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cf_map_ext.h
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1// -*- c++ -*-
2//*****************************************************************************
3/** @file cf_map_ext.h
4 *
5 * This file implements functions to map between extensions of finite fields
6 *
7 * @par Copyright:
8 * (c) by The SINGULAR Team, see LICENSE file
9 *
10 * @author Martin Lee
11 * @date 16.11.2009
12**/
13//*****************************************************************************
14
15#ifndef CF_MAP_EXT_H
16#define CF_MAP_EXT_H
17
18// #include "config.h"
19
20int findItem (const CFList& list, const CanonicalForm& item);
21
22CanonicalForm getItem (const CFList& list, const int& pos);
23
24/// maps a polynomial over \f$ GF(p^{k}) \f$ to a polynomial over
25/// \f$ GF(p^{d}) \f$ , d needs to be a multiple of k
26CanonicalForm GFMapUp (const CanonicalForm & F, int k);
27
28/// maps a polynomial over \f$ GF(p^{d}) \f$ to a polynomial over
29/// \f$ GF(p^{k})\f$ , d needs to be a multiple of k
30CanonicalForm GFMapDown (const CanonicalForm & F, int k);
31
32/// map F from \f$ F_{p} (\alpha ) \f$ to \f$ F_{p}(\beta ) \f$.
33/// We assume \f$ F_{p} (\alpha ) \subset F_{p}(\beta ) \f$.
35mapUp (const CanonicalForm& F, ///<[in] poly over \f$ F_{p} (\alpha ) \f$
36 const Variable& alpha, ///<[in] alg. variable
37 const Variable& beta, ///<[in] alg. variable
38 const CanonicalForm& prim_elem, ///<[in] primitive element of \f$ F_{p} (\alpha ) \f$
39 const CanonicalForm& im_prim_elem,///<[in] image of prim_elem in \f$ F_{p} (\beta ) \f$
40 CFList& source, ///<[in,out] look up lists
41 CFList& dest ///<[in,out] look up lists
42 );
43
44/// map F from \f$ F_{p} (\beta ) \f$ to \f$ F_{p}(\alpha ) \f$.
45/// We assume \f$ F_{p} (\alpha ) \subset F_{p}(\beta ) \f$ and F in
46/// \f$ F_{p}(\alpha ) \f$.
48mapDown (const CanonicalForm& F, ///<[in] poly over \f$ F_{p} (\beta ) \f$
49 const CanonicalForm& prim_elem, ///<[in] primitive element of \f$ F_{p} (\alpha ) \f$
50 const CanonicalForm& im_prim_elem,///<[in] image of prim_elem in \f$ F_{p} (\beta ) \f$
51 const Variable& alpha, ///<[in] alg. variable
52 CFList& source, ///<[in,out] look up lists
53 CFList& dest ///<[in,out] look up lists
54 );
55
56/// determine a primitive element of \f$ F_{p} (\alpha ) \f$,
57/// \f$ \beta \f$ is a primitive element of a field which is isomorphic to
58/// \f$ F_{p}(\alpha ) \f$
60primitiveElement (const Variable& alpha, ///< [in] some algebraic variable
61 Variable& beta, ///< [in,out] s.a.
62 bool& fail ///< [in,out] failure due to integer
63 ///< factorization failure?
64 );
65
66/// compute the image of a primitive element of \f$ F_{p} (\alpha ) \f$
67/// in \f$ F_{p}(\beta ) \f$.
68/// We assume \f$ F_{p} (\alpha ) \subset F_{p}(\beta ) \f$.
