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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 );

Quelle tools.gi Sprache: unbekannt

[ Dauer der Verarbeitung: 0.9 Sekunden (vorverarbeitet) ]