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Quellcode-Bibliothek straight.gi
Sprache: Shell
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#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Thomas Breuer, Alexander Hulpke, Max Neunhöffer.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the implementations of methods and functions
## for straight line programs.
##
## 1. Functions for straight line programs
## 2. Functions for elements represented by straight line programs
##
#############################################################################
##
## 1. Functions for straight line programs
##
#############################################################################
##
#V StraightLineProgramsFamily
#V StraightLineProgramsDefaultType
##
java.lang.StringIndexOutOfBoundsException: Range [0, 44) out of bounds for length 22
java.lang.StringIndexOutOfBoundsException: Range [14, 1) out of bounds for length 60
line :0123456789java.lang.StringIndexOutOfBoundsException: Range [64, 63) out of bounds for length 73
NewTypejava.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
#############################################################################
##
#F StraightLineProgram( <lines>[, <nrgens>] )
#F StraightLineProgram( <string>, <gens> )
#F StraightLineProgramNC( <lines>[, <nrgens>] )
#F StraightLineProgramNC( <string>, <gens> )
##
stallGlobalFunctionStraightLineProgramj=lenthen
local result;
if elif Length( arg ) (arg =then
if not IsStraightLineProgram{[ .len},script ) java.lang.StringIndexOutOfBoundsException: Range [70, 71) out of bounds for length 70
or not j: Length script ) + Length( gens );
ObjectifyWithAtt( prog ,[ [, 1, )java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 65
else
return result;
end );SetNrInputsOfStraightLineProgram( prog,java.lang.StringIndexOutOfBoundsException: Range [0, 1) out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Range [25, 13) out of bounds for length 16
localjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
# Get the arguments. +Lengthgens );
if##
];
functionstring,gens, {[ +1. }gens then
(rg[]
lines:= [];
if java.lang.StringIndexOutOfBoundsException: Range [14, 1) out of bounds for length 17
java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 17
fi;
:=Length( Add(script,[[ ,1,slen,1],java.lang.StringIndexOutOfBoundsException: Range [49, 15) out of bounds for length 15
elif '
lines :=fi;
nrgens := arg[2];
else
java.lang.StringIndexOutOfBoundsException: Range [0, 11) out of bounds for length 0
fi;
;
ObjectifyWithAttributes( prog, StraightLineProgramsDefaultType,
,lines ;
if IsBound( nrgens ) and IsPosInt( nrgens ) then
SetNrInputsOfStraightLineProgram )
;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
end );
pos:= First( [ 1 .. len ], i -> string{ [ 1 .. i ] } in gens );
##
#F StringToStraightLineProgram( <string>, <gens>, <script> )
##
InstallGlobalFunction( StringToStraightLineProgram,
function( string, gens, script )
local pos,
java.lang.StringIndexOutOfBoundsException: Range [72, 1) out of bounds for length 72
len,
java.lang.StringIndexOutOfBoundsException: Range [0, 11) out of bounds for length 2
,
sign,sign: ;
slen,
n
i j;
# If the string contains `*' signs then remove them.=-
if
string localdefined
fijava.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
# Split the string according to brackets `(' and `)'
pos:= Position( string, ' pos: pos+;
pos=failjava.lang.StringIndexOutOfBoundsException: Range [22, 23) out of bounds for length 22
#
extrep: ;
fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
:string[os len]}java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
od
if pos local needed ( )
needed:= Difference(line{ 1 .Length( line )- 1 ]}java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 66
pos:= java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
if pos < len java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
p:= ;
sign:= 1;
pos:= pos + 1;
if pos <=len and defined)java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 37
sign:=
pos:= pos + 1;
fi;
j:= needed:=(java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 39
xinput needed;
pos i
fi;
exp: sign * exp;
else
exp # Inspect the lines.
fi;
Append( extrep java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
;
if <>java.lang.StringIndexOutOfBoundsException: Range [35, 33) out of bounds for length 55
;
return true;
java.lang.StringIndexOutOfBoundsException: Range [11, 8) out of bounds for length 21
# Split before the bracket.
if not for i in [ 2 ..len
[1. pos1 ,,cript )then
open: open+;
fi;
j:= Length( scriptelifstring )java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 22
if java.lang.StringIndexOutOfBoundsException: Range [0, 12) out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
return false;
fi;
slen Length script )+
if j < slen then
Add( jjava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 23
fi;
return truejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
# Find the corresponding closing bracket.
open:= 0
:( j:= j +
forifjava.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 29
openslen=;
elif string[i] = ')' then
newjava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
j=
else
# The bracket may be powered or be multiplied.
]
exp=0java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
=+;
sign:= 1;
j: )+ gens)
:=-1java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
j:= j+1;
fi r:=ShallowCopy gens
( string[j])do
exp:= 10 * string{ [ 2.i- respos:;
:j+1;
od;
not(
string [2 ..i- ] } gens, script )then
return false;
fi;
slen:= Length( script ) + Length( gens ) + 1;
Add script,[[slen 1,sign *exp , ] ;
if j <= len then
elif 2 <= Lefi
:() (ensjava.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 55
falsejava.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
fi;
j ()Lengthgens ;
fi
else
if not StringToStraightLineProgram(
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
return
fi;
return r[ r ]
if StringToStraightLineProgram(
string{ [ i+1 .. len ] }, gens, script ) then
return false;
fi;
slen:= Length(#M Display( <prog> )
if j#
Add java.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 30
fi;
fi;
end ;
fi;
od;
java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
fi;
end )
#############################################################################
##
#M NrInputsOfStraightLineProgram( <prog> )
##
## If no lines of type 1. occur then the number of generators can be
## read off from the lines;
## it is equal to the maximum of positions such that in a step of the
## program the entry is accessed but the position has not been assigned
## before.
##
od NrInputsOfStraightLineProgram
"or java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
[ if IsBoundgensnames ) then
java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
local if not IsEmpty needed )
maxinput, current maximum of input neededi>( "g",String ) ifmaxinput <needed then
lines # lines of `prog'
endjava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
, # one line of the program
i j;# loop over the java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
defined:= [];
maxinput:= 0;
lines:= LinesOfStraightLineProgramif ForAll(line, IsInt )thenfor j in[2 4 . Length(line )2]do
len:= Length( lines );
function )
local needed;
needed:= Difference( (java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
defined );
)then
needed:= MaximumList( needed );
if maxinput < java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 22
maxinput:= needed;
fi;
fi;
end;
# Inspect the lines.
od;
line:= lines[i];
if ForAll( java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
if i = len (" input:n");
adjust( line );
else
##
fi;
elif Length( line ) =( ResultOfLineOfStraightLineProgram",
java.lang.StringIndexOutOfBoundsException: Range [26, 15) out of bounds for length 26
AddSet( defined, line[2] );
eliflenfor in46 .(line java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
for j in line do
adjust(else
fi;
java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 7
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 0
end;
#############################################################################
##
#M ResultOfStraightLineProgram( <prog>, <gens> )
##
BindGlobal "esultOfLineOfStraightLineProgram",
function(line r )
local respos, position of the current intermediate result of `prog'
new:=r[line[] ;
if linejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
new=new^^line[2;
fi;
for i in [ 4, 6 .. Length( linelen: len 1
if line[i] = 1 then
new=new *[line[ i1]]java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
else
new=new notIsEmpty )and java.lang.StringIndexOutOfBoundsException: Range [42, 40) out of bounds for length 56
fi;
od
return new;
end ) Add(r ResultOfLineOfStraightLineProgram( : (line ;
for [1.len 1]
"for elif = ) IsInt java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 24
[ IsStraightLineProgram, r[line[2]]:=ResultOfLineOfStraightLineProgram len ] )java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
function
r
respos, # position of the current intermediate result of `prog'
line; # loop over the lines
# Initialize the list of intermediate results.
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 2
# Loop over the program.##
for line
if java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
# The line describes a word to be appended.
Addjava.lang.StringIndexOutOfBoundsException: Range [13, 12) out of bounds for length 19
respos
2 ( IsInt] java.lang.StringIndexOutOfBoundsException: Range [56, 57) out of bounds for length 56
# The line describes a word that shall replace.
r[ line ;
respos:= line[ java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
else
# The line describes a list of words to be returned. linesjava.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
;
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
=recordgensnames;
# Return the result. gensnames ( )
return r java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
end )java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 10
#############################################################################
##
#M Display( <prog> )
#M Display( <prog>, <record> )
##
i ;
"for
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
function not IsList 2 java.lang.StringIndexOutOfBoundsException: Range [33, 31) out of bounds for length 46
( ( ;
end );
java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0
f astraight ,anda "java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
[ IsStraightLineProgram, IsRecord if not fi;
( prog,record )
mes,
listname,
PrintLinefi;
AddSet( defined 0<
lines,
len,
line,
jjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
# Get and check the arguments.
if
gensnames:= record.gensnames if not ( Print( "# input:\n" );
else
gensnames:=List 1 . NrInputsOfStraightLineProgram ) ]
fi
;
1 ;
listname:= java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 7
( java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
r
fi;
java.lang.StringIndexOutOfBoundsException: Range [14, 13) out of bounds for length 33
(,java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 40
or
r" [j1] ]java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
line]>1
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
Print( "*" )java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
od;
= ############################################################################
0
java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
linej ajava.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 34
Print( "^", java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
len:len +1java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
# Print the initialisation.
"n )java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
:= [";
if not IsEmpty( gensnames ) ;
Print( gensnames
fi;
len
(",[#
od;
";")
java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 26
: ;
len end ) (line[len ] );
Print
iin [
line:= lines[i];
if Length( java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 9
andjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 0
PrintLine( line[1] );
Print( ";\n" );
f 2] i=java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 52
len:= , .
