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/*****************************************************************************\
* Computer Algebra System SINGULAR
\*****************************************************************************/
/** @file facFqBivarUtil.h
*
* This file provides utility functions for bivariate factorization
*
* @author Martin Lee
*
**/
/*****************************************************************************/
#ifndef FAC_FQ_BIVAR_UTIL_H
#define FAC_FQ_BIVAR_UTIL_H
// #include "config.h"
#include "cf_map.h"
#include "ExtensionInfo.h"
#ifdef HAVE_NTL
#include "NTLconvert.h"
#endif
/// append @a factors2 on @a factors1
void append (CFList& factors1, ///< [in,out] a list of polys
const CFList& factors2 ///< [in] a list of polys
);
/// decompress a list of polys @a factors using the map @a N
void decompress (CFList& factors, ///< [in,out] a list of polys
const CFMap& N ///< [in] a map
);
/// as above
void decompress (CFFList& factors, ///< [in,out] a list of factors
const CFMap& N ///< [in] a map
);
/// first swap Variables in @a factors1 if necessary, then append @a factors2
/// and @a factors3 on @a factors1 and finally decompress @a factors1
void appendSwapDecompress (CFList& factors1, ///< [in,out] a list of polys
const CFList& factors2, ///< [in] a list of polys
const CFList& factors3, ///< [in] a list of polys
const bool swap1, ///< [in] indicates the need
///< to swap
const bool swap2, ///< [in] indicates the need
///< to swap
const CFMap& N ///< [in] a map
);
/// swap Variables in @a factors, then decompress @a factors
void swapDecompress (CFList& factors, ///< [in,out] a list of polys
const bool swap, ///< [in] indicates the need to swap
const CFMap& N ///< [in] a map
);
/// tests if F is not contained in a subfield defined by @a gamma (Fq case) or
/// @a k (GF case)
///
/// @return @a isInExtension returns true if @a F is not contained in a subfield
/// defined by @a gamma (Fq case) or @a k (GF case), false else
/// @sa appendTestMapDown()
bool isInExtension (const CanonicalForm& F, ///< [in] a poly over
///< F_p (alpha)=Fq or GF(p^l)
const CanonicalForm& gamma, ///< [in] a primitive element
///< defining a subfield of
///< Fq if we are not over some
///< GF
const int k, ///< some int k such that k
///< divides l if we are not
///< over some Fq
const CanonicalForm& delta, ///< [in] image of gamma
CFList& source, ///< [in,out] list of preimages
CFList& dest ///< [in,out] list of images
);
/// map a poly into a subfield of the current field, no testing is performed!
///
/// @return @a mapDown returns @a F mapped into a subfield of the current field
/// @sa appendTestMapDown(), appendMapDown()
CanonicalForm
mapDown (const CanonicalForm& F, ///< [in] a poly
const ExtensionInfo& info, ///< [in] information about the sub- and
///< current field
CFList& source, ///< [in,out] in case we are over some
///< F_p (alpha) and want to map down into
///< F_p (beta) source contains powers of
///< the primitive element of F_p (alpha)
CFList& dest ///< [in,out] as source but contains
///< the corresponding powers of the
///< primitive element of F_p (beta)
);
/// test if @a g is in a subfield of the current field, if so map it down and
/// append it to @a factors
///
/// @sa mapDown(), isInExtension()
void appendTestMapDown (CFList& factors, ///< [in,out] a list of polys
const CanonicalForm& f, ///< [in] a poly
const ExtensionInfo& info,///< [in] information about
///< extension
CFList& source, ///< [in,out] @sa mapDown()
CFList& dest ///< [in,out] @sa mapDown()
);
/// map @a g down into a subfield of the current field and append it to @a
/// factors
///
/// @sa mapDown(), appendTestMapDown()
void
appendMapDown (CFList& factors, ///< [in,out] a list of polys
const CanonicalForm& g, ///< [in] a poly
const ExtensionInfo& info,///< [in] information about extension
CFList& source, ///< [in,out] @sa mapDown()
CFList& dest ///< [in,out] @sa mapDown()
);
/// normalize factors, i.e. make factors monic
void normalize (CFList& factors ///< [in,out] a list of polys
);
/// as above
void normalize (CFFList& factors ///< [in,out] a list of factors
);
/// extract a subset given by @a index of size @a s from @a elements, if there
/// is no subset we have not yet considered noSubset is set to true. @a index
/// encodes the next subset, e.g. if s= 3, elements= {a,b,c,d},
/// index= {1, 2, 4, 0}, then subset= {a,c,d}. @a index is of size
/// @a elements.size().
///
/// @return @a subset returns a list of polys of length @a s if there is a
/// subset we have not yet considered.
