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InstallGlobalFunction( NumberOfDigitsOfTheNumber,
function(a)
return Length( String( a ) );
end);
# this functions prints a matrix in good form
InstallMethod( PTM,
[ IsMatrix ],
function( matrix )
local i,j,m,t,n;
m := 1;
n := 1;
for i in [ 1 .. Length( matrix ) ] do
if n < NumberOfDigitsOfTheNumber( matrix[ i ][ 1 ] ) then
n:= NumberOfDigitsOfTheNumber( matrix[ i ][ 1 ] );
fi;
od;
for i in [ 1 .. Length( matrix ) ] do
for j in [ 1 .. Length( matrix[ 1 ] ) ] do
if m < NumberOfDigitsOfTheNumber( matrix[ i ][ j ] ) then
m := NumberOfDigitsOfTheNumber( matrix[ i ][ j ] );
fi;
od;
od;
Print(" ");
for i in [ 1 .. Length( matrix[ 1 ] ) * ( m + 2 ) - 2 ] do
Print(" ");
od;
Print( " ", "\n" );
for i in [ 1 .. Length( matrix ) ] do
Print( " " );
for j in [ 1 .. Length( matrix[ 1 ] ) ] do
if j=1 then
for t in [ 1 .. n - NumberOfDigitsOfTheNumber( matrix[ i ][ j ] ) ] do
Print( " " );
od;
else
for t in [ 1 .. m + 2 - NumberOfDigitsOfTheNumber( matrix[ i ][ j ] ) ] do
Print(" ");
od;
fi;
Print( matrix[ i ][ j ] );
od;
Print(" ","\n");
od;
end );
##
InstallMethod( IsCompatiblePolyhedronList,
[ IsList ],
function ( list )
local i;
if not ForAll( [1,4,5], i -> list[i] in NonnegativeIntegers) then
Error( "The first five entries must be non-negative integers" );
fi;
if not( IsList( list[6]) and IsList( list[7] ) ) then
Error( "The last two arguments should be lists" );
fi;
if not IsEmpty( list[ 7 ] ) then
if NrRows( list[ 7 ] ) <> list[ 4 ] then
Error( "The matrix has the wrong number of rows" );
fi;
if NrCols( list[ 7 ] ) <> list[ 5 ] then
Error( "The matrix has the wrong number of columns" );
fi;
fi;
for i in list[ 6 ] do
if i > list[ 4 ] then
Error( "The linearity is not compatible" );
fi;
od;
return true;
end );
##
InstallMethod( LcmOfDenominatorRatInList,
[ IsList ],
function( list )
return Lcm( List( list, DenominatorRat ) );
end );
##
InstallGlobalFunction( LIST_TO_CDD_POLYHEDRON,
function( arg )
local numtype, matrix, L, temp1, temp2, temp3, temp4, p, i;
matrix := arg[ 5 ];
if not IsEmpty( matrix ) and NrRows( matrix ) > 0 then
matrix := CanonicalizeList( matrix, arg[ 1 ] );
fi;
if arg[ 1 ] = 2 then
temp2 := GiveGeneratingVerticesAndGeneratingRays( matrix, [ ] )[ 1 ];
if temp2 = [ List( [ 2 .. arg[ 3 ] ], i -> 0 ) ] and
not NrRows( matrix ) = 1 then
temp3 := StructuralCopy( matrix );
temp4 := StructuralCopy( arg[ 4 ] );
temp1 := [ 1 ];
Append( temp1, temp2[ 1 ] );
p := Position( temp3, temp1 );
Remove( temp3, p );
for i in [ p..Length( temp4 ) ] do
temp4[ i ]:= temp4[ i ] - 1;
od;
if Length( arg[ 4 ] ) = 0 then
return Cdd_PolyhedronByGenerators( temp3 );
else
return Cdd_PolyhedronByGenerators( temp3 , temp4 );
fi;
fi;
if Length( arg[ 4 ] ) = 0 then
return Cdd_PolyhedronByGenerators( matrix );
else
return Cdd_PolyhedronByGenerators( matrix , arg[ 4 ] );
fi;
else
if arg[ 2 ] = 0 then
L := ListWithIdenticalEntries( arg[ 3 ], 0 );
L[ 1 ] := 1;
return Cdd_PolyhedronByInequalities( [ L ] );
fi;
if Length( arg[ 4 ] ) = 0 then
return Cdd_PolyhedronByInequalities( matrix );
else
return Cdd_PolyhedronByInequalities( matrix , arg[ 4 ] );
fi;
fi;
end );
##
InstallMethod( CDD_POLYHEDRON_TO_LIST,
[ IsCddPolyhedron ],