fi;
elif not IsEmpty( ,
len:= len + 1;
Print("[ len, ]= )java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
PrintLine(line )
("\");
elif ForAll ;
values\[")
: Length =NrInputsOfStraightLineProgram)
for j [ 1 . len -1
l[j java.lang.StringIndexOutOfBoundsException: Index 31 out of bounds for length 31
Print , " ;
od;
if0<len
PrintLine if 2< 0
fi;
Print( " ]\java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
return;
fi;
od
value\[,len,"\ ;
end );
#############################################################################
##
#M IsInternallyConsistent( <prog> )
##
InstallMethod( java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 0
"for a straight line program",
[ IsStraightLineProgram,
line,
local lines,
,
defined,
testline,
lenifLength(arg)=2and IsStraightLineProgram [] )
i,
line;
lines:= LinesOfStraightLineProgram( prog
ifnot ( lines )or java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
alsejava.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
fi;
if HasNrInputsOfStraightLineProgram( prog ) then
nrgens:= NrInputsOfStraightLineProgramelif )= return falsejava.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
: [ .nrgens ;
else
defined:= [];
fi;
testline:= function( line if not (line) (line[1, ))then
local java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 11
external return false
len:=Length( line);
if len mod 2 <> 0 then
return false;
fi;
# and the generator numbers are stored at odd positions.
gens:= line{ [ 1, 3 . 1 ]}java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
if not ForAll( return ForAll( ,testline )
return false;
fi;
# If the number of generators is stored then check
# that only defined positions are accessed.
returnod;
end;
len: Length(lines)java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
for i in [ 1 .. len ] do
line:= lines[i];
if not IsList( line ) then
java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 21
elif (line ForAll(line, )then
if not testline( line ) or ( i < len and not IsBound( ( prog));
return false;
fi;
AddSet(defined Length( defined ) + 1 );
elif Length( line ) = 2 a[ respos ] )
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
return false;
fi;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
return false;
fi;
IsStraightLineProgram ,
elif i=len java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
and ForAll( x, IsInt ) ) then
return ForAll( line, testline );
else
# The syntax of the line is not correct.
return false;
fijava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
od;
return true;
end );
#############################################################################
##
#M PrintObj( <prog> )
##
InstallMethod( PrintObj,
"for a straight not java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 0
[ IsStraightLineProgram java.lang.StringIndexOutOfBoundsException: Range [0, 10) out of bounds for length 7
function( prog )
Print( "traightLineProgram( if not java.lang.StringIndexOutOfBoundsException: Range [29, 23) out of bounds for length 43
LinesOfStraightLineProgram(end );
if HasNrInputsOfStraightLineProgram
Print
fi;
Print { )java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 10
#############################################################################
##
#M ViewObj( <prog> )
##
(ViewObj,
"for
[ IsStraightLineProgram ],
function( prog )
Print( "<straight line local lines, ,lastline, inp2, max, i, java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
end );
#############################################################################
##
#F StringOfResultOfStraightLineProgram( <prog>, <gensnames>[, \"LaTeX\"] )
##
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
function(
local newjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
new: =false;
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Range [0, 13) out of bounds for length 9
Append( new, r[ line[ i-1 ] ] );
if not isatomic[ line[ i-1 ] ] then
Add( new, '(' );
fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
Append( new, r[ line[ i-1 ] ] );
if not isatomic[ java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 25
Add( new, 'java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
ror(" Error( "usage
^)
if LaTeX then
Add( new, '{' );
Unbijava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Append( new, String( line[i] ) fori in lastlinensnames )java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
if LaTeX then
Add( new, '}' );
fi
fi line in ( do
od;
return ;
end );
( StringOfResultOfStraightLineProgram, function( arg )
local ,a, ))java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
gensnames, a[ respos]=false;
LaTeX,
r,
if inp2 java.lang.StringIndexOutOfBoundsException: Range [23, 24) out of bounds for length 23
line,
result,
l [java.lang.StringIndexOutOfBoundsException: Range [19, 17) out of bounds for length 28
# Get and check the arguments.
java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 22
and IsList( arg[2] ]> java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
prog:= arg[1];
gensnames:= arg[2];
LaTeX
elif Length( arg ) = 3 and IsStraightLineProgram( java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 27
java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
and IsString( java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 41 out of bounds for length 34
: ]
gensnames:= arg[2];
else
Error#F java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
<>,"\ java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 44
fi ( ,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
#java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
r:= ShallowCopy( )
a:= ListWithIdenticalEntries( java.lang.StringIndexOutOfBoundsException: Range [8, 7) out of bounds for length 27
java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 19
# Loop over the program.
for line in LinesOfStraightLineProgram( prog ) do
if not IsEmpty(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
# The line describes a word to be appended.
Add( r, java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 2
r, a, LaTeX ) );
respos:## If a program overwrites some of the original generators then we first
max=
= ;
# The line describes a word that shall replace.
=2];
r : n, # number of inputs of all in `listofprogs
r, a, LaTeX );
a[ respos ]:= false;
else
# The line describes a list of words to be returned.Add , , ,java.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72
result:= "
for l do
Appendj; utputsjava.lang.StringIndexOutOfBoundsException: Range [48, 47) out of bounds for length 74
java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 22
Length java.lang.StringIndexOutOfBoundsException: Range [18, 17) out of bounds for length 32
,"java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 33
od;
if"java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 43
Remove ifjava.lang.StringIndexOutOfBoundsException: Range [21, 19) out of bounds for length 32
Remove(result );
fi;
Append( result, " ]" );
return result;
fi;
od;
return r[ respos ];
end );
#############################################################################
##
#F CompositionOfStraightLinePrograms( <prog2>, <prog1> )
##
# Append the lines of `prog2'.
java.lang.StringIndexOutOfBoundsException: Range [28, 12) out of bounds for length 28
for lineproglines= prog ;
lines:= ShallowCopy( LinesOfStraightLineProgram( prog1 ) );
len: Length(lines );
lastline:= lines[ len ];
: NrInputsOfStraightLineProgram );
if ForAll( lastline, IsList ) then
# Check that the programs fit together.
shiftgens: falsejava.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 24
inputs <>");
fi;
# The last line is a list of external representations of assoc. words.
# Copy them first to safe positions, then to the first positions.
max:= NrInputsOfStraightLineProgram( prog1 );
for i in[ Append , List [ .n] > i 1 ] i+offset ] )
if IsList( lines[i][1] ) then
max
else
max:= max + 1;
fi;
od;
Unbind( java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 9
pos:= max;
for i in lastline do
max:= max + 1;
Addlines, [i max ]);
od;
for i in [ 1 .. Length( lastline )## copy the generators.
Add lines [[pos +ijava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
od;
else
# java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
> 1 then
Error( "outputs of <prog1>results # results line of the result program
;
if Length( lastline ) = 2 and IsList( lastline[1] ) then
# The last line is a pair of the external representation of an assoc.
#
# Copy the word to position 1 if necessary.
if lastline[2] <> 1 then
Add( lines, [ [ lastline[2], 1 ], 1 ] );
fi;
else
The line externalrepresentation anassoc.word.
# Store it at position 1.
[ Length(ogs>ustbenonempty ,
fi;
fi : NrInputsOfStraightLineProgram [1])
# Append the lines of `prog2'.
# (Rewrite lines of type 1.)
max= ;
for line in LinesOfStraightLineProgram( prog2 ) do
if ForAll( line, IsList ) then
Add lines,line )
fi
max:= max + 1; of lines,the line,and offset.
Add( lines, [ line, max ] );
else
Loop over the programs, and add the results to `results'.
