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#############################################################################
##
#W cvec.gd GAP 4 package `cvec'
## Max Neunhoeffer
##
## Copyright (C) 2007 Max Neunhoeffer, Lehrstuhl D f. Math., RWTH Aachen
## This file is free software, see license information at the end.
##
## This file contains the higher levels for compact vectors over finite
## fields.
##
#############################################################################
## Info Class:
#############################################################################
DeclareInfoClass( "InfoCVec" );
#############################################################################
## The technical stuff for typing:
#############################################################################
BindGlobal("CVecFieldInfoFamily",NewFamily("CVecFieldInfoFamily"));
BindGlobal("CVecClassFamily",NewFamily("CVecClassFamily"));
DeclareRepresentation( "IsCVecRep",
IsDataObjectRep and HasLength and IsCopyable and CanEasilyCompareElements and
CanEasilySortElements and IsListDefault and IsSmallList and
IsConstantTimeAccessList and IsFinite and IsVectorObj, [] );
# How about IsNoImmediateMethodsObject???
DeclareFilter( "IsCVecRepOverSmallField" );
DeclareFilter( "IsCVecRepOverPrimeField" );
#############################################################################
## Information about the base fields:
#############################################################################
DeclareGlobalFunction( "CVEC_NewCVecClass" );
DeclareGlobalFunction( "CVEC_NewCVecClassSameField" );
## Do not change the following numbers without adjusting cvec.c!!!
DeclareRepresentation( "IsCVecFieldInfo", IsPositionalObjectRep, [] );
## Such an object holds the following information:
## We use the same symbolic names for these indices as exported from cvec.c
## in the CVEC record: CVEC_IDX_p and so on:
## ![1] : p: cardinality of prime field
## ![2] : d: degree of extension over prime field
## ![3] : q=p^d as GAP integer
## ![4] : a GAP string object containing the coefficients of the
## Conway polynomial as unsigned int []
## ![5] : bits per element of the prime field
## ![6] : prime field elements per Word
## Note that for 64 bit machines we always put only twice as much
## prime field elements into a Word than for 32 bit machines (even if
## one more would fit!) such that conversion between binary formats
## is easier later on.
## ![7] : a GAP string object containing C data for internal use, see C part
## ![8] : best grease level
## ![9] : length of a grease table
## ![10]: filter list for the creation of new vectors over this field
## ![11]: table for GF(q) -> [0..q-1] conversion for q <= MAXSIZE_GF_INTERNAL
## ![12]: table for [0..q-1] -> GF(q) conversion for q <= MAXSIZE_GF_INTERNAL
## ![13]: 0 for q <= MAXSIZE_GF_INTERNAL, otherwise 1 if q is an
## immediate integer, 2 else
## ![14]: the scalars family, vectors get the CollectionsFamily
## this is FFEFamily(p) from the GAP library
## ![15]: filter list for the creation of new cmats over this field
DeclareRepresentation( "IsCVecClass", IsPositionalObjectRep, [] );
## We use the same symbolic names for these indices as exported from cvec.c
## in the CVEC record: CVEC_IDX_fieldinfo and so on:
## ![1]: field info (see above) for base field
## ![2]: length of vectors
## ![3]: wordlen of vectors
## ![4]: starting type (mutable version) for new vectors in this class
## ![5]: GF(p,d)
## ![6]: CVEC_lens[pos] where pos = Position(CVEC_q,q)
## ![7]: CVEC_classes[pos] where pos = Position(CVEC_q.q)
## the latter are used for fast access to other cvec classes over
## the same field.
## ![8]: starting type (mutable vesion) for new cmats using vectors in
## this class
#############################################################################
# Access to the base field:
#############################################################################
DeclareOperation( "CVecClass", [IsObject] );
DeclareOperation( "CVecClass", [IsObject, IsInt] );
DeclareOperation( "CVecClass", [IsPosInt, IsPosInt, IsInt] );
#############################################################################
# Making of vectors and conversions:
#############################################################################
DeclareOperation( "CVec", [IsObject, IsPosInt, IsPosInt] );
DeclareOperation( "CVec", [IsObject, IsObject] );
DeclareOperation( "CVec", [IsObject] );
DeclareOperation( "IntegerRep", [IsObject] );
DeclareOperation( "CVecNumber", [IsInt, IsCVecClass] );
DeclareOperation( "CVecNumber", [IsInt, IsPosInt, IsPosInt, IsPosInt] );
DeclareGlobalFunction( "CVEC_New" );
DeclareGlobalFunction( "CVEC_HandleScalar" );
DeclareOperation( "Memory", [IsCVecRep] );
#############################################################################
# Frobenius automorphisms for vectors:
#############################################################################
DeclareOperation("^", [IsCVecRep, IsMapping and IsOne]);
DeclareOperation("^", [IsCVecRep, IsFrobeniusAutomorphism]);
#############################################################################
# Looking for nonzero entries from behind:
#############################################################################
DeclareOperation( "PositionLastNonZero", [IsList] );
#############################################################################
# Slicing and friends:
#############################################################################
DeclareGlobalFunction( "CVEC_Slice" );
DeclareGlobalFunction( "CVEC_SliceList" );
DeclareGlobalFunction( "CVEC_Concatenation" );
#############################################################################
# The making of good hash functions:
#############################################################################
DeclareGlobalFunction( "CVEC_HashFunctionForCVecs" );
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License,
## or (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
##
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