source: git/factory/facFqSquarefree.h @ 72bfc8

jengelh-datetimespielwiese
Last change on this file since 72bfc8 was 72bfc8, checked in by Martin Lee <martinlee84@…>, 11 years ago
chg: deleted @internal
  • Property mode set to 100644
File size: 4.7 KB
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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 **/
12/*****************************************************************************/
13
14#ifndef FAC_FQ_SQUAREFREE_H
15#define FAC_FQ_SQUAREFREE_H
16
17#include "cf_assert.h"
18#include "cf_factory.h"
19#include "fac_sqrfree.h"
20
21/// squarefree factorization over a finite field
22/// @a return a list of squarefree factors with multiplicity
23CFFList
24squarefreeFactorization
25                (const CanonicalForm & F, ///<[in] a poly
26                 const Variable & alpha   ///<[in] either an algebraic variable,
27                                          ///< i.e. we are over some F_p (alpha)
28                                          ///< or a variable of level 1, i.e.
29                                          ///< we are F_p or GF
30                );
31
32/// squarefree factorization over \f$ F_{p} \f$.
33/// If input is not monic, the leading coefficient is dropped
34///
35/// @return a list of squarefree factors with multiplicity
36inline
37CFFList FpSqrf (const CanonicalForm& F, ///< [in] a poly
38                bool sort= true         ///< [in] sort factors by exponent?
39               )
40{
41  Variable a= 1;
42  int n= F.level();
43  CanonicalForm cont, bufF= F;
44  CFFList bufResult;
45
46  CFFList result;
47  for (int i= n; i >= 1; i++)
48  {
49    cont= content (bufF, i);
50    bufResult= squarefreeFactorization (cont, a);
51    if (bufResult.getFirst().factor().inCoeffDomain())
52      bufResult.removeFirst();
53    result= Union (result, bufResult);
54    bufF /= cont;
55    if (bufF.inCoeffDomain())
56      break;
57  }
58  if (!bufF.inCoeffDomain())
59  {
60    bufResult= squarefreeFactorization (bufF, a);
61    if (bufResult.getFirst().factor().inCoeffDomain())
62      bufResult.removeFirst();
63    result= Union (result, bufResult);
64  }
65  if (sort)
66    result= sortCFFList (result);
67  result.insert (CFFactor (Lc(F), 1));
68  return result;
69}
70
71/// squarefree factorization over \f$ F_{p}(\alpha ) \f$.
72/// If input is not monic, the leading coefficient is dropped
73///
74/// @return a list of squarefree factors with multiplicity
75inline
76CFFList FqSqrf (const CanonicalForm& F, ///< [in] a poly
77                const Variable& alpha,  ///< [in] algebraic variable
78                bool sort= true         ///< [in] sort factors by exponent?
79               )
80{
81  int n= F.level();
82  CanonicalForm cont, bufF= F;
83  CFFList bufResult;
84
85  CFFList result;
86  for (int i= n; i >= 1; i++)
87  {
88    cont= content (bufF, i);
89    bufResult= squarefreeFactorization (cont, alpha);
90    if (bufResult.getFirst().factor().inCoeffDomain())
91      bufResult.removeFirst();
92    result= Union (result, bufResult);
93    bufF /= cont;
94    if (bufF.inCoeffDomain())
95      break;
96  }
97  if (!bufF.inCoeffDomain())
98  {
99    bufResult= squarefreeFactorization (bufF, alpha);
100    if (bufResult.getFirst().factor().inCoeffDomain())
101      bufResult.removeFirst();
102    result= Union (result, bufResult);
103  }
104  if (sort)
105    result= sortCFFList (result);
106  result.insert (CFFactor (Lc(F), 1));
107  return result;
108}
109
110/// squarefree factorization over GF.
111/// If input is not monic, the leading coefficient is dropped
112///
113/// @return a list of squarefree factors with multiplicity
114inline
115CFFList GFSqrf (const CanonicalForm& F, ///< [in] a poly
116                bool sort= true         ///< [in] sort factors by exponent?
117               )
118{
119  ASSERT (CFFactory::gettype() == GaloisFieldDomain,
120          "GF as base field expected");
121  return FpSqrf (F, sort);
122}
123
124/// squarefree part of @a F/g, where g is the product of those squarefree
125/// factors whose multiplicity is 0 mod p, if @a F a pth power pthPower= F.
126///
127/// @return @a sqrfPart returns 1, if F is a pthPower, else it returns the
128///         squarefree part of @a F/g, where g is the product of those
129///         squarefree factors whose multiplicity is 0 mod p
130CanonicalForm
131sqrfPart (const CanonicalForm& F,  ///< [in] a poly
132          CanonicalForm& pthPower, ///< [in,out] returns F is F is a pthPower
133          const Variable& alpha    ///< [in] algebraic variable
134         );
135
136/// p^l-th root extraction, where l is maximal
137///
138/// @return @a maxpthRoot returns a p^l-th root of @a F, where @a l is maximal
139/// @sa pthRoot()
140CanonicalForm
141maxpthRoot (const CanonicalForm & F, ///< [in] a poly which is a pth power
142            const int & q,           ///< [in] size of the field
143            int& l                   ///< [in,out] @a l maximal, s.t. @a F is
144                                     ///< a p^l-th power
145           );
146
147#endif
148/* FAC_FQ_SQUAREFREE_H */
149
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