, line );
fi;
od;
# Construct and return the new program.
#
NrInputsOfStraightLineProgram( prog1 ) );
end );
#############################################################################
##
#F IntegratedStraightLineProgram( <listofprogs> )
##
## The idea is to concatenate the lists of lines of the programs in the list
## <listofprogs> after shifting the positions they refer to.
## If a program overwrites some of the original generators then we first
## copy the generators.
##
(lines .( )-
function( listofprogs )
local n, # number of inputs of all in `listofprogs'
lines, # list of lines of the result program offset:= offset - n;
results, # results line of the result program
nextoffset, # maximal position used up to now
prog over `'
proglines, # list of lines of `prog'
offset, # maximal position used before the current program
shiftgens,
i,line, # loop over `proglines'
newline, # line with shifted source positions
;# loop over the odd positions in `newline'
# Check the input.
if not # (Increase
newline=ShallowCopy )java.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 40
or not ForAll( listofprogs,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Error( "<listofprogs> must be a nonempty list ",
"of straight line programs" );
fi; od
n:= NrInputsOfStraightLineProgram(
if not ForAll( listofprogs,
prog ->#M StraightLineProgElmType(<fam>)
Error( "all2 ( IsIntjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fi
#
]java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
results:= [];
sr:=rec(seeds:=eeds)java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
((java.lang.StringIndexOutOfBoundsException: Range [53, 52) out of bounds for length 75
=java.lang.StringIndexOutOfBoundsException: Range [33, 31) out of bounds for length 52
proglines:= LinesOfStraightLineProgram( prog );
# Set the positions used up to here.
offset= nextoffset;
# If necessary protect the original generators from being replaced,
# and work with a shifted copy.
shiftgens:= false
ForAny >Length ) 2
and IsList(line[1]
and line[2] in [ 1 .. n ] ) java.lang.StringIndexOutOfBoundsException: Index 66 out of bounds for length 43
Append( lines, List( [ 1 .. n ], i -> [ [ n j java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
nextoffset;
shiftgens: ;
( ;
offset:= java.lang.StringIndexOutOfBoundsException: Range [0, 23) out of bounds for length 5
fi;
# Loop over the program.
for ijava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 0
line:= proglines[iPrint")java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
if not IsEmpty( # Construct and return the new program.
# The line describes a word to be appended.
# (Increase the positions by `offset'.)
## 2. Functions for elements represented by straight line programs#############################################################################
if shiftgens #M OneOp(<slpel>)
newline[j]:= newlineInstallMethod(OneOp,straight line program #################################
fi;
odjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
if(FamilyObj(slp)java.lang.StringIndexOutOfBoundsException: Index 29 out of bounds for length 29
else
Add( lines, newline )#
nextoffset:= nextoffset + 1;
fi;
elif ##
# The line describes a word that shall replace.
,(prog
localjava.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
for j in [ 1, 3 .. Length( java.lang.StringIndexOutOfBoundsException: Range [0, 44) out of bounds for length 0
if shiftgens or
sr:=rec(seeds:rec(eeds:=eeds);
fi;
od; fi;
if i = Length(return Objectify(traightLineProgElmTypejava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 0
Add
else
newline:= [ newline, line[2] + offset ];
Add( lines, ##
if [IsStraightLineProgElm]0,nverseSLPElm);
java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 0
fijava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
fi;
else
# The line describes a list of words to be returned.
line:= List( line, ShallowCopy );
for newline in line do
for j in [ 1, 3 .. Length( newline )-1 ##
if shiftgens or n < newline[j] then
newline[j]:= newline[j] + offset;
fi;
od;
od;
Append( results, line );
fi;
od;
od;
Add the results line.
Add lines,resultsend;
# Construct and return the new program.
return StraightLineProgramNC lines, n )java.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
end );
#############################################################################
##
## 2. Functions for elements represented by straight line programs
##
#############################################################################
##
#M StraightLineProgElmType(<fam>)
##
""true[],0,
function(fam)
if IsOnereturn;fi
;
#############################################################################
Print(">");
#F StraightLineProgElm(<seed>,<prog>)
##
InstallGlobalFunction(StraightLineProgElm,BindGlobal""function,#
local sr;
if IsRecord(seeds) java.lang.StringIndexOutOfBoundsException: Range [0, 25) out of bounds for length 2
sr:=seeds;
seeds:sr.
else
sr:=rec(seeds:=seeds);
fi
return Objectify(StraightLineProgElmType(java.lang.StringIndexOutOfBoundsException: Index 46 out of bounds for length 5
end);
#############################################################################
##
#F EvalStraightLineProgElm(<slpel>)
##
InstallGlobalFunction(EvalStraightLineProgElm,# an SLP.
return ResultOfStraightLineProgram(slp![2],slp![1].seeds);
end);
#############################################################################
##
#F StraightLineProgGens(<gens>)
##
InstallGlobalFunction laa,lba, # last entries absolute
local gens,sgens,seed;
gens:=arg[1];
sgens:=Set(gens);
:recs:sgens);
if Length(arg)>1 and end )
seed.base:=arg[2];
fi;
return List([1..Length# -- so we must duplicate the installation here as well
StraightLineProgramNCjava.lang.StringIndexOutOfBoundsException: Range [26, 23) out of bounds for length 23
end);
#############################################################################
##
#M ViewObj(<slpel>)
##
InstallMethod(##
IsStraightLineProgElm]0,
function(slp)
Print("<");
p; # position
if Sum(LinesOfStraightLineProgram(slp![2]),Length)<50 then
Print(|);
ViewObj .seeds);
fi;end)
Print(")java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
end);
#############################################################################
##
#M OneOp(<slpel>)
##
InstallMethod(function(slp,x];
[IsStraightLineProgElm],0,
function(slp)
return One(FamilyObj(slp));
end);
#############################################################################
##
#M InverseOp(<slpel>)
##
BindGlobal( "InverseSLPElm", function(slp)
local l,n;
l:=LinesOfStraightLineProgram(slp![2]);
l:=ShallowCopy(l);
n:=Length(l);
# invert last
[n]);
return StraightLineProgElm(slp![1],
java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 8
;
# words in fp elements have separate methods for `Inverse' and `InverseOp'
# -- so we must duplicate the installation here as well
IsBound( if IsBound(a.base
[IsStraightLineProgElm],0,InverseSLPElm);
InstallMethod([IsStraightLineProgElmIsStraightLineProgElm]0,
[sStraightLineProgElm],0,InverseSLPElm :=ist(.seedsi-(seed.eedsi);
#############################################################################
##
#M Order(<slpel>)
##
("linejava.lang.StringIndexOutOfBoundsException: Range [43, 42) out of bounds for length 58
# we have to be better than specialized methods
10,
function(,,# ditto new
return Order(EvalStraightLineProgElm(slp)) ,,
end);
#############################################################################
##
#M \*
##
\*"line program with ,true,
[IsStraightLineProgElm,IsMultiplicativeElement],0,
function(lp,)
if IsOne(x) then return slp;fi;
return EvalStraightLineProgElm(*x;
end);
InstallMethod(\*#bleu,# corresponding ble
[IsMultiplicativeElement,IsStraightLineProgElm],0,
function(x,slp)
if IsOne(x) then return slp;fi;
return *EvalStraightLineProgElmslp)
end);
#T this would be better recoded as variant of the substring algorithm in
#T steps of 2
BindGlobal(PosSublOdd,(,)
local p;
p:=PositionSublist(a,b);
whileIsInt() if IsIdenticalObj(seedjava.lang.StringIndexOutOfBoundsException: Range [20, 19) out of bounds for length 32
p:PositionSublista,,)java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
od;
return p;
end);
InstallMethod(\*,"ta=1.] translation of the numbers the numbers
[,IsStraightLineProgElm,,
function(aob IsSubsetbseeds,seedseeds)
# this multiplication routine tries to find duplicate patterns. It
# implicitly assumes, however that the input is in some way ``reduced'' as
# an SLP.
local a, seed:=:=;
aep,fi
ta l[Length(l)]:=e;
tal,tbl, # up to this index, old and new indices are the same
lalb,# lengths
laa,lba, # last entries absolute
ap,bp, # processing indices old
anp,bnp, # ditto new
asn,bsn, # lengths of original seeds
as,bs, # subset
l, # result list
ale,ble, # indices in l of a/b entries
i,j,k, # index
seed, # seed
ei, # inverse
,# bs-entries that have been taken earlier
bleu, # corresponding ble
# substring found?
# flag when dealing with the last elements.
# position
seed:=aob![1];
asn:= :tbl1java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
aep:=Lengthseed.seeds);
b:=bob![1];
bep:Length(.seeds);
bsn:Length(b.seeds);
if IsIdenticalObj(seed,b) then
# identical seeds -- easiest case
:java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
tb:=[1..bep];
(seedseeds,.seeds)then
# b is a subset of a
ta:=[1..aep]; # translation of the numbers
,->osition(java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 48
elif IsSubset(b.seeds,seed.seeds) then
# a is a subset of b
ist(.eedsiPosition(bjava.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
tb:[.bep]
seed:=b;
# none is a subset of the other
a=;
seed:=rec(seeds:=Union forj()=[(]b];
if IsBound(a.lmp) and IsBound(b.lmp) then
edaximumlmp,.p;
fie=od
if IsBound(.base)and IsBound(.ase)then
.ase:Uniona.,b);
fi;
:(a.seeds,-Positionseed,));
tb:=List(b.seeds,i->Position(seed.seeds,i));
fi;
=seed.eeds;
tal:=First([1..Length(ta)],i->ta[i]<>i);
if tal=fail then
tal:=Length(ta);
else
tal:=tal-1;
fi;
tbl:=First([1..Length else
if tbl=fail then
tbl:=Length(tb);
se
tbl:=tbl-1;
fi;
:=(ob!)
b:=LinesOfStraightLineProgram(bob![2]);
l:=[];
la in 1.() java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
lb:=Length(b)-1;
#java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 54
if0Length([) java.lang.StringIndexOutOfBoundsException: Range [33, 34) out of bounds for length 33
a:[]java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
l:=ShallowCopy(b);
# translate
Append(tb,seen+[1..Length(b)]);
for i in [1..
