############################################################################
##
#M DesignFamily
##
InstallMethod(
DesignFamily,
"default",
true,
[IsInt, IsInt, IsInt, IsInt],
0,
function ( t, v, k, lambda )
local fam;
for fam in DESIGN_FAMILIES do
if fam!.parameters = [t,v,k,lambda] then
return famjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
fi;
od;
fam: (DesignFamily.."java.lang.StringIndexOutOfBoundsException: Index 42 out of bounds for length 42
IsDesign,
points ;
IsDesignFamily );
fam!.parameters := [t,v
fam! : ,IsDesignDefaultRep ;
Add( blocks = BlocksOfDesignD)
return fam;
end );
############################################################################
##
#M IsPointIncidentBlock( <D>, <pointnr>, <blocknr> )
##
InstallMethod(fi
,
" ;
,
###########################################################################
0,
function##
local points, blocks;
points := java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 11
blocks =BlocksOfDesignD )
if points[pointnr] in blocksfunction ( ,blocknrs )
java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
=(D;
return false;
end);
############################################################################
##
#M PointsIncidentBlocks( <D>, <blocknrs> )
##
InstallMethod(
PointsIncidentBlocks,
"default",
true,
[IsDesign, IsList],
0,
function ( D, blocknrs )
local points, blocks, pibnrs,
x, y;
points := PointsOfDesign( D );
blocks := BlocksOfDesign( D );
pibnrs := Filtered( [1..Size( points )],
x -> ForAll( blocknrs, y -> points[x] in blocks[y] ) );
return pibnrs;
end );
############################################################################
##
#M BlocksIncidentPoints( <D>, <pointnrs> )
##
InstallMethod(
BlocksIncidentPoints,
"default",
true,
[IsDesign, IsList],
0,
function ( D, pointnrs )
local points, blocks, bipnrs,
x, y;
points := PointsOfDesign( D );
blocks := BlocksOfDesign( D );
bipnrs := Filtered( [1..Size( blocks )],
x -> ForAll( pointnrs, y -> points[y] in blocks[x] ) );
return bipnrs;
end );
############################################################################
##
#A DesignParameter( <D> )
##
InstallMethod(
DesignParameter,
"default",
true,
[IsDesign],
0,
function ( D )
local points,blocks,
t, v, b, r, k, lambda, l, sets,
i;
points := PointsOfDesign( D );
blocks := BlocksOfDesign( D );
v := Size( points );
b := Size( blocks );
k := Size( blocks[1] );
for i in [2..b] do
if Size( blocks[i] ) <> k then
return ("Error: blocks are not of equal size");
fi;
od;
r := Size( BlocksIncidentPoints( D, [1] ) );
for i in [2..v] do
if Size( BlocksIncidentPoints( D, [1] ) ) <> r then
return
("Error: not all points are incident with the same number of blocks");
fi;
od;
lambda := r;
# test for <t> and <lambda>
for t in [2..k] do
l := Size( BlocksIncidentPoints( D, [1..t] ) );
sets := Combinations( [1..v], t );
if ForAll( sets, x -> Size( BlocksIncidentPoints( D, x ) ) = l ) then
lambda := l;
else
return [t-1, v, b, r, k, lambda];
fi;
od;
return [t, v, b, r, k, lambda];
end );
############################################################################
##
#A IncidenceMat( <D> )
##
InstallMethod(
IncidenceMat,
"default",
true,
[IsDesign],
0,
function ( D )
local points, blocks, incmat,
row, p, b;
points := PointsOfDesign( D );
blocks := BlocksOfDesign( D );
incmat := [];
for p in points do
row := [];
for b in blocks do
if p in b then
Append( row, [1] );
else
Append( row, [0] );
fi;
od;
Append( incmat, [row] );
od;
SetIncidenceMat( D, incmat );
return incmat;
