175 lines
7.1 KiB
Plaintext
175 lines
7.1 KiB
Plaintext
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/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2009, 2008 William Hart
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Copyright (C) 2011 Sebastian Pancratz
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Copyright (C) 2011 Fredrik Johansson
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Copyright (C) 2012 Lina Kulakova
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******************************************************************************/
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*******************************************************************************
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Factorisation
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*******************************************************************************
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void fmpz_mod_poly_factor_init(fmpz_mod_poly_factor_t fac)
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Initialises \code{fac} for use. An \code{fmpz_mod_poly_factor_t}
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represents a polynomial in factorised form as a product of
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polynomials with associated exponents.
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void fmpz_mod_poly_factor_clear(fmpz_mod_poly_factor_t fac)
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Frees all memory associated with \code{fac}.
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void fmpz_mod_poly_factor_realloc(fmpz_mod_poly_factor_t fac, slong alloc)
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Reallocates the factor structure to provide space for
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precisely \code{alloc} factors.
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void fmpz_mod_poly_factor_fit_length(fmpz_mod_poly_factor_t fac, slong len)
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Ensures that the factor structure has space for at
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least \code{len} factors. This function takes care
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of the case of repeated calls by always, at least
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doubling the number of factors the structure can hold.
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void fmpz_mod_poly_factor_set(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_factor_t fac)
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Sets \code{res} to the same factorisation as \code{fac}.
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void fmpz_mod_poly_factor_print(const fmpz_mod_poly_factor_t fac)
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Prints the entries of \code{fac} to standard output.
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void fmpz_mod_poly_factor_insert(fmpz_mod_poly_factor_t fac,
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const fmpz_mod_poly_t poly, slong exp)
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Inserts the factor \code{poly} with multiplicity \code{exp} into
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the factorisation \code{fac}.
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If \code{fac} already contains \code{poly}, then \code{exp} simply
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gets added to the exponent of the existing entry.
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void fmpz_mod_poly_factor_concat(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_factor_t fac)
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Concatenates two factorisations.
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This is equivalent to calling \code{fmpz_mod_poly_factor_insert()}
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repeatedly with the individual factors of \code{fac}.
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Does not support aliasing between \code{res} and \code{fac}.
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void fmpz_mod_poly_factor_pow(fmpz_mod_poly_factor_t fac, slong exp)
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Raises \code{fac} to the power \code{exp}.
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int fmpz_mod_poly_is_irreducible(const fmpz_mod_poly_t f)
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Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0.
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int fmpz_mod_poly_is_irreducible_ddf(const fmpz_mod_poly_t f)
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Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0.
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Uses fast distinct-degree factorisation.
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int fmpz_mod_poly_is_irreducible_rabin(const fmpz_mod_poly_t f)
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Returns 1 if the polynomial \code{f} is irreducible, otherwise returns 0.
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Uses Rabin irreducibility test.
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int _fmpz_mod_poly_is_squarefree(const fmpz * f, slong len, const fmpz_t p)
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Returns 1 if \code{(f, len)} is squarefree, and 0 otherwise. As a
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special case, the zero polynomial is not considered squarefree.
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There are no restrictions on the length.
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int fmpz_mod_poly_is_squarefree(const fmpz_mod_poly_t f)
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Returns 1 if \code{f} is squarefree, and 0 otherwise. As a special
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case, the zero polynomial is not considered squarefree.
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int fmpz_mod_poly_factor_equal_deg_prob(fmpz_mod_poly_t factor,
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flint_rand_t state, const fmpz_mod_poly_t pol, slong d)
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Probabilistic equal degree factorisation of \code{pol} into
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irreducible factors of degree \code{d}. If it passes, a factor is
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placed in \code{factor} and 1 is returned, otherwise 0 is returned and
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the value of factor is undetermined.
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Requires that \code{pol} be monic, non-constant and squarefree.
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void fmpz_mod_poly_factor_equal_deg(fmpz_mod_poly_factor_t factors,
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const fmpz_mod_poly_t pol, slong d)
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Assuming \code{pol} is a product of irreducible factors all of
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degree \code{d}, finds all those factors and places them in factors.
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Requires that \code{pol} be monic, non-constant and squarefree.
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void fmpz_mod_poly_factor_distinct_deg(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_t poly, slong * const *degs)
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Factorises a monic non-constant squarefree polynomial \code{poly}
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of degree n into factors $f[d]$ such that for $1 \leq d \leq n$
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$f[d]$ is the product of the monic irreducible factors of \code{poly}
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of degree $d$. Factors $f[d]$ are stored in \code{res}, and the degree $d$
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of the irreducible factors is stored in \code{degs} in the same order
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as the factors.
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Requires that \code{degs} has enough space for $(n/2)+1 * sizeof(slong)$.
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void fmpz_mod_poly_factor_squarefree(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_t f)
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Sets \code{res} to a squarefree factorization of \code{f}.
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void fmpz_mod_poly_factor(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_t f)
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Factorises a non-constant polynomial \code{f} into monic irreducible
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factors choosing the best algorithm for given modulo and degree.
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Choise is based on heuristic measurments.
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void fmpz_mod_poly_factor_cantor_zassenhaus(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_t f)
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Factorises a non-constant polynomial \code{f} into monic irreducible
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factors using the Cantor-Zassenhaus algorithm.
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void fmpz_mod_poly_factor_kaltofen_shoup(fmpz_mod_poly_factor_t res,
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const fmpz_mod_poly_t poly)
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Factorises a non-constant polynomial \code{poly} into monic irreducible
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factors using the fast version of Cantor-Zassenhaus algorithm proposed by
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Kaltofen and Shoup (1998). More precisely this algorithm uses a
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``baby step/giant step''<27> strategy for the distinct-degree factorization
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step.
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void fmpz_mod_poly_factor_berlekamp(fmpz_mod_poly_factor_t factors,
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const fmpz_mod_poly_t f)
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Factorises a non-constant polynomial \code{f} into monic irreducible
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factors using the Berlekamp algorithm.
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