e:=ShallowCopy(l[i]);
Length-][b1]then
eLengthe):e[Length()+[2]
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
l[i]:=e;
od;
e:=l[Length(l)];
if e[]ta if e[1]=ta[a
e[2]:=e[ ;
if e[2]=0 then
e: d
fi
else;
e:=Concatenation([ta[a[1]],java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 10
fi;
l
elif lb=0 and Length(b[1])=2 then
b:=b[1];
l:=ShallowCopy(a);
# translate
Append(ta,java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 16
for 1L(l]do
e:=ShallowCopy(l[i]);
for j in [1,3..Length(e)-1] do
e as:=[.-]}
od;
l[i]:=e;
od;
e=[Length(l];
if e[Length(e)-1]=tb[b
eLength(]:[Length()+[]java.lang.StringIndexOutOfBoundsException: Index 38 out of bounds for length 38
if e[e]0then
e={1L-2}
fi;
else
e:=Concatenation(e,[tb[b[1] ;
fi;
l[Length(l)##
### Copyright of GAP belongs to its developers, whose names are too numerous
ap:=1##
#############################################################################
tjava.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 55
ble:[;#bCDATA,3,)(1# ( (## gap> hom:=GroupHomomorphismByImages(g,g,GeneratorsOfGroup(g),
laro ##
java.lang.StringIndexOutOfBoundsException: Range [26, 9) out of bounds for length 26
## Let <M>U</M> be the image of <A>epi</A>.
## <M>g</M
#Print(">",ap,",",bp,"\n");
# how many ap's do use up to generator aep;
anp:=ap## ^(1,2,3)
whileanp= ForAllanp{13.aa]-]i>=ep
anp:=anp+1;
od;
as:= ##
# translate the generator numbers
if aep>tal ## If <A>homs</A> is empty, it computes all subgroups.
for i## Group([ (1,2,3), (4,5,6), (7,8,9) ])
if p>## [ Group([ (7,8,9), (4,5,6), (1,2,3) ]),
in[13.ength()-]do
##
# inverse
e[j]:## a list [<A>subspaces</A>,<A>action</A>], where <A>subspaces</A> is a list of all the
e[j+1]:=-e[j+1];
fi;
od;
#F SubgroupsSolvableGroup(<G>[,<opt>])##
od;
fi## using the homomorphism principle.
# how many bp's do use up to generator bep;
bnp
## explicit test for the desired properties (which is not done by default, as
bnp:=bnp+1;
od;# must be a list of automorphisms of <A>G</A>. If given, only groups;
bs:=ns</C> (defined :[1
# translate the generator numbers
if bep>tbl## <Item>
for i in [1..Length(bs)] do
e:=ShallowCopy p
[1,## relation <M>F \geq C > A > N > B > M</M>.1,
j## in <M>F/N</M>.
if else
# inverse
[## If it returns <K>false</K> then
e[j# Add,bs[j]);
fi;
od;
bs[#ameterisused permit calculations of some subgroups if the
od;
fi;
bpre:=[];
bleu:=[];
# add the as
for## of subgroups but also a corresponding list <C>norms</C> of normalizers
e:=as[i];
repeat
# search substring in recorded b-parts
found:=false;
j:=1;
## is an elementary abelian series of <A>G</A> which will be used for
p:PosSublOdde## <Item>
found:=p<>fail;
## gap> g:=Group((1,2,3),(1,2),(4,5,6),(4,5),(7,8,9),(7,8));
java.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
if## gap> l:=SubgroupsSolvableGroup(g,rec(actions:=[hom]));;
j:=ble[j-1]+1; # the other case will always add 1.
else
# search substring in bsDeclareGlobalFunction"";
j:#F SizeConsiderFunction(<size>) returns `consider' function
while
eijava.lang.StringIndexOutOfBoundsException: Range [32, 31) out of bounds for length 35
:# > consider:=SizeConsiderFunction(6)));;
if not j in bpre then
record thisbs l
Add(l,bs[j]);
AddSet(bleu,## </Description>
(bprej);# this one is AddSet(bpre,j); # this one is taken
java.lang.StringIndexOutOfBoundsException: Range [0, 22) out of bounds for length 0
j##
## <Func Name="ExactSizeConsiderFunction" Arg='size'/>
# we stored it already
j:=
;
fi;
;
lter It is guaranteed that allsubgroups fulfilling the
ion>
DeclareGlobalFunction(" =;
# the subentry starts at index p
# j is the l-index of the entry which is sub+1
ncatenation({[.p-1]}[+seen-,]
[j-1])..ength()]};
else
# search substring in recorded b-parts (inverse)
java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
j: found> k:=Positio,bs]
while found=false andjava.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
pP(lj])
found:=p<>fail;
j:=j+1;
od;
if found=true then
j:=ble[j- od
else
# search substring in bs
j:=1;
while found=false and j<Lengthbse=e1ength(+--lj-]]}
j+een-1,1,
if p<>fail then
found ei=)
if not j in bpre then
AddSet(bpre [++-1:Length(
# record this bs in l
if bs[j] in l then
# happens to be coincidence.
k:fi
tb[bsn+bp+j-1]: if e inl then
j:=k; # position of the l-entry that is sub # the replacement could rarely produce duplicates
Add(
AddSet(bleu, laro then
tb[bsn+bp+j-1]:=Length(l)+seen; # store the index
j:=Length(l); # position of the l-entry that is sub
=java.lang.StringIndexOutOfBoundsException: Range [30, 29) out of bounds for length 43
else
# we stored it already
j:=Position(l,bs[j]);
fi
fi;
j:j
od;
fi;
found> then
# the subentry starts at index p in the inverse
e=e[1.Lengthjava.lang.StringIndexOutOfBoundsException: Range [46, 47) out of bounds for length 31
[ ;
found:p>;
ei:=RepAssWorInv(;
fi;
fi;
until # the subentry starts at index p in the inverse
# finally store, unless trivial and not the last one
if Length(e)>2 or AbsInt(e[# search substring in recorded a-parts
if e in l then
#
taasn while fjava.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 55
else
(le)
if not laro then
# do not add in the last step -- this might confuse b
AddSet(ale,Length java.lang.StringIndexOutOfBoundsException: Range [52, 51) out of bounds for length 63
fi;
ta[asn+ap+i-1]:=Length(l)+seen;
fi;
else
# complete replacement
ta[else
fi;
od;:)java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
AddSet(java.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 38
# add the bs
for i in [1..Length(bs)] do
if# complete replacement
[bsn++i1]:e2]*[]java.lang.StringIndexOutOfBoundsException: Index 49 out of bounds for length 49
repeat
# search substring in recorded a-parts
found: tb[+bp1]=le)
j:=1;
while found=false and j<=Length(ale) do
p:=PosSublOdd(e,l[ale[j]]);
found:=p<>fail;
j:=j+1;
od;
if found<>false then
# the subentry starts at index p
# j is the l-index of the entry which is sub+1
j:=java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 11
e:# finally multiply the last entries.
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
else
# search substring in recorded a-parts
found:=false;
j:=1;
ensureslast arelast
while f andale) do
p:=PosSublOdd(e,l[ale[j]]);
found:=java.lang.StringIndexOutOfBoundsException: Range [0, 26) out of bounds for length 7
j:=j+1;
od;
if e:=l[Length(l)1]java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 26
# the subentry starts at index p in the inverse
j:=ale[j-1]Add([a1,b1);
e:=oncatenation(e{[1.;
[j+seen-1,-1],
e{[Length(e)-p+2..java.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 46
Remove
fi;
fi;
until found=false; # several substrings might occur
# finally store
if Length(e)>2 or java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 24
if e in l then
-1]:(,)
else
Add(l,e);
java.lang.StringIndexOutOfBoundsException: Range [0, 22) out of bounds for length 12
tb[
;
else
# complete replacement
tb[#java.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76
;
fi;
od;
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
bp:=bnp;
aep:=aep+;
bep:=bep+1;
od;
java.lang.StringIndexOutOfBoundsException: Index 60 out of bounds for length 60
1
lb:else
laro:=# Print("case3\n");
od;