end );
############################################################################
##
#M PrintIncidenceMat( <D> )
##
InstallMethod(
PrintIncidenceMat,
"default",
true,
[IsDesign],
0,
function ( D )
local incmat,
row, j;
incmat := IncidenceMat( D );
row := incmat[1];
#81
if Length( row ) > 100 then
return ( "Error : too many blocks to print incidence matrix" );
fi;
for row in incmat do
for j in row do
if j = 0 then
Print( "." );
elif j = 1 then
Print( 1 );
fi;
od;
Print( "\n" );
od;
return;
end );
############################################################################
##
#F BlockIntersectionNumbers( <D> [, <k>] )
##
BlockIntersectionNumbers := function( arg )
local D,k,binrs;
if Length( arg ) = 1 then
D := arg[1];
binrs := [];
for k in [1..Size( BlocksOfDesign( D ) )] do
Append( binrs, [BlockIntersectionNumbersK( D, k )] );
od;
elif Length( arg ) = 2 then
D := arg[1];
k := arg[2];
binrs := BlockIntersectionNumbersK( D, k );
else
Error( "usage: BlockIntersectionNumbers( <D> [, <blocknr>] )" );
fi;
return binrs;
end;
############################################################################
##
#M BlockIntersectionNumbersK( <D>, <k> )
##
InstallMethod(
BlockIntersectionNumbersK,
"default",
true,
[IsDesign, IsInt],
0,
function ( D, k )
local blocks,B,binrs,points,
x;
blocks := BlocksOfDesign( D );
B := blocks[k];
# binrs := List( blocks, x -> Size( IntersectionSet( B, x ) ) );
binrs := List( blocks, x -> Size( Intersection( B, x ) ) );
return binrs;
end );
############################################################################
##
#M IsCircularDesign( <D> )
##
## only for designs that are a result of DesignFromPlanarNearRing or
## DesignFromFerreroPair
##
InstallMethod(
IsCircularDesign,
"nearring-designs",
true,
[IsDesign],
0,
function ( D )
local v,b,t,k,circular,l,
x;
v := Size( PointsOfDesign( D ) );
b := Size( BlocksOfDesign( D ) );
t := QuoInt( b, v );
k := Size( BlocksOfDesign( D )[1] );
circular := ForAll( [1..t],
x -> IsSubset( [0,1,2,k], Set( BlockIntersectionNumbersK( D, x ) ) ) );
SetIsCircularDesign( D, circular);
return circular;
end );
############################################################################
##
#M DesignFromPointsAndBlocks( <points>, <blocks> )
##
InstallMethod(
DesignFromPointsAndBlocks,
"default",
true,
[IsList, IsList],
0,
function( points, blocks )
local fam, D, lambda,
x;
lambda := Size( Filtered( blocks, x -> points[1] in x ) );
fam := DesignFamily( 1, Size( points ), Size( blocks[1] ), lambda );
D := Objectify( fam!.defaultKind, rec() );
SetPointsOfDesign( D, points );
SetBlocksOfDesign( D, blocks );
SetName( D, Concatenation( "<an incidence structure with ",
String( Size( points ) ), " points and ",
String( Size( blocks ) ), " blocks>" ) );
return D;
end );
############################################################################
##
#M DesignFromIncidenceMat( M )
##
InstallMethod(
DesignFromIncidenceMat,
"default",
true,
[IsMatrix],
0,
function( M )
local dim, points, blocks, b,
i, x;
dim := DimensionsMat( M );
points := [1..dim[1]];
blocks := [];
for i in [1..dim[2]] do
b := Filtered( points, x -> M[x][i] = 1 );
Append( blocks, [Set( b )] );
od;
return DesignFromPointsAndBlocks( Set( points ), Set( blocks ) );
end );
############################################################################
##
#F DesignFromFerreroPair( <G>, <Phi>, <type> )
##
DesignFromFerreroPair := function( G, Phi, type )
local D;
if type = "*" then
D := DesignFromFerreroPairStar( G, Phi );
