152 lines
5.7 KiB
Plaintext
152 lines
5.7 KiB
Plaintext
/*=============================================================================
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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) 2011 Andy Novocin
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Copyright (C) 2011 Sebastian Pancratz
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******************************************************************************/
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*******************************************************************************
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Memory management
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*******************************************************************************
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void fmpz_poly_factor_init(fmpz_poly_factor_t fac)
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Initialises a new factor structure.
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void fmpz_poly_factor_init2(fmpz_poly_factor_t fac, slong alloc)
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Initialises a new factor structure, providing space for
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at least \code{alloc} factors.
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void fmpz_poly_factor_realloc(fmpz_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_poly_factor_fit_length(fmpz_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 functions 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_poly_factor_clear(fmpz_poly_factor_t fac)
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Releases all memory occupied by the factor structure.
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*******************************************************************************
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Manipulating factors
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*******************************************************************************
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void fmpz_poly_factor_set(fmpz_poly_factor_t res, const fmpz_poly_factor_t fac)
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Sets \code{res} to the same factorisation as \code{fac}.
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void fmpz_poly_factor_insert(fmpz_poly_factor_t fac,
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const fmpz_poly_t p, slong e)
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Adds the primitive polynomial $p^e$ to the factorisation \code{fac}.
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Assumes that $\deg(p) \geq 2$ and $e \neq 0$.
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void fmpz_poly_factor_concat(fmpz_poly_factor_t res,
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const fmpz_poly_factor_t fac)
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Concatenates two factorisations.
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This is equivalent to calling \code{fmpz_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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*******************************************************************************
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Input and output
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*******************************************************************************
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void fmpz_poly_factor_print(const fmpz_poly_factor_t fac)
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Prints the entries of \code{fac} to standard output.
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*******************************************************************************
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Factoring algorithms
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*******************************************************************************
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void fmpz_poly_factor_squarefree(fmpz_poly_factor_t fac, fmpz_poly_t F)
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Takes as input a polynomial $F$ and a freshly initialized factor
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structure \code{fac}. Updates \code{fac} to contain a factorization
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of $F$ into (not necessarily irreducible) factors that themselves
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have no repeated factors. None of the returned factors will have
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the same exponent. That is we return $g_i$ and unique $e_i$ such that
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\begin{equation*}
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F = c \prod_{i} g_i^{e_i}
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\end{equation*}
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where $c$ is the signed content of $F$ and $\gcd(g_i, g_i') = 1$.
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void fmpz_poly_factor_zassenhaus_recombination(fmpz_poly_factor_t
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final_fac, const fmpz_poly_factor_t lifted_fac,
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const fmpz_poly_t F, const fmpz_t P, slong exp)
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Takes as input a factor structure \code{lifted_fac} containing a
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squarefree factorization of the polynomial $F \bmod p$. The algorithm
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does a brute force search for irreducible factors of $F$ over the
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integers, and each factor is raised to the power \code{exp}.
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The impact of the algorithm is to augment a factorization of
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\code{F^exp} to the factor structure \code{final_fac}.
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void _fmpz_poly_factor_zassenhaus(fmpz_poly_factor_t final_fac,
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slong exp, fmpz_poly_t f, slong cutoff)
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This is the internal wrapper of Zassenhaus.
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It will attempt to find a small prime such that $f$ modulo $p$ has
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a minimal number of factors. If it cannot find a prime giving less
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than \code{cutoff} factors it aborts. Then it decides a $p$-adic
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precision to lift the factors to, hensel lifts, and finally calls
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Zassenhaus recombination.
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Assumes that $\len(f) \geq 2$.
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Assumes that $f$ is primitive.
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Assumes that the constant coefficient of $f$ is non-zero. Note that
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this can be easily achieved by taking out factors of the form $x^k$
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before calling this routine.
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void fmpz_poly_factor_zassenhaus(fmpz_poly_factor_t final_fac, fmpz_poly_t F)
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A wrapper of the Zassenhaus factoring algorithm, which takes as input
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any polynomial $F$, and stores a factorization in \code{final_fac}.
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The complexity will be exponential in the number of local factors
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we find for the components of a squarefree factorization of $F$.
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