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#############################################################################
##
#A util2.gd GUAVA library Reinald Baart
#A &Jasper Cramwinckel
#A &Erik Roijackers
#A &David Joyner
##
## This file contains miscellaneous functions
##
## several functions added 12-16-2005
##
########################################################################
##
#F AllOneVector( <n> [, <field> ] )
##
## Return a vector with all ones.
##
DeclareOperation("AllOneVector", [IsInt, IsField]);
########################################################################
##
#F AllOneCodeword( <n>, <field> )
##
## Return a codeword with <n> ones.
##
DeclareOperation("AllOneCodeword", [IsInt, IsField]);
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##
#F IntCeiling( <r> )
##
## Return the smallest integer greater than or equal to r.
## 3/2 => 2, -3/2 => -1.
##
DeclareOperation("IntCeiling", [IsRat]);
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##
#F IntFloor( <r> )
##
## Return the greatest integer smaller than or equal to r.
## 3/2 => 1, -3/2 => -2.
##
DeclareOperation("IntFloor", [IsRat]);
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##
#F KroneckerDelta( <i>, <j> )
##
## Return 1 if i = j,
## 0 otherwise
##
DeclareOperation("KroneckerDelta", [IsInt, IsInt]);
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##
#F BinaryRepresentation( <elements>, <length> )
##
## Return a binary representation of an element
## of GF( 2^k ), where k <= length.
##
## If elements is a list, then return the binary
## representation of every element of the list.
##
## This function is used to make to Gabidulin codes.
## It is not intended to be a global function, but including
## it in all five Gabidulin codes is a bit over the top
##
## Therefore, no error checking is done.
##
########################################################################
##
#F SortedGaloisFieldElements( <size> )
##
## Sort the field elements of size <size> according to
## their log.
##
## This function is used to make to Gabidulin codes.
## It is not intended to be a global function, but including
## it in all five Gabidulin codes is not a good idea.
##
########################################################################
##
#F VandermondeMat( <Pts> , <a> )
##
## Input: Pts=[x1,..,xn], a >0 an integer
## Output: Vandermonde matrix (xi^j),
## for xi in Pts and 0 <= j <= a
## (an nx(a+1) matrix)
##
DeclareOperation("VandermondeMat", [IsList, IsInt]);
###########################################################
##
#F MultiplicityInList(L,a)
##
## Input: a list L
## an element a of L
## Output: the multiplicity a occurs in L
##
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##
#F MostCommonInList(L,a)
##
## Input: a list L
## Output: an a in L which occurs at least as much as any other in L
##
########################################################################
##
#F SupportToCodeword( <set> , <num> )
##
## Input: <set>, a subset of [1 .. <num>]
## Output: A codeword over GF(2) with wordlength <num> whose support is <set>
##
## For binary codes this function gives an inverse for Support().
DeclareOperation("SupportToCodeword", [IsSet, IsInt]);
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2026-03-28
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