elif type = " " then
D := DesignFromFerreroPairBlank( G, Phi );
fi;
return D;
end;
############################################################################
##
#M DesignFromFerreroPairStar
##
InstallMethod(
DesignFromFerreroPairStar,
"default",
true,
[IsGroup, IsGroup],
0,
function ( G, Phi )
local t,v,k,lambda,
elms,basis,points,blocks,b,
fam,D,
i,j;
elms := ShallowCopy( AsList( G ) );
v := Size( G );
k := Size( Phi );
t := 2;
lambda := k-1;
elms := Difference( elms, [Identity( G )] );
basis := Orbits( Phi, elms );
blocks := ShallowCopy( basis );
for b in elms do
Append( blocks, basis*b );
od;
fam := DesignFamily( t, v, k, lambda );
D := Objectify( fam!.defaultKind, rec() );
points := AsList( G );
SetPointsOfDesign( D, points );
SetBlocksOfDesign( D, blocks );
# D!.group := G;
# D!.Phi := Phi;
SetName( D, Concatenation( "<a 2 - ( ", String( v ), ", ",
String( k ), ", ", String ( k-1 ),
" ) nearring generated design>" ) );
return D;
end );
############################################################################
##
#M DesignFromFerreroPairBlank
##
InstallMethod(
DesignFromFerreroPairBlank,
"default",
true,
[IsGroup, IsGroup],
0,
function ( G, Phi )
local t,v,k,lambda,
elms,id,basis,points,blocks,b,block,
fam,D,
i,j;
elms := ShallowCopy( AsList(G) );
id := Identity( G );
v := Size( G );
k := Size( Phi )+1;
elms := Difference( elms, [id] );
basis := List( Orbits( Phi, elms ), x -> Concatenation( x, [id] ) );
if v mod k = 0 and IsPrimePowerInt( k ) and
ForAny( basis, x -> Size(Group(x)) = k ) then
## some basis blocks are subgroups of G, not all their translates are distinct
Error( "some basis blocks form groups \n" );
fi;
t := 2;
lambda := k;
blocks := List( basis, Set );
for b in elms do
Append( blocks, basis*b );
od;
fam := DesignFamily( t, v, k, lambda );
D := Objectify( fam!.defaultKind, rec() );
points := AsList( G );
SetPointsOfDesign( D, points );
SetBlocksOfDesign( D, blocks );
# D!.group := G;
# D!.Phi := Phi;
SetName( D, Concatenation( "<a 2 - ( ", String( v ), ", ",
String( k ), ", ", String ( k ),
" ) nearring generated design>" ) );
return D;
end );
###
##
#F DesignFromPlanarNearRing( <N>, type> )
#
InstallGlobalFunction(
java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 2
function , type)
java.lang.StringIndexOutOfBoundsException: Index 7 out of bounds for length 0
if type =""then
java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 14
= " then
D: DesignFromPlanarNearRingBlank N)
;
eturn;
end )java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
####################java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
##
#
#
InstallMethod(
DesignFromPlanarNearRingStar,
"default",
,
[IsNearRing],
0,
function
local t,v,k,lambda,
elms,zero,a,l,basis,points,blocks,b,
,,
i
: ));
= elms1];
elms = Difference( lms,zero])java.lang.StringIndexOutOfBoundsException: Index 39 out of bounds for length 39
l := ShallowCopy( elms );
basis := [];
l: ;
while
:l[
B := Difference( Set( elms*a ), [zero] );
Append( basis, [B] );
l := Difference(
f l=[
all := true;
fi
od;
t := 2;
vIncidenceMat
k: (basis[1]);
[IsDesign,
blocks: java.lang.StringIndexOutOfBoundsException: Range [26, 25) out of bounds for length 35
for incmat;
for block in basis do
ransblock := [];
for i in block do
Append(transblock [+b );
od;
Append( blocks, [transblockPrintIncidenceMat,
od;
od
fam := DesignFamily( t, v, k,
D =Objectify( !defaultKind, rec))
java.lang.StringIndexOutOfBoundsException: Range [11, 10) out of bounds for length 28