function( poly )
local L, matrix, lin, temp;
L := [ ];
if (poly!.rep_type = "H-rep" ) then
L[ 1 ] := 1;
else
L[ 1 ] := 2;
fi;
matrix := poly!.matrix;
L[ 2 ] := NrRows( matrix );
L[ 3 ] := NrCols( matrix );
L[ 4 ] := poly!.linearity;
L[ 5 ] := matrix;
L[ 6 ] := 0;
L[ 7 ] := [ ];
return L;
end );
##
InstallMethod( CanonicalizeList,
[ IsList, IsInt ],
function( matrix, rep )
local res, i;
res:= [ ];
if rep = 1 then
for i in [ 1.. Length( matrix ) ] do
if not IsZero( matrix[ i ] ) then
res[ i ] := LcmOfDenominatorRatInList( matrix[ i ] )*
matrix[ i ] / Iterated(
LcmOfDenominatorRatInList( matrix[ i ] )*matrix[ i ], Gcd
);
else
res[ i ] := matrix[ i ];
fi;
od;
return res;
fi;
for i in [ 1.. Length( matrix ) ] do
if matrix[ i ][ 1 ] = 0 then
res[ i ]:= LcmOfDenominatorRatInList( matrix[ i ] )*
matrix[ i ] / Iterated(
LcmOfDenominatorRatInList( matrix[ i ] )*matrix[ i ], Gcd
);
else
res[ i ] := matrix[ i ];
fi;
od;
return res;
end );
InstallMethod( LinearProgramToList,
[IsCddLinearProgram ],
function( lp )
local result;
result:= ShallowCopy( CDD_POLYHEDRON_TO_LIST( Cdd_H_Rep( lp!.polyhedron ) ) );
if lp!.objective = "max" then
result[ 6 ] := 1;
else
result[ 6 ] := 2;
fi;
result[ 7 ] := lp!.rowvector;
return result;
end );
###
InstallMethod( GiveGeneratingVerticesAndGeneratingRays,
[ IsList, IsList ],
function( matrix, linearity )
local generating_vertices, generating_rays, current, temp, l, i;
generating_vertices:= [ ];
generating_rays:= [ ];
temp := StructuralCopy( matrix );
l := Length( temp );
for i in [ 1..l ] do
current := temp[ i ];
if current[ 1 ] = 1 then
Remove( current, 1 );
if i in linearity then
Add( generating_vertices, current );
Add( generating_vertices, -current );
else
Add( generating_vertices, current );
fi;
else
Remove( current, 1 );
if not IsZero( current ) then
if i in linearity then
Add( generating_rays, current );
Add( generating_rays, -current );
else
Add( generating_rays, current );
fi;
else
Add( generating_vertices, current );
fi;
fi;
od;
return [ generating_vertices, generating_rays ];
end );
####
InstallMethod( GiveInequalitiesAndEqualities,
[ IsList, IsList ],
function( matrix, linearity )
local equalities, inequalities , current, temp, l, i;
inequalities:= [];
equalities:= [];
l:= Length( matrix );
for i in [ 1..l ] do
current:= matrix[ i ];
if i in linearity then
Add( equalities, current );
else
Add( inequalities, current );
fi;
od;
return [ inequalities, equalities ];
end );
InstallMethod( GetRidOfLinearity,
[ IsCddPolyhedron ],
function( poly )
local i, temp;
if poly!.rep_type = "V-rep" then
Error( "This function is written for H-rep polyhedra" );
fi;
temp:= StructuralCopy( poly!.matrix );
for i in poly!.linearity do
Add( temp, -temp[ i ] );
od;
return Cdd_PolyhedronByInequalities( temp );
end );
##
InstallGlobalFunction( CanonicalizeListOfFacesAndInteriorPoints,
function( L )
local new_L;
if IsInt( L ) then
return [];
elif IsList( L ) and Length( L ) = 3 and IsInt( L[ 1 ] ) then
new_L := List( L, ShallowCopy );
return [ new_L ];
else
return Concatenation( List( L, CanonicalizeListOfFacesAndInteriorPoints ) );
fi;
end );
[ Dauer der Verarbeitung: 0.5 Sekunden
(vorverarbeitet)
]
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