# finally multiply the last entries.
# get the indices in l of the corresponding last entries
# the -1 in the argument only undoes the +1 at the end of the `while' loop
la=[asn]java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
lb:=tb[lb+bsn-1];# ForAny([1..Length(l)],i->ForAny([1..i-1],j->PositionSublist(l[i],l[j])<>fail)));
laa:=AbsInt(la);
lba:=AbsInt(lb);
if2java.lang.StringIndexOutOfBoundsException: Range [37, 36) out of bounds for length 71
# last a is in the but last position
if
# Print("case1\n");
# last b is in the last position: combine last two
e:=l[Length(l)-1];
j:=l[Length(l)];
# does b refer to a?
if ForAny([1#fi;
Add(l,[la,1,lb,1]);
else
lL()-:Ejava.lang.StringIndexOutOfBoundsException: Index 40 out of bounds for length 13
:S(seed,(l,een)java.lang.StringIndexOutOfBoundsException: Index 63 out of bounds for length 63
fi;
else
Error("spurious last entry");
fi;
# last a is not in the but last position
if lb=Length(l)+seen then
# Print("case2\n");
od([la],l[ength(l))java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 58
# last b is not in the last position:
if L(l+seen then
# Print("case3\n");
# but a is: change a in last position
InstallMethreturn a;
else
# Print("case4\n");
# last b is not in the last position or inverses used: Add another
Add(l,;
fi;
fi;
fi;
fi;
#Error(a,"*",b,"=",l,"\n");
#if ForAny(l,i->Length(i)=2) then
# Error("hui");
#fi;
if Length(l[Length(l)])=0 then
(aob;
else
#if ForAny([2..Length(l)],i->Length(l[i])=2 and AbsInt(l[i][2])=1) then
# Error();
#fi;
# Assert(1,not
# ForAny([1..Length(l)],i->ForAny([1..i-1],j->PositionSublist(l[i],l[j])<>fail)));
Assert( I,java.lang.StringIndexOutOfBoundsException: Range [52, 48) out of bounds for length 52
l:=traightLineProgElmseed,StraightLineProgramNC(l,seen));
Assert(2,EvalStraightLineProgElm(aob)*EvalStraightLineProgElm(bob)=
end;
return l;
fi
end);
InstallMethod(\^,"power straight line program elements",true,
[IsStraightLineProgElm,IsInt],0e)java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
functiona,
local l,n;
if e=0 then
java.lang.StringIndexOutOfBoundsException: Range [16, 10) out of bounds for length 18
elif e=1fa)
return a;
elif e=-1 then
return Inverse(a);
fi;
l:=e:=EvalStraightLineProgElm(a);
n:=Length(a![1].seeds)s=niona![1InstallMethodjava.lang.StringIndexOutOfBoundsException: Range [41, 40) out of bounds for length 79
if Length(l)=1 and Length(l[1])=2 then
# special case: generators
l:=[[l[1][1],l[1][2]*e]];
else
fi;
Add(,[Length(l)ne);
fi;
return StraightLineProgElm(a![1],StraightLineProgramNC(l,n));
end);
allMethod=, program element "I,
I,java.lang.StringIndexOutOfBoundsException: Range [50, 48) out of bounds for length 52
java.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 21
return EvalStraightLineProgElm(slp)=x;
end)
InstallMethod(\,"traightline program element with x",IsIdenticalObj,
[IsStraightLineProgElm a!]basethen
java.lang.StringIndexOutOfBoundsException: Range [44, 15) out of bounds for length 44
return EvalStraightLineProgElm(slp)<x;
end);
InstallMethod(a2#java.lang.StringIndexOutOfBoundsException: Index 50 out of bounds for length 50
[IsMultiplicativeElement,IsStraightLineProgElm],0,
function(x,slp)
return x<EvalStraightLineProgElm(slp);
end);
#############################################################################
##
#O StretchImportantSLPElement(<elm>)
##
InstallMethod(x,slp)
[ java.lang.StringIndexOutOfBoundsException: Range [11, 8) out of bounds for length 40
Ignore);
nstallMethod(," line program "true,
[IsStraightLineProgElm],0,
functionajava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
local ,sr
e:=LinesOfStraightLineProgram(a![2]);
if Product(e,i->Sum(List(i{[2,4..Length(i)]},AbsInt)))>200 then
e=EvalStraightLineProgElm(a);
s:=Union(a![1].seeds,[e]);
e:=Position(s,e);
r:=rec( else
if java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
e:=l[n-m];
.:a!];
fi;
if IsBound(a![1].base) then
# transfer base information for perms.
r.base else
fi;
a[]rjava.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 13
a![2java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
fi;
end);
##
## special methods for straight line permutations
##
InstallMethod(\=,"x with straight line program element",IsIdenticalObj,
[IsMultiplicativeElement,IsStraightLineProgElm],0,
else
return x :l-]java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
end ei].1
BindGlobal("ImgElmSLP",function(x,slp,pre)
local s,m,l,trace;
# trace through
trace:=function(y,n)
local ,i,j;
if n<0 then
n:=-n;
if n<=m forj [.e[+1]
return y/s[n];
ejava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12
for :!1.
if e[i+1]<0 then
for j in [e[i+1]..-1] do
if pre then
od;
se
for j in [1..e[i+1]] do
y:=trace(y,-e[i]) return(x-(engthl)m)java.lang.StringIndexOutOfBoundsException: Index 36 out of bounds for length 36
od;nd);
fi;
od;
fi;
elif n
return y^[]java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
else
e:ln-]java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
iin 13.java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 0
if e[i+1]<0 then
for j in [e[i+1]..-1] do
y:=trace(y,-e[java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 8
l[;
else
forlocals,l,tackpos,row,ndstep,cntve,isp,ae;
:trace(,e[]);
od;
fi;
od;
fi;
return y;
end;
s:=slp![1].seeds;
m:=Length(s)row:l[];
l:=LinesOfStraightLineProgram(slp![2]);
if pre then
# preimage!
return trace(x ind:1;
else
return trace(x,-(Length(l)+m));
fi;
end);
# The following function ought to perform better, being nonrecursive.
# In practice the recursion, being executed in the kernel, works out
# better. However this function ought to give the better performance if
# compiled.
BindGlobalx=[]java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
local s,m,l,stack,pos,row,ind,step,cnt,v,e,i,spex=x^[]java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
s:=slp![1].seeds;
m:=Length(s);
l:=LinesOfStraightLineProgram(slp![2]);
stack:=[];
sp:0java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
pos:=Length(l);
row:=l[pos];
if npre then
ind:=1;
step:=2;
else
gthrow-java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 23
step:=-2;
fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
cnt:=0;
repeat
v:=row[ind];
e:=row[ind+1];
ae:=AbsInt(e);
if not npre then
e:=-e;
fi;
if v<=m then
# do the most simple cases themselves
if e=-1 then
x:x/[v]
elif e=1 then
x:=x^s[v];
elif e>0 then
for i in [1..e] do
x:=^[;
od;
else
for i if sp then
x:xs[v];
od;
fi;
cnt:=ae; # did all
else
#push
sp:=sp+1;
stack[sp]:=[pos,ind,step,cnt];
pos:=v-m;
row:=l[pos];
npre=>;
if npre then
ind:=1;
step: AbsIntr[ind+1;
else
ind:=Length(row)-1;
step:=-2;
fi;
cnt:=0; # we just started
fi;
while cnt>=ae do
:ind+tepjava.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
cnt:=0;
ind>row ind<
# pop
if sp=0 then
# through!
return x;
fi;
row:=stack[sp];
sp:=sp-1;
=;
ind:=row[2];
step:=row[3]java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
npre:=tep0java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
cnt:=row[4]+1; # +1 since we did one
row:=l[os]java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
:=bsInt(owi+];
fi;
od;
until false; # we will stop by returning the result
end)java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
InstallOtherMethodod(^" withstraight ,,
[IsInt,IsStraightLineProgElm and IsPerm],0,
function(x,slp)
# do not use for straight line elements!
if IsStraightLineProgElm(x) then
TryNextMethod();
fi;
return ImgElmSLP(x,slp,true);
end);
InstallOtherMethod(\/,"x with straight line perm",true,
IsPosInt,sStraightLineProgElmIsPerm,0,
(x,)
return ImgElmSLP(x,slp,false);
end);
# takes a seed record and fetches/adds a largest moved point entry
BindGlobal("LMPSLPSeed :p100;
if not IsBound(r.lmp) then
r.lmp:=LargestMovedPoint
fi;
return r.lmp;
end);
InstallMethod(LargestMovedPoint,"straight line program permutation[and IsPerm,]0,
[IsStraightLineProgElm and IsPerm],0,
function()
local p,q;
p:=LMPSLPSeed(slp![1]); return(slp;
if p
q:=p-100;
else
q:=0;
fi;
while p>q and ImgElmSLP(p,slp,true)=p do fi;
p:=p # the element seems to be the identity. Expand!
