This file is indexed.

/usr/share/gap/lib/partitio.gd is in gap-libs 4r6p5-3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
#############################################################################
##
#W  partitio.gd                 GAP library                    Heiko Theißen
##
##
#Y  Copyright (C)  1997,  Lehrstuhl D für Mathematik,  RWTH Aachen, Germany
#Y  (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y  Copyright (C) 2002 The GAP Group
##

#############################################################################
##
#F  Partition( <list> ) . . . . . . . . . . . . . . . . partition constructor
##
DeclareGlobalFunction("Partition");

#############################################################################
##
#F  PartitionSortedPoints( <list> )
##
DeclareGlobalFunction("PartitionSortedPoints");

      
#############################################################################
##
#F  IsPartition( <P> )  . . . . . . . . . . . . test if object is a partition
##
DeclareGlobalFunction( "IsPartition" );
#T state this in the definition of a partition!


#############################################################################
##
#F  NumberCells( <P> )  . . . . . . . . . . . . . . . . . . . number of cells
##
DeclareGlobalFunction( "NumberCells" );


#############################################################################
##
#F  Cell( <P>, <m> )  . . . . . . . . . . . . . . . . . . . . .  cell as list
##
DeclareGlobalFunction( "Cell" );


#############################################################################
#F  Cells( <Pi> ) . . . . . . . . . . . . . . . . . partition as list of sets
##
DeclareGlobalFunction( "Cells" );

#############################################################################
##
#F  CellNoPoint( <part>,<pnt> )
##
##  Number of cell that contains <pnt>.
##
DeclareGlobalFunction("CellNoPoint");

#############################################################################
##
#F  PointInCellNo( <part>,<pnt>,<no> )
##
##  Is <pnt> in cell <no> of <part>?
##
DeclareGlobalFunction("PointInCellNo");

#############################################################################
##
#F  CellNoPoints( <part>,<pntlst> )
##
##  Numbers of cell that contains <pntlst>.
##
DeclareGlobalFunction("CellNoPoints");


#############################################################################
##
#F  Fixcells( <P> ) . . . . . . . . . . . . . . . . . . . .  fixcells as list
##
##  Returns a list of the points along in their  cell, ordered as these cells
##  are ordered
##
DeclareGlobalFunction( "Fixcells" );


#############################################################################
##
#F  SplitCell( <P>, <i>, <Q>, <j>, <g>, <out> ) . . . . . . . .  split a cell
##
##  Splits <P>[ <i> ],  by taking out all  the points that are also contained
##  in <Q>[ <j> ]  ^ g. The  new cell is appended to  <P> unless it would  be
##  empty. If the old cell would remain empty, nothing is changed either.
##
##  Returns the length of the new cell, or `false' if nothing was changed.
##
##  Shortcuts of  the  splitting algorithm:  If  the last  argument  <out> is
##  `true', at least one point will  move out. If <out> is  a number, at most
##  <out> points will move out.
##
DeclareGlobalFunction( "SplitCell" );


#############################################################################
##
#F  IsolatePoint( <P>, <a> )  . . . . . . . . . . . . . . . . isolate a point
##
##  Takes point <a> out of its cell in <P>, putting it into a new cell, which
##  is appended to <P>. However, does nothing, if <a> was already isolated.
##
##  Returns the  number of the cell   from <a> was  taken out,  or `false' if
##  nothing was changed.
##
DeclareGlobalFunction( "IsolatePoint" );

#############################################################################
##
#F  UndoRefinement( <P> ) . . . . . . . . . . . . . . . . . undo a refinement
##
##  Undoes the  effect of   the  last  cell-splitting actually performed   by
##  `SplitCell' or `IsolatePoint'. (This means that  if the last call of such
##  a function had no effect, `UndoRefinement' looks at the second-last etc.)
##  This fuses the last cell of <P> with an earlier cell.
##
##  Returns  the number of the  cell with which  the  last cell was fused, or
##  `false'   if the last  cell starts   at  `<P>.points[1]', because then it
##  cannot have been split off.
##
##  May behave undefined if there was no splitting before.
##
DeclareGlobalFunction( "UndoRefinement" );


#############################################################################
##
#F  FixpointCellNo( <P>, <i> )  . . . . . . . . .  fixpoint from cell no. <i>
##
##  Returns the first point of <P>[ <i> ] (should be a one-point cell).
##
DeclareGlobalFunction( "FixpointCellNo" );


#############################################################################
##
#F  FixcellPoint( <P>, <old> )  . . . . . . . . . . . . . . . . . . . . local
##
##  Returns a random cell number which is not yet contained  in <old> and has
##  length 1.
##
##  Adds this cell number to <old>.
##
DeclareGlobalFunction( "FixcellPoint" );


#############################################################################
##
#F  FixcellsCell( <P>, <Q>, <old> )  . . . . . . . . . . . local
##
##  Returns [ <K>, <I>  ] such that  for j=1,...|K|=|I|,  all points  in cell
##  <P>[  <I>[j] ] have value  <K>[j] in <Q.cellno> (i.e.,
##  lie   in cell <K>[j]  of the partition <Q>.
##  Returns `false' if <K> and <I> are empty.
##
DeclareGlobalFunction( "FixcellsCell" );


#############################################################################
##
#F  TrivialPartition( <Omega> ) . . . . . . . . . one-cell partition of a set
##
DeclareGlobalFunction( "TrivialPartition" );


#############################################################################
##
#F  OrbitsPartition( <G>, <Omega> ) partition determined by the orbits of <G>
##
DeclareGlobalFunction( "OrbitsPartition" );


#############################################################################
##
#F  SmallestPrimeDivisor( <size> )  . . . . . . . . .  smallest prime divisor
##
DeclareGlobalFunction( "SmallestPrimeDivisor" );


#############################################################################
##
#F  CollectedPartition( <P>, <size> ) . orbits on cells under group of <size>
##
##  Returns a  partition into unions of cells  of <P> of equal length, sorted
##  by  this length. However,  if there are $n$ cells  of equal length, which
##  cannot be fused under the action of a group of  order <size> (because $n$
##  < SmallestPrimeDivisor(  <size>  )), leaves   these $n$  cells   unfused.
##  (<size> = 1 suppresses this extra feature.)
##
DeclareGlobalFunction( "CollectedPartition" );


#############################################################################
##
#E