# source:git/factory/facFqSquarefree.h@eacb7aa

jengelh-datetimespielwiese
Last change on this file since eacb7aa was eacb7aa, checked in by Martin Lee <martinlee84@…>, 11 years ago
fix: include (in case of build without NTL)
• Property mode set to 100644
File size: 3.4 KB
Line
1/*****************************************************************************\
2 * Computer Algebra System SINGULAR
3\*****************************************************************************/
4/** @file facFqSquarefree.h
5 *
6 * This file provides functions for squarefrees factorizing over
7 * \f$F_{p} \f$ , \f$F_{p}(\alpha ) \f$ or GF.
8 *
9 * @author Martin Lee
10 *
11 * @internal @version \$Id$
12 *
13 **/
14/*****************************************************************************/
15
16#ifndef FAC_FQ_SQUAREFREE_H
17#define FAC_FQ_SQUAREFREE_H
18
19#include "cf_assert.h"
20#include "cf_factory.h"
21
22
23/// squarefree factorization over a finite field
24/// @a return a list of squarefree factors with multiplicity
25CFFList
26squarefreeFactorization
27                (const CanonicalForm & F, ///<[in] a poly
28                 const Variable & alpha   ///<[in] either an algebraic variable,
29                                          ///< i.e. we are over some F_p (alpha)
30                                          ///< or a variable of level 1, i.e.
31                                          ///< we are F_p or GF
32                );
33
34/// squarefree factorization over \f$F_{p} \f$.
35/// If input is not monic, the leading coefficient is dropped
36///
37/// @return a list of squarefree factors with multiplicity
38inline
39CFFList FpSqrf (const CanonicalForm& F ///< [in] a poly
40               )
41{
42  Variable a= 1;
43  CFFList result= squarefreeFactorization (F, a);
44  result.insert (CFFactor (Lc(F), 1));
45  return result;
46}
47
48/// squarefree factorization over \f$F_{p}(\alpha ) \f$.
49/// If input is not monic, the leading coefficient is dropped
50///
51/// @return a list of squarefree factors with multiplicity
52inline
53CFFList FqSqrf (const CanonicalForm& F, ///< [in] a poly
54                const Variable& alpha   ///< [in] algebraic variable
55               )
56{
57  CFFList result= squarefreeFactorization (F, alpha);
58  result.insert (CFFactor (Lc(F), 1));
59  return result;
60}
61
62/// squarefree factorization over GF.
63/// If input is not monic, the leading coefficient is dropped
64///
65/// @return a list of squarefree factors with multiplicity
66inline
67CFFList GFSqrf (const CanonicalForm& F ///< [in] a poly
68               )
69{
70  ASSERT (CFFactory::gettype() == GaloisFieldDomain,
71          "GF as base field expected");
72  Variable a= 1;
73  CFFList result= squarefreeFactorization (F, a);
74  result.insert (CFFactor (Lc(F), 1));
75  return result;
76}
77
78/// squarefree part of @a F/g, where g is the product of those squarefree
79/// factors whose multiplicity is 0 mod p, if @a F a pth power pthPower= F.
80///
81/// @return @a sqrfPart returns 1, if F is a pthPower, else it returns the
82///         squarefree part of @a F/g, where g is the product of those
83///         squarefree factors whose multiplicity is 0 mod p
84CanonicalForm
85sqrfPart (const CanonicalForm& F,  ///< [in] a poly
86          CanonicalForm& pthPower, ///< [in,out] returns F is F is a pthPower
87          const Variable& alpha    ///< [in] algebraic variable
88         );
89
90/// p^l-th root extraction, where l is maximal
91///
92/// @return @a maxpthRoot returns a p^l-th root of @a F, where @a l is maximal
93/// @sa pthRoot()
94CanonicalForm
95maxpthRoot (const CanonicalForm & F, ///< [in] a poly which is a pth power
96            const int & q,           ///< [in] size of the field
97            int& l                   ///< [in,out] @a l maximal, s.t. @a F is
98                                     ///< a p^l-th power
99           );
100
101#endif
102/* FAC_FQ_SQUAREFREE_H */
103
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