CFList subset (int index [], ///< [in,out] an array encoding the next
///< subset
const int& s, ///< [in] size of the subset
const CFArray& elements, ///< [in] an array of polys
bool& noSubset ///< [in,out] if there is no subset we
///< have not yet considered @a noSubset
///< is true
);
/// write elements of @a list into an array
///
/// @return an array of polys
CFArray copy (const CFList& list ///< [in] a list of polys
);
/// update @a index
void indexUpdate (int index [], ///< [in,out] an array encoding a
///< subset of size subsetSize
const int& subsetSize, ///< [in] size of the subset
const int& setSize, ///< [in] size of the given set
bool& noSubset ///< [in,out] if there is no subset we
///< have not yet considered @a
///< noSubset is true
);
/// compute the sum of degrees in Variable(1) of elements in S
///
/// @return @a subsetDegree returns the sum of degrees in Variable(1) of
/// elements in S
int subsetDegree (const CFList& S ///< [in] a list of polys
);
/// determine multiplicity of the factors
///
/// @return a list of factors of F with their multiplicity
CFFList multiplicity (CanonicalForm& F, ///< [in] a poly
const CFList& factors ///< [in] a list of factors of F
);
/// compute the coefficients of the logarithmic derivative of G mod
/// Variable (2)^l over Fq
///
/// @return an array of coefficients of the logarithmic derivative of G mod
/// Variable (2)^l
CFArray logarithmicDerivative (const CanonicalForm& F,///<[in] a bivariate poly
const CanonicalForm& G, ///<[in] a factor of F
int l, ///<[in] lifting precision
CanonicalForm& Q ///<[in,out] F/G
);
/// compute the coefficients of the logarithmic derivative of G mod
/// Variable (2)^l over Fq with oldQ= F/G mod Variable (2)^oldL
///
/// @return an array of coefficients of the logarithmic derivative of G mod
/// Variable (2)^l
CFArray
logarithmicDerivative (const CanonicalForm& F, ///< [in] bivariate poly
///< truncated at Variable(2)^l
const CanonicalForm& G, ///< [in] a factor of F
int l, ///< [in] lifting precision
int oldL, ///< [in] old precision
const CanonicalForm& oldQ,///< [in] F/G mod
///< Variable(2)^oldL
CanonicalForm& Q ///< [in, out] F/G
);
/// compute bounds for logarithmic derivative as described in K. Belabas,
/// M. van Hoeij, J. Klüners, and A. Steel, Factoring polynomials over global
/// fields
///
/// @return @a computeBounds returns bounds as described above
int *
computeBounds (const CanonicalForm& F,///< [in] compressed bivariate polynomial
int& n, ///< [in,out] length of output
bool& isIrreducible ///< [in,out] check if poly is irreducible
);
/// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is
/// a variable of level 1
///
/// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$
/// @sa {getCoeffs (const CanonicalForm&, const int, const Variable&),
/// getCoeffs (const CanonicalForm&, const int, const int, const int,
/// const Variable&, const CanonicalForm&, const mat_zz_p&)}
CFArray
getCoeffs (const CanonicalForm& F,///< [in] compressed bivariate poly over F_p
const int k ///< [in] some int
);
/// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is
/// a variable of level 1
///
/// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$
/// @sa {getCoeffs (const CanonicalForm&, const int),
/// getCoeffs (const CanonicalForm&, const int, const int, const int,
/// const Variable&, const CanonicalForm&, const mat_zz_p&)}
CFArray
getCoeffs (const CanonicalForm& F,///< [in] compressed bivariate poly over
///< F_p(alpha)
const int k, ///< [in] some int
const Variable& alpha ///< [in] algebraic variable
);
#ifdef HAVE_NTL
/// extract coefficients of \f$ x^i \f$ for \f$i\geq k\f$ where \f$ x \f$ is
/// a variable of level 1
///
/// @return coefficients of \f$ x^i \f$ for \f$i\geq k\f$
/// @sa {getCoeffs (const CanonicalForm&, const int, const Variable& alpha),
/// getCoeffs (const CanonicalForm&, const int)}
CFArray
getCoeffs (const CanonicalForm& F, ///< [in] compressed bivariate poly
const int k, ///< [in] some int
const int l, ///< [in] precision
const int degMipo, ///< [in] degree of minimal poly
const Variable& alpha, ///< [in] algebraic variable
const CanonicalForm& evaluation,///< [in] evaluation point
const mat_zz_p& M ///< [in] bases change matrix
);
#endif
/// write A into M starting at row startIndex
void
writeInMatrix (CFMatrix& M, ///< [in,out] some matrix
const CFArray& A, ///< [in] array of polys
const int column, ///< [in] column in which A is written
const int startIndex///< [in] row in which to start
);
/// checks if a substitution x^n->x is possible
///
/// @return an integer n > 1, if a substitution described as above is possible
/// else n <= 1
int substituteCheck (const CFList& L ///< [in] a list of univariate polys
);
/// substitute x^d by x in F
void
subst (const CanonicalForm& F, ///< [in] a polynomial
CanonicalForm& A, ///< [in,out] returns F with x^d replaced by x
const int d, ///< d > 1 such that a substitution x^d -> x
///< [in] is possible
const Variable& x ///< [in] a Variable
);
/// reverse a substitution x^d->x
///
/// @return a poly with x replaced by x^d
CanonicalForm
reverseSubst (const CanonicalForm& F, ///< [in] a poly
const int d, ///< [in] an integer > 0
const Variable& x ///< [in] a Variable
);
/// reverse a substitution x^d->x
void
reverseSubst (CFList& L, ///< [in,out] a list of polys, returns the
///< given list with x replaced by x^d
const int d, ///< [in] an integer > 0
const Variable& x ///< [in] a Variable
);
/// check if a substitution x^n->x is possible
///
/// @return an integer n > 1, if a substitution described as above is possible
/// else n <= 1
int
substituteCheck (const CanonicalForm& F, ///<[in] a polynomial
const Variable& x ///<[in] some variable
);
#endif
/* FAC_FQ_BIVAR_UTIL_H */
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