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GAP 4 Package cvec

Compact vectors over finite fields

Version 2.4

September 2012

Max Neunhöffer
Email: neunhoef@mcs.st-and.ac.uk
Homepage: http://www-groups.mcs.st-and.ac.uk/~neunhoef
Address:
School of Mathematics and Statistics Mathematical Institute North Haugh St Andrews, Fife KY16 9SS Scotland, UK

Copyright

© by Max Neunhöffer

This package may be distributed under the terms and conditions of the GNU Public License Version 2.

Contents

1.2 Overview over this manual

2 Installation of the cvec-Package

3 The Data Structures

3.1 Finite field elements

3.2 Compressed Vectors in Memory

  3.2-1 Packing of prime field elements
  3.2-2 Extension Fields
  3.2-3 How is information about the base field stored?
  3.2-4 Limits that follow from the Data Format

3.3 Compressed Matrices

3.4 External Representation of Matrices on Storage

3.4-1 Byte ordering and word length
3.4-2 The header of a cmat file

  4.1-1 CVec
  4.1-2 CVec
  4.1-3 CVec
  4.1-4 CVec
  4.1-5 CVec
  4.1-6 CVec
  4.1-7 CVecClass
  4.1-8 CVecClass
  4.1-9 CVecClass
  4.1-10 CVecClass
  4.1-11 CVecClass
  4.1-12 CVecClass
  4.1-13 ZeroSameMutability
  4.1-14 ShallowCopy
  4.1-15 Randomize

  4.2-1 Handling of scalars in arithmetic operations
  4.2-2 \+
  4.2-3 \-
  4.2-4 AdditiveInverseSameMutability
  4.2-5 AdditiveInverseMutable
  4.2-6 \*
  4.2-7 AddRowVector
  4.2-8 MultRowVector
  4.2-9 ScalarProduct
  4.2-10 ZeroMutable
  4.2-11 ZeroVector

4.3 Element access and slicing

  4.3-1 ELM_LIST
  4.3-2 ASS_LIST
  4.3-3 ELMS_LIST
  4.3-4 CVEC_Slice
  4.3-5 CopySubVector
  4.3-6 CVEC_Concatenation

4.4 Comparison of Vectors and other information

  4.4-1 =
  4.4-2 LT
  4.4-3 IsZero
  4.4-4 PositionNonZero
  4.4-5 PositionLastNonZero
  4.4-6 Length

4.5 Changing representation, Unpacking

  4.5-1 Unpack
  4.5-2 IntegerRep
  4.5-3 NumberFFVector
  4.5-4 CVecNumber

4.6 Access to the base field

  4.6-1 BaseDomain
  4.6-2 BaseField
  4.6-3 Characteristic
  4.6-4 DegreeFFE

4.7 Hashing techniques for cvecs

4.7-1 CVEC_HashFunctionForCVecs
4.7-2 ChooseHashFunction

  5.1-1 CMat
  5.1-2 CMat
  5.1-3 CMat
  5.1-4 CMat
  5.1-5 CVEC_ZeroMat
  5.1-6 CVEC_IdentityMat
  5.1-7 CVEC_RandomMat
  5.1-8 MutableCopyMat
  5.1-9 Matrix

5.2 Matrices as lists

  5.2-1 Add
  5.2-2 Remove
  5.2-3 ELM_LIST
  5.2-4 ASS_LIST
  5.2-5 ELMS_LIST
  5.2-6 ASSS_LIST
  5.2-7 Length
  5.2-8 ShallowCopy
  5.2-9 Collected
  5.2-10 DuplicateFreeList
  5.2-11 Append
  5.2-12 Filtered
  5.2-13 Unbind

  5.3-1 \+
  5.3-2 \-
  5.3-3 AdditiveInverseSameMutability
  5.3-4 AdditiveInverseMutable
  5.3-5 \*
  5.3-6 \*
  5.3-7 \^
  5.3-8 \*
  5.3-9 ZeroSameMutability
  5.3-10 ZeroMutable
  5.3-11 OneSameMutability
  5.3-12 OneMutable
  5.3-13 InverseMutable
  5.3-14 InverseSameMutability
  5.3-15 TransposedMat
  5.3-16 KroneckerProduct

5.4 Comparison of matrices and other information

  5.4-1 =
  5.4-2 LT
  5.4-3 IsZero
  5.4-4 IsOne
  5.4-5 IsDiagonalMat
  5.4-6 IsUpperTriangularMat
  5.4-7 IsLowerTriangularMat
  5.4-8 CVEC_HashFunctionForCMats
  5.4-9 ChooseHashFunction

5.5 Slicing and submatrices

5.5-1 ExtractSubMatrix
5.5-2 CopySubMatrix

5.6 Information about matrices

  5.6-1 BaseField
  5.6-2 Characteristic
  5.6-3 DegreeFFE
  5.6-4 DefaultField

5.7 Input and output

  5.7-1 CVEC_WriteMat
  5.7-2 CVEC_WriteMatToFile
  5.7-3 CVEC_WriteMatsToFile
  5.7-4 CVEC_ReadMat
  5.7-5 CVEC_ReadMatFromFile
  5.7-6 CVEC_ReadMatsFromFile

5.8-1 GreaseMat
5.8-2 UnGreaseMat

5.9 Everything else

  5.9-1 Randomize
  5.9-2 OverviewMat
  5.9-3 Unpack

8 Cooperation with the GAP library

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