SetPointsOfDesign( D, points );
SetBlocksOfDesign( D, blocksfi;
# D!.nearring := nrjava.lang.StringIndexOutOfBoundsException: Index 22 out of bounds for length 22
SetNameif j 0 then
elif j= 1then
fi;
return D;
end );
###################################################
##
#DesignFromPlanarNearRingBlank
##
BlockIntersect=functionarg
DesignFromPlanarNearRingBlank
fault"
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
[,
0java.lang.StringIndexOutOfBoundsException: Index 3 out of bounds for length 3
function(nr
local t,v,k,lambda,
elms,zero inrs := BlockIntersectionNumbersK D,k );
D
,B,transblock
v := Size( nrend
lms );
zero := 0*elms[1]
l
l(l,[zero )
basis := [];
all=false;
0
a := l[1];
B locks];
k := Size(B);
if v mod k = 0 and IsPrimePowerInt( k java.lang.StringIndexOutOfBoundsException: Index 44 out of bounds for length 15
(ListBA) =
## some basis #
#
Error(,
fi;
java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 3
,B java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
l= java.lang.StringIndexOutOfBoundsException: Range [20, 21) out of bounds for length 20
all := truex-> [,,,k] (
i
od;
t := 2;
=Size( 1)
lambda := k;
= )
elms := Difference
elmsdo
transblock := [[ java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 18
for i in block java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Append( transblock,
od;
Append( blocks, [transblock] );
od;
od;
fam , blocks );
return D
points :=
SetPointsOfDesign( D, points#####################
,blocks ;
# D!.nearring := nr;
SetName( D, Concatenation""
)" " ( )
"function(M )
return ;
end;
##
#java.lang.StringIndexOutOfBoundsException: Range [17, 13) out of bounds for length 69
##
#
## java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
##
############################################
elif " then
#M DesignFromWdNearRing
##
##
## only for wd nearrings withfi
##
nstallMethod
DesignFromFerreroP
"cyclicjava.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0
true,
[IsNearRingG,Phijava.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 21
0,,java.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 28
function= ( ;
: k-;
t,v,k,lambda,
apointsblocks,,
,,
i,j,,B,block,transblock,c, x;
Q := List( NilpotentElements for b elms
C := Difference(od;
# elms := AsList( nr );
a := AdditiveGenerators( nr )[1];
c := afam:t ,k )
# =elms;
v := Size( nr
points :=[a];
for i in [2..SetPointsOfDesign(D, )java.lang.StringIndexOutOfBoundsException: Index 35 out of bounds for length 35
c : ca
(points, )
od;
if ),,String(k ,
rrorisnot )
ret D;
#end);
# java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
l := java.lang.StringIndexOutOfBoundsException: Range [0, 20) out of bounds for length 6
elms,b,pointsblocksb,
allfalse
while not all do
a: [1;
B := Set( points*a );
basis B ;
l: java.lang.StringIndexOutOfBoundsException: Range [23, 21) out of bounds for length 30
if l = [] then
all := true;
fi;
od;
t=1;
k := Size( basis[1] );
blocks := ShallowCopy( basis );
# take all translates of the basis blocks
for b in points{[1..v-1]} dofi
for block inlambda := k;
transblock := [];
for iblocks := List(basis, Set );
Append( transblock,[i+b]);
od;
Append( blocks, [Append(blocks,basis*b );
od;
od;
b := Length( blocks );
lambda :b*v
fam := DesignFamily( t,java.lang.StringIndexOutOfBoundsException: Range [25, 21) out of bounds for length 39
D: (!.defaultKindrec()
SetPointsOfDesign( D, points );
SetBlocksOfDesign( D,blocks)
SetName( D, java.lang.StringIndexOutOfBoundsException: Index 23 out of bounds for length 13
