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This file implements functions to map between extensions of finite fields. More...
Go to the source code of this file.
Functions | |
| int | findItem (const CFList &list, const CanonicalForm &item) |
| helper function More... | |
| CanonicalForm | getItem (const CFList &list, const int &pos) |
| helper function More... | |
| CanonicalForm | GFMapUp (const CanonicalForm &F, int k) |
maps a polynomial over to a polynomial over , d needs to be a multiple of k More... | |
| CanonicalForm | GFMapDown (const CanonicalForm &F, int k) |
maps a polynomial over to a polynomial over , d needs to be a multiple of k More... | |
| 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 . More... | |
| 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 . More... | |
| 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 More... | |
| CanonicalForm | mapPrimElem (const CanonicalForm &prim_elem, const Variable &alpha, const Variable &beta) |
compute the image of a primitive element of in . We assume . More... | |
| CanonicalForm | GF2FalphaRep (const CanonicalForm &F, const Variable &alpha) |
| changes representation by primitive element to representation by residue classes modulo a Conway polynomial More... | |
| CanonicalForm | Falpha2GFRep (const CanonicalForm &F) |
| change representation by residue classes modulo a Conway polynomial to representation by primitive element More... | |
| CanonicalForm | map (const CanonicalForm &primElem, const Variable &alpha, const CanonicalForm &F, const Variable &beta) |
map from to such that is mapped onto More... | |
| CanonicalForm | findMinPoly (const CanonicalForm &F, const Variable &alpha) |
compute minimal polynomial of via NTL More... | |
This file implements functions to map between extensions of finite fields.
Definition in file cf_map_ext.h.
| CanonicalForm Falpha2GFRep | ( | const CanonicalForm & | F | ) |
change representation by residue classes modulo a Conway polynomial to representation by primitive element
| [in] | F | some poly over F_p(alpha) where alpha is a root of a Conway poly |
Definition at line 170 of file cf_map_ext.cc.
| int findItem | ( | const CFList & | list, |
| const CanonicalForm & | item | ||
| ) |
| CanonicalForm findMinPoly | ( | const CanonicalForm & | F, |
| const Variable & | alpha | ||
| ) |
compute minimal polynomial of
via NTL
| [in] | F | an element of |
| [in] | alpha | algebraic variable |
Definition at line 434 of file cf_map_ext.cc.
| CanonicalForm getItem | ( | const CFList & | list, |
| const int & | pos | ||
| ) |
| CanonicalForm GF2FalphaRep | ( | const CanonicalForm & | F, |
| const Variable & | alpha | ||
| ) |
changes representation by primitive element to representation by residue classes modulo a Conway polynomial
| [in] | F | some poly over GF |
| [in] | alpha | root of a Conway poly |
Definition at line 162 of file cf_map_ext.cc.
| CanonicalForm GFMapDown | ( | const CanonicalForm & | F, |
| int | k | ||
| ) |
maps a polynomial over
to a polynomial over
, d needs to be a multiple of k
Definition at line 243 of file cf_map_ext.cc.
| CanonicalForm GFMapUp | ( | const CanonicalForm & | F, |
| int | k | ||
| ) |
maps a polynomial over
to a polynomial over
, d needs to be a multiple of k
Definition at line 207 of file cf_map_ext.cc.
| CanonicalForm map | ( | const CanonicalForm & | primElem, |
| const Variable & | alpha, | ||
| const CanonicalForm & | F, | ||
| const Variable & | beta | ||
| ) |
map from
to
such that
is mapped onto
| [in] | primElem | primitive element of |
| [in] | alpha | algebraic variable |
| [in] | F | an element of , whose minimal polynomial defines a field extension of of degree |
| [in] | beta | algebraic variable, root of F's minimal polynomial |
Definition at line 400 of file cf_map_ext.cc.
| 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
.
| [in] | F | poly over |
| [in] | prim_elem | primitive element of |
| [in] | im_prim_elem | image of prim_elem in |
| [in] | alpha | alg. variable |
| [in,out] | source | look up lists |
| [in,out] | dest | look up lists |
Definition at line 358 of file cf_map_ext.cc.
| CanonicalForm mapPrimElem | ( | const CanonicalForm & | prim_elem, |
| const Variable & | alpha, | ||
| const Variable & | beta | ||
| ) |
compute the image of a primitive element of
in
. We assume
.
| [in] | prim_elem | primitive element |
| [in] | alpha | algebraic variable |
| [in] | beta | algebraic variable |
Definition at line 377 of file cf_map_ext.cc.
| 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
.
| [in] | F | poly over |
| [in] | alpha | alg. variable |
| [in] | beta | alg. variable |
| [in] | prim_elem | primitive element of |
| [in] | im_prim_elem | image of prim_elem in |
| [in,out] | source | look up lists |
| [in,out] | dest | look up lists |
Definition at line 366 of file cf_map_ext.cc.
| 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
| [in] | alpha | some algebraic variable |
| [in,out] | beta | s.a. |
| [in,out] | fail | failure due to integer factorization failure? |
Definition at line 310 of file cf_map_ext.cc.