od
if p>then
return p;
elif q=0 then
return q;
else
# catch the () case quickly if base given.
if IsBound(slp![1].base) and IsOne(slp) then
return 0;
fi;
# the element seems to be the identity. Expand!
q:=EvalStraightLineProgElmfunctionperm
return LargestMovedPoint(q);
fi;
end);
(=,straight program element with perm",IsIdenticalObj,
[IsStraightLineProgElm and IsPerm,IsPerm],0,
function(slp,perm)
local r;
r:=LargestMovedPoint(perm);
if r=0 then
return IsOne(slp);
else
r^perm<>mgElmSLP((r,slp,,true)then
return false;
fi;
fi;
if IsBoundslp![].base) then
return ForAll(slp![1].base,i->ImgElmSLP(i,slp,true)=i^perm)
and<s![]);
fi; and<=LMPSLPSeed(lp[1];
return EvalStraightLineProgElm(slp)=perm;
end);
InstallMethod(\=,"perm with straight line program element",IsIdenticalObj,
[IsPerm,IsStraightLineProgElm and IsPerm],0,
function(perm,slp)
local r;
r:=LargestMovedPoint(perm);
if r=0 then
return IsOne(slp);
else
if r^perm<>ImgElmSLP(r,slp,true) then
return false;
fi;
fi;
if IsBound(slp![1].base) then
ForAllslp[1]basei>ImgElmSLP(,slp,true)=^)
and r<=LMPSLPSeed(slp![1]);
fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
return perm=EvalStraightLineProgElm(slp);
end);
(\,straight lineprogramperms,IsIdenticalObj,
IsStraightLineProgElm and IsPerm,IsStraightLineProgElm false;
function(a,b)
local l,;
if not IsIdenticalObj(a![1],b![1]) then
l:=Maximum if 1000then
m:0;
l:=LMPSLPSeed(a![1]);
fi;
if IsBound(a![1].base) and java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 13
return
ForAll(Union(a![1].base,b![1].base),
i->ImgElmSLP(i,a,true)=ImgElmSLP(i,b,true));
fi;
if l<1000 thenfi;
m=0;
else
m:=l-100;
fi;
> do
java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
return false;
fi;
l:=l-1
od;
if l=0 then
return true;
fi;
# the elements look very similar, but there are a lot of points.
return EvalStraightLineProgElm(a)=EvalStraightLineProgElm(b);
end); :l[sStraightLineProgElm and IsPermsStraightLineProgElm IsPerm,,
InstallMethod(\<,"straight line program perms",IsIdenticalObj,
[IsStraightLineProgElm and IsPerm,IsStraightLineProgElm and IsPerm],0,
function(a,b)
local l,m,x,y;
:1
if not IsIdenticalObj(a![1],b![1]) then
m:=Maximum(LMPSLPSeed(a![1]),LMPSLPSeed(b![1]));
else
m:=LMPSLPSeed(a the elements look very similar, but there are a lot of points.
;
if m>1000 then
m:=1000;
fi;
while l<m do
x:= x:=ImgElmSLP:ImgElmSLPl,true)
y:=y:=ImgElmSLP)java.lang.StringIndexOutOfBoundsException: Index 27 out of bounds for length 27
if x<y then return true;
elif yx then return ;
fi;
l=l+1
od;
# the elements look very similar, but there are a lot of points.=+;
return EvalStraightLineProgElm(a)<EvalStraightLineProgElm(b);
end);
InstallMethod(IsOne ;
[ while l do
function(slp)
java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 31
return ForAll(slp![1].base,i->ImgElmSLP(i,slp,true)=i);
fi;
l:=LMPSLPSeed(slp![1]);
if l<1000 [IsStraightLin and,0java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
m:=0;
else
m:=l-100;
fi;
while l>m do
if ImgElmSLP(l,slp,true)<>l then
return false;
fi;
l:=l-1;
od;
if l=0 then
return true;
fi;
return IsOne( EvalStraightLineProgElm(slp) );
end);
InstallOtherMethod( CycleLengthOp, "straight line program perms", true,
[ IsPerm and IsStraightLineProgElm, IsInt ],1,
function(p,e)
local,f;
i:=0;
f:=e;
repeat
f: return false;
i:=i java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
until f=e;
return i;
end);
InstallOtherMethod( CycleOp, "straight line program perms", true IsOneEvalStraightLineProgElm))java.lang.StringIndexOutOfBoundsException: Index 47 out of bounds for length 47
[ IsPerm and IsStraightLineProgElm, IsInt ],e
function(p,e)
local c,i,f;
i:=0;
f:=e;
c:=[];
repeat
Add(,);
f:=f^plocal ,f
i:=i+1;
untiljava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
return c;
end)
InstallOtherMethod( CycleStructurePerm, "straight c,i,;
[ IsPerm and IsStraightLineProgElm ],1,
function(p)
return CycleStructurePerm);
end);
InstallOtherMethod( SignPerm, "straight line program java.lang.StringIndexOutOfBoundsException: Index 58 out of bounds for length 11
[java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
function(p)
return SignPerm(EvalStraightLineProgElm());
)
InstallOtherMethod( RestrictedPermNC, "straight line program perms", true,
[ IsPerm and IsStraightLineProgElm,IsList ],1,
function(p,l)
EvalStraightLineProgElmljava.lang.StringIndexOutOfBoundsException: Index 56 out of bounds for length 56
end);
##
## special methods for straight line assoc words
##
#############################################################################
##
#M ExtRepOfObj
##
InstallMethod(ExtRepOfObj,"for a straight line program word",true,
[IsAssocWord and IsStraightLineProgElm],0,
function
return ExtRepOfObj( return RestrictedPermNC(EvalStraightLineProgElm
ExtRepOfObj,for java.lang.StringIndexOutOfBoundsException: Range [41, 37) out of bounds for length 49
#############################################################################
##
#M LetterRepAssocWord
##
nstallMethod(java.lang.StringIndexOutOfBoundsException: Range [34, 32) out of bounds for length 73
[IsAssocWord and IsStraightLineProgElm],0,
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 5
return LetterRepAssocWord(EvalStraightLineProgElm(slp));
end);
#############################################################################
##
#M NumberSyllables
##
InstallMethod(NumberSyllables,"for a straight line program word"#M GeneratorSyllable
InstallMethod(,"for a straight line java.lang.StringIndexOutOfBoundsException: Range [60, 60) out of bounds for length 5
function(slp)
return NumberSyllables(EvalStraightLineProgElm(slp));
end);
#############################################################################
##
#M GeneratorSyllable
##
InstallMethod(GeneratorSyllable,"for a straight line program word",true,
[ andIsStraightLineProgElm,IsPosInt],0,
function(returnjava.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
return GeneratorSyllable(EvalStraightLineProgElm(slp#M GeneratorSyllable
end);
#############################################################################
##
#M ExponentSyllable
##
InstallMethod(ExponentSyllable,"for a straight line program word",true,
[IsAssocWord and IsStraightLineProgElm,IsPosInt],0,
function(#M ExponentSyllable
java.lang.StringIndexOutOfBoundsException: Range [0, 8) out of bounds for length 2
end);
#############################################################################
##
#M Length
##
InstallMethod(Length,"for a straight line program word",true,
[IsAssocWord and IsStraightLineProgElm],0,
function()
return Length(EvalStraightLineProgElm(slp));
end);
#############################################################################
##
#M Subword
##
InstallOtherMethod(Subword,"for a straight line program word",true,
[IsAssocWord and IsStraightLineProgElm,IsInt,IsInt],0,
function(slp,a#M ExponentSumWord
return InstallMethodExponentSumWord"a programword, Subword
end);
#############################################################################
##
#M MappedWord
##
InstallMethod(MappedWord,"for a java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
IsElmsCollsX,
[ ##
java.lang.StringIndexOutOfBoundsException: Range [22, 8) out of bounds for length 23
# evaluate in mapped generators
return ResultOfStraightLineProgram(slp![2],List(slp![1].seeds
i->MappedWord(i,gens,imgs)) # images of the roots
;
end)
#############################################################################
##
#M ExponentSumWord
##
InstallMethod(ExponentSumWord,"for a straight line program word",
IsIdenticalObj, [IsAssocWord and local ,yj;
function(slp,e)
return ExponentSumWord(java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 32
EvalStraightLineProgElm(e));
# words represented as tree elements (those are useful for decoding subgroup
# presentations)
#############################################################################
##
#F TreeRepresentedWord( <roots>,<tree>,<nr> )
##
## these elements are represented as straight line program elements
TreeRepresentedWordfunction,xj)
local z,d,l,count ;
z=engtht])
b:=Length(r);
if n<=b then
return StraightLineProgElm(r,StraightLineProgramNC([[n,1]]f<
fijava.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5
# which elements are referred to ? set count negative
:(,)java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
count:=function(i)
if i>b((t[][]);
if d[i]=0 then
count(AbsInt(t[1][i]));
count(AbsInt(t[2][i]));
fi;
d[]=d[]1
fi;
end;
count(n);
# now we will collect in d slp entries (or indices in l by positive numbers)
l:=[];
d[n]:=-2; # this will force element n to be stored as word (and it will be
# at the end of l)
count:=function(i)
local e,f,x,y,j;
if i<=b then
return i;
elif not (IsInt(d[i]) and d[i]<0) then
d[]
fi;
e:=count(AbsInt(t[1][i]));
f:=count(AbsInt(t[2][i]));
x:=SignInt(t[1][i]);
y:=SignInt(t[2][i]);
# put together
if IsInt(e) and ;
if =f then
if x+y=0 then
Error( ;
ejava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fi;
else
e:=[e,x,f,y];
fi;
else
# take care of inverses
if IsList(e) and x<1 then
x:=[]; #revert
for j in [Length(e)-1,Length(e)-3..1] do
Add(x,j);
Add(x,+1)java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
od;
e:=e{x};
x:=[2,4..Length(e#F SLPChangesSlots( <l>, <nrinputs> )
e{x}:=-e{x};
fi;
fand<
y:=[]; #revert
for j in [Length(f)-## appended to the list, namely the number of the biggest slot used.