return D;
nd)
########################
#
# : java.lang.StringIndexOutOfBoundsException: Range [47, 46) out of bounds for length 54
##
# the group sizesize k ofa group G
## of prime power order if existing
##
InstallGlobalFunction(
AutomorphismGroupOfCyclicGroupfi;
function( G, k e)java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
ocal ,p ,g ,h, ,
phi1, phi2, phi3;
n:Size( )java.lang.StringIndexOutOfBoundsException: Index 19 out of bounds for length 19
p : n)
d := LogInt true,
sizeAut := (p-1function(nr
not ( G)or notp
Error( "no cyclic group of prime,,java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 28
elif RemInt( sizeAut,k) >0then
("G> hasno groupgroup order <")
fi;
g := GeneratorsOfGroup( G )[wjava.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 20
if p Append(basis, B ;
h := LogInt( k, 2 );
# there are 3 possible types of java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 20
o k:= java.lang.StringIndexOutOfBoundsException: Range [15, 13) out of bounds for length 26
phi3 := for in do
GroupHomomorphismByImages][^(-1]) ;
if 2 then
eturn java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 20
fi;
( D, blocks ;
phi2 := Groupjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
return [phi1, phi2, phi3];
else
a := PrimitiveRootMod( n );
o : String( k ), ", ", String ( k-1 ),
return Group( java.lang.StringIndexOutOfBoundsException: Range [0, 45) out of bounds for length 13
;
end );
#########################################################java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
#
# DesignFromPair(GPhi
##
## nct (nr)
## <Phi>
java.lang.StringIndexOutOfBoundsException: Index 20 out of bounds for length 2
java.lang.StringIndexOutOfBoundsException: Range [16, 15) out of bounds for length 16
function =]
local p, ppowers, n,
t,v,whilenot
sisp,b,,
famD, ,C
i,j,x,a,c,
o;
id := Identity( G );
a := GeneratorsOfGroup( G )[1];
=id;
v := Size( G );
p := SmallestRootInt( v );
n := LogInt
elms :fi;
for i java.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 0
c := bin elmsdo
Add( elms, c );
if (i =0
Add( Q: [];
else
Add( C, c );
fi;
od
od
basis := []; ppowers := List( [0..n-1], x -> ;
while C <> [] do
a := C[1];
block( ppowers,x- ^x)) )
C := Difference( C, block );
block := Concatenation( [id], block );
Add( basis, block );
od;
k := Size(basis[] ;
blocks := basis;
for inelmsdo
for block in basis do
AddSetg:=nr;
od;
od;
t := 1;
b := Length( blocks );
lambda : bv
fam := DesignFamilyreturn ;
D := Objectify(
SetPointsOfDesign(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
SetBlocksOfDesign( D, blocks );
# D!.# from wd nearrincyclicgroupsofprime power order
##experimental
SetName( D, Concatenation( "
String
#
D;
end
####"java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 10
##
F (G, Phi )
##
##
##
BindGlobal( "ZeroAssociates,,,java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 33
erms,,java.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 55
h, i points:=elms;
a := java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 17
n := Size( G );
c : +a;
: ( )
perms := List
Length(java.lang.StringIndexOutOfBoundsException: Range [28, 25) out of bounds for length 38
PPhi
(PPhi,)
delta := Orbits( java.lang.StringIndexOutOfBoundsException: Index 26 out of bounds for length 0
else
elms := [1..n-1];
delta := [B: a ;
while elms <> [] do
d := Set( Flat( Orbits( PPhi l[
elms := Differenceod
Add( delta, d );
