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#############################################################################
##
#W misc.gi HAPcryst package Marc Roeder
##
##
##
##
#Y Copyright (C) 2006 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
##
# there seems to be not method for rationals, even though SignInt
# did work in all of the cases I tried.
InstallMethod(SignRat, "for rationals",[IsRat],
function(rat)
if rat>0
then
return 1;
elif rat<0
then
return -1;
elif rat=0
then
return 0;
else
Error("cannot calculate sign of rational");
fi;
#return SignInt(rat*DenominatorRat(rat));
end);
##############################
InstallMethod(IsSquareMat,"for matrices",[IsMatrix],
function(mat)
return Size(Set(mat,Size))=1;
end);
##############################
InstallMethod(DimensionSquareMat,"for matrices",[IsMatrix],
function(mat)
if not IsSquareMat(mat)
then
Error("Matrix is not square");
else
return DimensionsMat(mat)[1];
fi;
end);
##############################
#
# Return the linear part of an affine matrix. This is sometimes called
# "rotational part" for crystallographic groups.
#
InstallMethod(LinearPartOfAffineMatOnRight,"for affine matrices on right",
[IsMatrix],
function(mat)
local dim;
if not IsAffineMatrixOnRight(mat)
then
Error("matrix must be an affine matrix acting from the right");
fi;
dim:=DimensionSquareMat(mat);
return mat{[1..dim-1]}{[1..dim-1]};
end);
##############################
#
# Calculate what a basis change of $n$ dimensional space does to an affine
# transformation represented by an affine $(n+1)\times(n+1)$ matrix.
#
InstallMethod(BasisChangeAffineMatOnRight,"for affine matrices on right",
[IsMatrix,IsMatrix],
function(transform,mat)
local dim, linpart, transpart, transformed;
dim:=DimensionSquareMat(mat);
if not dim>1 and IsAffineMatrixOnRight(mat)
then
Error("This matrix is not affine acting on right");
fi;
linpart:=LinearPartOfAffineMatOnRight(mat);
transpart:=mat[dim]{[1..dim-1]};
transformed:=IdentityMat(dim);
transformed{[1..dim-1]}{[1..dim-1]}:=linpart^transform;
transformed[dim]{[1..dim-1]}:=transpart*transform;
return transformed;
end);
##############################
#
# Return an affine matrix on right which represents the translation
# by <vector>
#
InstallMethod(TranslationOnRightFromVector,
[IsVector],
function(vector)
local dim, translation;
dim:=Size(vector)+1;
translation:=IdentityMat(dim);
translation[dim]{[1..dim-1]}:=ShallowCopy(vector);
return translation;
end);
##############################
#
#
InstallMethod(VectorModOne,
[IsVector],
function(vector)
return List(vector,FractionModOne);
end);
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