70mapPrimElem (const CanonicalForm& prim_elem, ///< [in] primitive element
71 const Variable& alpha, ///< [in] algebraic variable
72 const Variable& beta ///< [in] algebraic variable
73 );
74
75/// changes representation by primitive element to representation by residue
76/// classes modulo a Conway polynomial
77CanonicalForm GF2FalphaRep (const CanonicalForm& F, ///< [in] some poly over GF
78 const Variable& alpha ///< [in] root of a Conway
79 ///< poly
80 );
81
82/// change representation by residue classes modulo a Conway polynomial
83/// to representation by primitive element
84CanonicalForm Falpha2GFRep (const CanonicalForm& F ///<[in] some poly over
85 ///< F_p(alpha) where alpha
86 ///< is a root of a Conway
87 ///< poly
88 );
89
90/// map from \f$ F_p(\alpha) \f$ to \f$ F_p(\beta) \f$ such that
91/// \f$ F\in F_p(\alpha) \f$ is mapped onto \f$ \beta \f$
92///
93/// @return @a map returns the image of @a primElem such that the above
94/// described properties hold
96map (const CanonicalForm& primElem,///< [in] primitive element of
97 ///< \f$ F_p (\alpha) \f$
98 const Variable& alpha, ///< [in] algebraic variable
99 const CanonicalForm& F, ///< [in] an element of \f$ F_p (\alpha) \f$,
100 ///< whose minimal polynomial defines a field
101 ///< extension of \f$ F_p \f$ of degree
102 ///< \f$ F_p (\alpha):F_p \f$
103 const Variable& beta ///< [in] algebraic variable, root of \a F's
104 ///< minimal polynomial
105 );
106
107/// compute minimal polynomial of \f$ F\in F_p(\alpha)\backslash F_p \f$ via NTL
108///
109/// @return @a findMinPoly computes the minimal polynomial of F
111findMinPoly (const CanonicalForm& F, ///< [in] an element of
112 ///< \f$ F_p(\alpha)\backslash F_p \f$
113 const Variable& alpha ///< [in] algebraic variable
114 );
115
116#endif
int k
Definition: cfEzgcd.cc:99
int findItem(const CFList &list, const CanonicalForm &item)
helper function
Definition: cf_map_ext.cc:41
CanonicalForm mapDown(const CanonicalForm &F, const CanonicalForm &prim_elem, const CanonicalForm &im_prim_elem, const Variable &alpha, CFList &source, CFList &dest)
map F from to . We assume and F in .
Definition: cf_map_ext.cc:431
CanonicalForm GFMapDown(const CanonicalForm &F, int k)
maps a polynomial over to a polynomial over , d needs to be a multiple of k
Definition: cf_map_ext.cc:276
CanonicalForm primitiveElement(const Variable &alpha, Variable &beta, bool &fail)
determine a primitive element of , is a primitive element of a field which is isomorphic to
Definition: cf_map_ext.cc:342
CanonicalForm findMinPoly(const CanonicalForm &F, const Variable &alpha)
compute minimal polynomial of via NTL
Definition: cf_map_ext.cc:640
CanonicalForm mapUp(const CanonicalForm &F, const Variable &alpha, const Variable &beta, const CanonicalForm &prim_elem, const CanonicalForm &im_prim_elem, CFList &source, CFList &dest)
map F from to . We assume .
Definition: cf_map_ext.cc:439
CanonicalForm getItem(const CFList &list, const int &pos)
helper function
Definition: cf_map_ext.cc:53
CanonicalForm Falpha2GFRep(const CanonicalForm &F)
change representation by residue classes modulo a Conway polynomial to representation by primitive el...
Definition: cf_map_ext.cc:203
CanonicalForm GFMapUp(const CanonicalForm &F, int k)
maps a polynomial over to a polynomial over , d needs to be a multiple of k
Definition: cf_map_ext.cc:240
CanonicalForm GF2FalphaRep(const CanonicalForm &F, const Variable &alpha)
changes representation by primitive element to representation by residue classes modulo a Conway poly...
Definition: cf_map_ext.cc:195
CanonicalForm map(const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta)
map from to such that is mapped onto
Definition: cf_map_ext.cc:504
CanonicalForm mapPrimElem(const CanonicalForm &prim_elem, const Variable &alpha, const Variable &beta)
compute the image of a primitive element of in . We assume .
Definition: cf_map_ext.cc:450
factory's main class
Definition: canonicalform.h:86
factory's class for variables
Definition: variable.h:33
Variable alpha
Definition: facAbsBiFact.cc:51
Variable beta
Definition: facAbsFact.cc:95