abs"`` or ``"fixed-mod"``, the precision type of the ring.
.. NOTE::
Because of the way templates work, this function imports the class of its return value from the appropriate element files. This means that the returned PowComputer will have the appropriate compile-time-type for Cython.
EXAMPLES::
sage: from sage.rings.padics.pow_computer_flint import PowComputer_flint_maker sage: R.<x> = ZZ[] sage: A = PowComputer_flint_maker(3, 20, 20, 20, False, x^3 + 2*x + 1, 'capped-rel'); type(A) <type 'sage.rings.padics.qadic_flint_CR.PowComputer_'> sage: A = PowComputer_flint_maker(3, 20, 20, 20, False, x^3 + 2*x + 1, 'capped-abs'); type(A) <type 'sage.rings.padics.qadic_flint_CA.PowComputer_'> sage: A = PowComputer_flint_maker(3, 20, 20, 20, False, x^3 + 2*x + 1, 'fixed-mod'); type(A) <type 'sage.rings.padics.qadic_flint_FM.PowComputer_'>
""" else: raise ValueError("unknown prec_type `%s`" % prec_type) |