odjava.lang.StringIndexOutOfBoundsException: Range [13, 10) out of bounds for length 35
fi;
returntransblock ]java.lang.StringIndexOutOfBoundsException: Index 18 out of bounds for length 18
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 6
###################################
##
#F fam := DesignFamily , )
##
#
## <D>
##
##
al java.lang.StringIndexOutOfBoundsException: Range [33, 32) out of bounds for length 34
function( D )
local G, Phi, n, p#
h ,j,jay,,y ;
n := Size( PointsOfDesign( #
java.lang.StringIndexOutOfBoundsException: Range [24, 20) out of bounds for length 26
a :
# n =Size(G ;
elms := List( [1..n-1], x -> a^x );
: java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 30
b := Size( BlocksOfDesign( D ) );
k : QuoInt n^2*(-1), p*b );
Phi := AutomorphismGroupOfCyclicGroup( G, k );
f : GeneratorsOfGroup Phi )1]java.lang.StringIndexOutOfBoundsException: Index 37 out of bounds for length 37
fperm := PermList( List( elms <>hasno java.lang.StringIndexOutOfBoundsException: Range [38, 37) out of bounds for length 60
PPhi := Group( fperm );
if RemInt( Size( PPhi ), := ,2)
:= Orbits( PPhi[1.n-1]);
else
elms := [1..n-1];
delta := [];
while :2^(d-);
d: Set ,elms1 elms])) ;
elms := Difference( elms, d );
Add( delta, ( ,G,[g] g^(-)]) ;
od;
fi;
u := Length( delta );
P ];
for h in [f;
y:=java.lang.StringIndexOutOfBoundsException: Range [21, 19) out of bounds for length 73
Ph: [];
for j
( delta[] >(+y)mod ;
Add( Ph, List( [1..u], i
java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
Add( P, Ph );
od;
return P;
end );;
#########################
##
#FPrintDesignParameterPBIBD(D )
##
## returns the association
## <D> and gives informationDesignFromPair,
##
InstallGlobalFunction(
PrintDesignParameterPBIBD
)
caln ,,, , ,java.lang.StringIndexOutOfBoundsException: Range [44, 42) out of bounds for length 50
h, i,j, x y, ay;
n :=o
G := CyclicGroup( n
a :=id:G )
p := SmallestRootIntjava.lang.StringIndexOutOfBoundsException: Range [30, 26) out of bounds for length 35
b:Size(BlocksOfDesign );
k :p ()java.lang.StringIndexOutOfBoundsException: Index 30 out of bounds for length 30
Phi :=elms =];Q=[;C =[;
delta := ZeroAssociates( Gc= *a
u := while C <> [] do
Print( "\n" );
for C: java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 34
" ," := y-in ,deltai,"")
od;
Print( "\n" );
;
Print( " n", i t: 1
;
Print( "\n" );
for i in [1..u] do
lambda := Set( SetBlocksOfDesign(,blocks ;
Size( BlocksIncidentPoints( D.: G;
if Size( D, Concatenation( "<a 1 - ( ", String( v ), ", ",
Print
(" Error: not all pairs of points associated by R", i, java.lang.StringIndexOutOfBoundsException: Range [9, 8) out of bounds for length 11
\ aretogetherjava.lang.StringIndexOutOfBoundsException: Range [28, 27) out of bounds for length 71
i," = ", java.lang.StringIndexOutOfBoundsException: Index 14 out of bounds for length 2
else
(" i , 1], \" ;
fi;
od;
Print( "\n\n = Size( ;
P := [];
for h in [1..u] do
y := delta[
Ph := java.lang.StringIndexOutOfBoundsException: Range [15, 13) out of bounds for length 41
for j in [1..u] do
jay elms = [..n-1];
Add( Ph:= [
od;
Add( :java.lang.StringIndexOutOfBoundsException: Range [10, 9) out of bounds for length 58
("",h,"=\nn" )java.lang.StringIndexOutOfBoundsException: Index 34 out of bounds for length 34
PrintArray( Ph );
Print( "\
od;
returnF AssociationMatrices( )
end#returns association the java.lang.StringIndexOutOfBoundsException: Range [57, 56) out of bounds for length 78
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