Add(y,j);
Add(y,j+1);
od;
f=f{y};
y:=[2,4..Length(f)]; # exponent indices
f{y}:=-f{y};
fi;
if IsInt(e) then
e:=Concatenation([e,x],f);
elif IsInt(f) then
e:=Concatenation(e,[f,y]);
else
f=)
while Length(e)> {}:=e Add(ch(changes,ne2)
# same variables: reduce
[2]+[engthe]java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
if f[2]=0 then
f=f{[..ength(f)];
;
e:=e{[1 ( " slp:java.lang.StringIndexOutOfBoundsException: Index 43 out of bounds for length 43
od;
e:=Concatenation(e,f);
fi;
fi;
if d[i]<-1 then
# this becomes a new definition
Add(l,e);
e:=Length(l)+b; # number of this definition##
d[i]:=e; # store
return e;
end;
count(n);
if Length(l)>0 and Length(l[Length(l)])=0 then
return One(r[1]);
fi;
return StraightLineProgElm(r,StraightLineProgramNC(l,Length(r)));
end);
#############################################################################
##
## 3. Functions for straight line programs, mostly needed for memory objects:
##
##
#F SLPChangesSlots( <l>, <nrinputs> )
##
## l must be the lines of an slp, nrinps the number of inputs.
## This function returns a list with the same length than l, containing
## at each position the number of the slot that is changed in the
## corresponding line of the slp. In addition one more number is
## appended to the list, namely the number of the biggest slot used.
## For the moment, this function is intentionally left undocumented.
##
InstallGlobalFunction( SLPChangesSlots,
function(l,nrinps)
local biggest,changes,i,line;
line of the slp,which
# says, which element is changed
biggest := nrinps;
for i in [1..java.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 13
line := l[i]fijava.lang.StringIndexOutOfBoundsException: Index 15 out of bounds for length 15
if IsInt(line[java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
biggest : biggest +1;
Add(changes,biggest);
elif Length(line) = 2 and IsInt(line[2]) i : i-1java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
# the second case, provided that we have not been in the first
Add(changes,line[2]);
if line[2] > #F SLPReversedRenumbered( <ll>,<slotsused>,<nrinps>,<invtab> )
biggest := line[2];
fi;
elif i < Length(l) then
(" slp " ;
else
Add(changes,0);
# the last line does not change anything in this case
fi;
od;
Add(changes,biggest);
return changes;
end);
##
#F SLPOnlyNeededLinesBackward( <l>,<i>,<nrinps>,<changes>,<needed>,
## <slotsused>,<ll> )
##
## l is a list of lines of an slp, nrinps the number of inputs.
## i is the number of the last line, that is not a line of type 3 (results).
## changes is the result of SLPChangesSlots for that slp.
## needed is a list, where those entries are bound to true that are
## needed in the end of the slp. slotsused is a list that should be
## initialized with [1..nrinps] and which contains in the end the set
## of slots used.
## ll is any list.
## This functions goes backwards through the slp and adds exactly those
## lines of the slp to ll that have to be executed to produce the
## result (in backward order). All lines are transformed into type 2
## lines ([assocword,slot]). Note that needed is changed underways.
## For the moment, this function is intentionally left undocumented.
##
InstallGlobalFunction( SLPOnlyNeededLinesBackward,
functionl,,rinps,changes,slotsusedll)
local j,line;
java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 19
if IsBound(fi;
AddSet(slotsused, IsIntine] then # the first case
needed[[# as this line overwrites it,
line := l[i];
if IsInt(line[1]) then
Add(ll,[ShallowCopy(line),changes[i]]);
else
Add(ll,[ShallowCopy(line[1]),line[2]]); # copy the line
line := line[1];
fi;
for j in [1## k. The argument
needed[line[j else
fi;
i := i - 1;
od;
end);
##
#F SLPReversedRenumbered( <ll>,<slotsused>,<nrinps>,<invtab> )
##
## Internally used function.
##
InstallGlobalFunction( SLPReversedRenumbered#F SLPOnlyNeededLinesBackward( <l>,<i>,<nrinps>,<changes>,<needed>,
function(ll,slotsused,nrinps,invtab)
# invtab must be an empty list and is modified!
local## l is a list of lines of an slp, nrinps the number of inputs.
for i in## i is the number of the last line, that is not a line of type 3 (results).
invtab[slotsused[i]] := i;
od;
lll := []; # here we collect the final program
biggest := nrinps;
for i in [Length(ll),Length(ll)-1 .. else
resultslot := invtab[llfi;
if resultslot = biggest+1 then # we can use a type 1 line
## This functions goes backwards through the slp and adds exactly those
for## result (in backward order). All lines are transformed into type 2
Add(kl,invtab[ll[i][1][kk]]);
Add(kl,ll[i][1][kk+1##
od;
functionli,rinps,changes,needed,slotsused,ll)
biggest := biggest + 1;
else
kl := [];
forkkin[1 whilei= do
Addklinvtab[][ lotsused,hanges[];
(kl[]][1)
od;
Add(lll line = l[];
>biggest then
biggest : resultslot;
fi;
fi;
od
return lll;
end);
##
#F RestrictOutputsOfSLP( <slp>, <k> )
##
## slp must be a straight line program returning a tuple
## of values. This function
## returns a new slp that calculates only those outputs specified by
## k. The argument
## k may be an integer or a list of integers. If k is an integer,
## the resulting slp calculates only the result with that number
## in the original output tuple.
## If k is a list of integers, the resulting slp calculates those
## results with indices k in the original output tuple.
## In both cases the resulting slp
## does only what is necessary. Obviously, the slp must have a line with
## enough expressions (lists) for the supplied k as its last line.
## slp is either an slp or a pair where the first entry are the lines
## of the slp and the second is the number of inputs.
##
InstallGlobalFunction( java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 0
function:;
local forin[rom1ength]:
needed,nrinps,slotsused;
if IsInt(k) then
klist : [];
else
klist := k;
fi;
IsStraightLineProgramslp)then
l := Add(kl,invtab[j
nrinps := java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 21
else
l := slp[1];
nrinps: slp[2]java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
fi;
# The following has to be done, because the SLP might overwrite its
# intermediate results:
changes := biggest := resultslotreturn StraightLineProgramNC[(]nrinps;
biggest := changes[java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 15
ll := []; # Here we collect the lines of the result, but reversed
;
needed := []; # here we mark the needed entries for the rest of the prog.
i
## Returns a new slp that calculates only the value of slot <k>
if Length## slp must be a straight line program returning a tuple
Error("slp does not have result number ",k);
fi;
## If you know that your SLP does not overwrite slots, please use
for j in ## in the original output tuple.
needed[word[j]] := true;
od;
if Length(word) > 2 then
[1 : [ShallowCopy,biggest+1];
AddSet(slotsused,biggest+1);
lastline := fail;
# if Length(word)=2 and word[2]=1 then the last result is the result
# if the SLP has actually no lines, then we fix this further down!
else # a list of results:
lastline := []; # Here we collect results
for =slp1]
word := l]n]java.lang.StringIndexOutOfBoundsException: Index 28 out of bounds for length 28
for j in [1,3..Length(word)-1] do
needed[word[j]] := true;
od
Add(lastline,ShallowCopy(word));
od;
fi;
SLPOnlyNeededLinesBackwardli-,,,s,l);
# Now we have the program in reversed order in ll. The slots used
# during that calculation are in slotsused. We want to renumber
# them from [1..Length(slotsused)]:
invtab := [];
lll : SLPReversedRenumbered : slp[]
lastline< failthen
# Add the results line:ifLengthll)=0 ( slotsused) then
kkl := [];
# intermediate results:
kl := [];
kkin[,3.Length
Add( java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
Add(j+1];
od;
Add(kkl,kl);
od
Add(lll,kkl);
fi;
# One of the original generators!
#k fijava.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 11
# also, word must be of length 2 and second component equal to 1
return StraightLineProgramNC##
else
return StraightLineProgramNC(lll, nrinps);
fi;
end);
##
#F IntermediateResultOfSLP( <slp>, <k> )
##
## Returns a new slp that calculates only the value of slot <k>
## at the end of <slp> doing only what is necessary.
## slp is either an slp or a pair where the first entry are the lines
## of the slp and the second is the number of inputs.
## Note that this assumes a general SLP with possible overwriting.
## If you know that your SLP does not overwrite slots, please use
## "IntermediateResultOfSLPWithoutOverwrite", which is much faster in this
## case.
##
InstallGlobalFunction( IntermediateResultOfSLP,
function(slp,k)
local changes,i,invtab,l,ll,lll,needed,nrinps,slotsused;
if IsStraightLineProgram(slp) then
l := java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 28
(slp ;
else
l := slp[1];
nrinps := slp[2];
fi;
# The following has to be done, because the SLP might overwrite its
# intermediate results:
changes := SLPChangesSlots(l,nrinps);
slotsused := [1..nrinps]; # set of slots used at allAdd(line);
needed = [] # here we mark the needed entries for the rest of the prog.
