#############################################################################
##
#W designs.gd RDS Package Marc Roeder
##
##
##
##
#Y Copyright (C) 2006-2011 Marc Roeder
#Y
#Y This program is free software; you can redistribute it and/or
#Y modify it under the terms of the GNU General Public License
#Y as published by the Free Software Foundation; either version 2
#Y of the License, or (at your option) any later version.
#Y
#Y This program is distributed in the hope that it will be useful,
#Y but WITHOUT ANY WARRANTY; without even the implied warranty of
#Y MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#Y GNU General Public License for more details.
#Y
#Y You should have received a copy of the GNU General Public License
#Y along with this program; if not, write to the Free Software
#Y Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA
##
############################################################################
##
#O DevelopmentOfRDS(<diffset>,<Gdata>);
##
## This calculates the development of a (partial relative) difference set
## <diffset> in the group given by <Gdata>.
## That is, the associated block design.
##
## <diffset> can be given as a list of group
## elements or a list of integers (positions in the set of group elements).
## <Gdata> can either be the record returned by
## "PermutationRepForDiffsetCalculations" or a group or a set of group elements.
##
## In either case, the returned object is a `BlockDesign' in the sense of
## L. Soichers DESIGN package.
##
DeclareOperation("DevelopmentOfRDS",[IsDenseList,IsObject]);
#############################################################################
##
#O IsProjectivePlane(plane) test, if block design is a projective plane
##
## Tests if the BlockDesign <plane> is a projective plane.
## This adds the entry <.isProjectivePlane> to the block design <plane>.
## If <plane> is a projective plane, an entry called <.block> is generated
## as well. This is a matrix with $ij$th entry the number of the block
## connecting the points $i$ and $j$.
##
DeclareOperation("IsProjectivePlane",[IsRecord]);
#############################################################################
##
#O PointJoiningLinesProjectivePlane(<plane>) generate additional data for projective planes
##
## Returns a matrix which has as $ij$th entry the point wich is contained
## in the blocks with numbers $i$ and $j$. This matrix is also stored in
## <plane>. Some operations are faster if <plane> contains this matrix.
## If <plane> is not a projective plane, an error is issued.
##
DeclareOperation("PointJoiningLinesProjectivePlane",[IsRecord]);
#############################################################################
##
#O ProjectivePlane( <blocks> ) generate projective plane from blocks
##
## Given a list of lists <blocks> which represents the blocks of a
## projective plane, a block design is generated. If the <blocks> is not
## a set of sets of the integers `[1..v]' for some $v$, the points are
## sorted and enumerated and the blocks are changed accordingly.
## But the original names are known to the returned BlockDesign.
##
## The block design generated this way will contain two extra entries,
## <jblock> and <isProjectivePlane>. The matrix <.jblock> contains the
## number of the block containing the points $i$ and $j$ at the $(i,j)$th
## position. And <isProjectivePlane> will be `true'.
## If <blocks> do not form the lines of a projective plane, an error is
## issued.
##
DeclareOperation("ProjectivePlane",[IsMatrix]);
#############################################################################
##
#E END
##
¤ Dauer der Verarbeitung: 0.1 Sekunden
¤
*© Formatika GbR, Deutschland