needed[k] := true;
# we are interested only in the value of slot k in the end
ll := []; # Here we collect the lines of the result, but reversed
i := Length(l);
if changes[i] = 0 then # we are not interested in a result line
i := i - 1;
fi;
SLPOnlyNeededLinesBackward(l,i,nrinps,changes,needed,slotsused,ll);
if Length(ll) = 0 or not(k in slotsused) then
# the slot was never assigned!
Error("Slot not used in SLP!");
fi;
# Now we have the program in reversed order in ll. The slots used
# during that calculation are in slotsused. We want to renumber
# them from [1..Length(slotsused)]:
invtab := [];
(java.lang.StringIndexOutOfBoundsException: Range [46, 45) out of bounds for length 61
return StraightLineProgramNC(lll, nrinps);
# TO BE DEBUGGED HERE
end);
##
#F IntermediateResultsOfSLPWithoutOverwriteInner( ... )
##
## Internal function.
##
InstallGlobalFunction( od;
function ;
# Only used internally.
,needed,
if IsStraightLineProgram(slp) then
l := LinesOfStraightLineProgram( slp );
nrinps := NrInputsOfStraightLineProgram( slp );
else
[1];
nrinps := slp[2];
fi;
m := Maximum(k);
needed := Set(k);
# here we note the needed entries for the rest of the prog.
ll := []; # Here we collect the lines of the result, but reversed
kk [,3.(-1
while Length(needed) > 0 do
i := Remove(needed);
if i > nrinps then
Add(slotsused,i); # this slot is used
line := l[i-nrinps];
# We know that all lines are plain lists of integers!
java.lang.StringIndexOutOfBoundsException: Range [66, 1) out of bounds for length 66
java.lang.StringIndexOutOfBoundsException: Range [15, 14) out of bounds for length 23
L-
AddSet(needed,line[j]);
od;
fi
od;
k,ll[]k]: ;
# during that calculation are in slotsused. We want to renumber
# them from [1..Length(slotsused)]:
if Length(slotsused) > 0 then
invtab : slotsused
else
invtab := [];
fi;
nrslotsused := Length(slotsused);
for i in [1..nrslotsused] do
invtab[lotsused[] =nrinps+nrslotsused+ ( <>, <k )
od;
for ## in the list k.
invtab[i] := i;
java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
lll := []; # here we collect the final program:=Length()
for java.lang.StringIndexOutOfBoundsException: Range [29, 26) out of bounds for length 69
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
for kk injava.lang.StringIndexOutOfBoundsException: Range [4, 1) out of bounds for length 7
Add(kl, Lengthll)=0 ]java.lang.StringIndexOutOfBoundsException: Index 16 out of bounds for length 16
Add(kl,ll[i][kk+1]);
od;
Add(lll,kl);
od;
return [nrinps,invtab, Addline,[0);
endjava.lang.StringIndexOutOfBoundsException: Range [12, 13) out of bounds for length 12
##
#F IntermediateResultsOfSLPWithoutOverwrite( <slp>, <k> )
##
## Returns a new slp that calculates only the value of slots contained
## in the list k.
## Note that <slp> must not overwrite slots but only append!!!
## Use "IntermediateResultOfSLP" in the other case!
## <slp> is either a slp or a pair where the first entry is the lines
## of the slp and the second is the number of inputs.
##
InstallGlobalFunction( IntermediateResultsOfSLPWithoutOverwrite,
,)
local i,function(slp,k
Call the real code:
r := IntermediateResultsOfSLPWithoutOverwriteInner(slp,k);
nrinps := r[1];
invtab := r[2];
lll := r[3];
# Construct the last line:
line := [];
for i in k do
if i = 0 then
Add(line,[1,0]);
else
Add(line,[invtab[i],1]);
fi;
od;
Add(lll,line); # the result
return StraightLineProgramNC(lll, nrinps);
end);
##
#F IntermediateResultOfSLPWithoutOverwrite( <slp>, <k> )
##
## Returns a new slp that calculates only the value of slot <k>, which
## must be an integer.
## Note that <slp> must not overwrite slots but only append!!!
## Use IntermediateResultOfSLP in the other case!
## <slp> is either an slp or a pair where the first entry is the lines
## of the slp and the second is the number of inputs.
##
InstallGlobalFunction( IntermediateResultOfSLPWithoutOverwrite
(slp,)
local r;
java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 8
if k = 0 then
return StraightLineProgramNCinvtab =[ ;
elif k <= r[1] then # a generator
StraightLineProgramNC[k], [1)
else
return StraightLineProgramNC(r[3], r[1]);
fi## number of inputs. This function constructs an slp that returns the result
end);
##
#F ProductOfStraightLinePrograms( <s1>, <s2> )
##
## <s1> and <s2> must be two slps that return a single element with the same
## number of inputs. This function constructs an slp that returns the result
## <s1>(g_1,...,g_n) * <s2>(g_1,...,g_n) for all possible inputs g_1,...,g_n.
##
InstallGlobalFunction( ProductOfStraightLinePrograms,
(s2
bjava.lang.StringIndexOutOfBoundsException: Range [27, 26) out of bounds for length 71
newline,nrinps;
l1 := ShallowCopy(LinesOfStraightLineProgram(s1));
=java.lang.StringIndexOutOfBoundsException: Range [39, 36) out of bounds for length 41
nrinps := NrInputsOfStraightLineProgram (ll[[ =changes2[(]
if nrinps <> NrInputsOfStraightLineProgram(s2) then
Error("s1 and s2 do not have the same First we make a copy of the original generators:
fi;
1.java.lang.StringIndexOutOfBoundsException: Range [29, 26) out of bounds for length 31
biggest := changes[Length(changes)];
changes2 := SLPChangesSlots(l2, newline :=[ShallowCopy(),[java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
biggest2 := java.lang.StringIndexOutOfBoundsException: Index 24 out of bounds for length 2
biggest3 := Maximum(biggest,biggest2);
# First we make a copy of the original generators:
l3 : ;
for in1. do
dd,1,java.lang.StringIndexOutOfBoundsException: Range [31, 30) out of bounds for length 35
od;
# Now make a copy of l1, we have to use lines of type 2:
line := l1[i];
if IsInt(line[1]) then # a line without overwriting
newline := [ShallowCopy = [;
else # a line with overwriting
j;
fi;
Add(l3,newline line := []
od;
# Copy result up:
Add(l3,[[ if= 0
# Now append the second program, change low slots to high ones:
fori[.()]
line := l2[i];
if notjava.lang.StringIndexOutOfBoundsException: Range [20, 20) out of bounds for length 12
line := line[1];
fi;
newline := [];
java.lang.StringIndexOutOfBoundsException: Index 10 out of bounds for length 0
if line[j] > nrinps then
newline,ine[)
Addj+;
java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 7
Addnewline,,[j+])
od;
if changes2[i] <= nrinps then
Add(l3,[newline,changes2[i]+biggest3]);
else
Add(l3,[newline,changes2
fi;
od;
# the result of s2 is now in slot results2
if changes2[Length(l2)] <= nrinps then
Add(l3,[biggest3+## The prospective inputs are already standing java.lang.StringIndexOutOfBoundsException: Index 51 out of bounds for length 2
else
,hanges2[(]#
fi;
return StraightLineProgramNC(l3,nrinps);
end## without result line so far. <lsu> must be the largest used slot of the
##
#F RewriteStraightLineProgram(<s>,<l>,<lsu>,<inputs>,<tabuslots>)
##
## The purpose of this function is the following: Append the slp <s> to
## the one currently built in <l>.
## The prospective inputs are already standing somewhere and some
## slots may not be used by the new copy of <s> within <l>.
##
## <s> must be a GAP straight line program.
## <l> must be a mutable list making the beginning of a straight line program
## without result line so far. <lsu> must be the largest used slot of the
## slp in <l> so far. <inputs> is a list of slot numbers, in which the
## inputs are, that the copy of <s> in <l> should work on, that is, its length
## must be equal to the number of inputs <s> takes. <tabuslots> is a list of
## slot numbers which will not be overwritten by the new copy of <s> in <l>.
## This function changes <l> and returns a record with components
## `l' being <l>, `results' being
## a list of slot numbers, in which the results of <s> are stored in the end
## and `lsu' being the number of the largest slot used by <l> up to now.
##
InstallGlobalFunction( TranslateAssocWord := function(assocword
function(s,l,lsu,inputs,tabuslots)
local for i in [1,3.(java.lang.StringIndexOutOfBoundsException: Range [36, 35) out of bounds for length 42
nextnew,nrinps,oldwrite,res,results ;
FindNextNew := function(nextnew)
repeat
nextnew := nextnew + 1;
until nextnewintabuslots nextnew inputs;
return nextnew;
end;
TranslateAssocWord: (fi;
local i,new;
new )java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
for i in [1,3..Length(assocword : java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 16
i =i]java.lang.StringIndexOutOfBoundsException: Index 32 out of bounds for length 32
od;
return new;
end;
li := LinesOfStraightLineProgram(s);
nrinps = rInputsOfStraightLineProgram(s);
if nrinps <> Length(inputs) then
Error("inputs must be a list of the biggest2 oldwrite :=max1;
return fail;
elif ()=2and IsInt(line[]) then
tabuslots := Set(tabuslots);
trans := ShallowCopy(inputs); # we start with this translation
max := nrinps;
nextnew := FindNextNew(0);
results := [0];
for i in [1..Length(li)] do
line := li[i];
if IsInt(line[1]) then # a line without a writing position
newline := TranslateAssocWord(line);
java.lang.StringIndexOutOfBoundsException: Range [19, 18) out of bounds for length 28 | | |
