Extended support for subperiodic groups

.gitignore

@@ -10,3 +10,5 @@
 /doc/manual.ps
 /doc/manual.toc
 /htm/
+**/*.swp
+**/.DS_Store

doc/cryst.tex

@@ -470,7 +470,7 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \Section{Wyckoff positions}
 
-A Wyckoff position of a space group <S> is an equivalence class of
+A Wyckoff position of a crystallographic group <S> is an equivalence class of
 points in Euclidean space, having stabilizers which are conjugate
 subgroups of <S>.  Apart from a subset of lower dimension, which
 contains points with even bigger stabilizers, a Wyckoff position
@@ -480,7 +480,7 @@
 
 \>WyckoffPositions( <S> ) A
 
-returns the list of Wyckoff positions of the space group <S>.
+returns the list of Wyckoff positions of the group <S>.
 
 \beginexample
 gap> S := SpaceGroupIT(2,14);
@@ -501,12 +501,12 @@
 
 In the previous example, <S> has three kinds of special points
 (the basis is empty), whose representatives all have a stabilizer 
-with the same point group (with label 1), one kind of special line
+with the same point group (with label 3), one kind of special line
 (the basis has length 1), and the general position.
 
 \>WyckoffPositionsByStabilizer( <S>, <sub> ) O
 
-where <S> is a space group and <sub> a subgroup of the point group or
+where <S> is a group and <sub> a subgroup of the point group or
 a list of such subgroups, determines only the Wyckoff positions whose
 representatives have a stabilizer with a point group equal to the 
 subgroup <sub> or contained in the list <sub>, respectively.
@@ -553,7 +553,7 @@
 
 \>WyckoffSpaceGroup( <W> ) O
 
-returns the space group of which <W> is a Wyckoff position.
+returns the crystallographic group of which <W> is a Wyckoff position.
 
 \beginexample
 gap> WyckoffSpaceGroup( W[1] );
@@ -564,7 +564,7 @@
 
 returns the stabilizer of the (generic) points in the representative
 affine subspace of the Wyckoff position <W>. This stabilizer is a
-subgroup of the space group of <W>, and thus an `AffineCrystGroup'.
+subgroup of the crystallographic group of <W>, and thus an `AffineCrystGroup'.
 
 \beginexample
 gap> stab := WyckoffStabilizer( W[4] );
@@ -576,13 +576,13 @@
 \>WyckoffOrbit( <W> ) O
 
 determines the orbit of the representative affine subspace <A> of the 
-Wyckoff position <W> under the space group <S> of <W> (modulo lattice 
+Wyckoff position <W> under the crystallographic group <S> of <W> (modulo lattice 
 translations). The affine subspaces in this orbit are then converted 
 into a list of Wyckoff positions, which is returned. The Wyckoff 
 positions in this list are just different representations of <W>. 
 Their `WyckoffBasis' and `WyckoffTranslation' are chosen such that 
 the induced parametrizations of their representative subspaces are 
-mapped onto each other under the space group operation.
+mapped onto each other under the crystallographic group operation.
 
 \beginexample
 gap> orb := WyckoffOrbit( W[4] );
@@ -881,8 +881,9 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \Section{International Tables}
 
-For the user's convenience, a table with the 17 plane groups and the
-230 space groups is included in {\Cryst}. These groups are given in 
+For the user's convenience, tables with the 17 plane groups, 230
+space groups, 7 frieze groups, 75 rod groups, and 80 layer groups
+are included in {\Cryst}. These groups are given in 
 exactly the same settings (i.e., choices of basis and origin) as in 
 the International Tables. Space groups with a centered lattice are
 therefore given in the non-primitive basis crystallographers are
@@ -904,6 +905,34 @@
 in a rhombohedral basis (setting `\pif{r}\pif'). `\pif{h}\pif' is the 
 default setting.
 
+For the frieze groups, two different settings are available.
+The possible settings are labelled with the characters `\pif{a}\pif'
+and `\pif{b}\pif'. `\pif{a}\pif' is the default setting.
+
+For the orthorhombic rod groups, six settings are available.
+These are labelled with the string `\pif\pif{abc}\pif\pif' or permutations
+of its characters. These correspond to permutations of the <a>,
+<b>, and <c> directions. `\pif\pif{abc}\pif\pif' is the default setting.
+
+For some of the tetragonal, trigonal, and hexagonal rod groups,
+two basis choices exist: `\pif{1}\pif' and `\pif{2}\pif'. `\pif{1}\pif'
+is the default setting.
+
+For layer groups 5 and 7, three cell choices exist, which differ
+by whether the glide vector is along the <a> direction (setting
+`\pif{1}\pif'), the <a+b> direction (setting `\pif{2}\pif'), or the
+<b> direction (setting `\pif{3}\pif'). `\pif{1}\pif' is the default
+setting.
+
+For some orthorhombic layer groups, they have two settings,
+`\pif{a}\pif' for the abc setting, and `\pif{b}\pif' for the bac setting.
+`\pif{a}\pif' is the default setting.
+
+For some layer groups (52, 62, and 64), there exists a point of higher
+symmetry than the origin of the `\pif{1}\pif' setting. In such cases,
+a second setting `\pif{2}\pif' which has this higher symmetry point as
+the origin is available and is the default setting.
+
 \>SpaceGroupSettingsIT( <dim>, <nr> ) F
 
 returns a string, whose characters label the available settings of
@@ -940,5 +969,49 @@
 SpaceGroupOnRightIT(3,146,'r')
 \endexample
 
+The subperiodic group functions accept an argument <type>, which is
+a string which is either `\pif\pif{Frieze}\pif\pif', `\pif\pif{Rod}\pif\pif', or
+`\pif\pif{Layer}\pif\pif'. This specifies the type of subperiodic group.
+
+\>SubPeriodicGroupSettingsIT( <type>, <nr> ) F
+
+returns a string (or list), whose characters (or strings, for
+multi-character settings) label the available settings of
+the subperiodic group with number <nr> and type <type>.
+
+\> SubPeriodicGroupOnRightIT( <type>, <nr> ) F
+\> SubPeriodicGroupOnRightIT( <type>, <nr>, <setting> ) F
+
+returns subperiodic group number <nr> with type <type> in the
+representation acting on the right. In the third argument,
+the desired setting can be specified. Otherwise, the
+group is returned in the default setting for that group.
+
+\> SubPeriodicGroupOnLeftIT( <type>, <nr> ) F
+\> SubPeriodicGroupOnLeftIT( <type>, <nr>, <setting> ) F
+
+returns subperiodic group number <nr> with type <type> in the
+representation acting on the left. In the third argument,
+the desired setting can be specified. Otherwise, the
+group is returned in the default setting for that group.
+
+\> SubPeriodicGroupIT( <type>, <nr> ) F
+\> SubPeriodicGroupIT( <type>, <nr>, <setting> ) F
+
+returns either `SubPeriodicGroupOnRightIT' or `SubPeriodicGroupOnLeftIT' with
+the same arguments, depending on the value of `CrystGroupDefaultAction'.
+
+\> FriezeGroupIT( <nr> ) F
+\> FriezeGroupIT( <nr>, <setting> ) F
+
+returns `SubPeriodicGroupIT(\pif\pif{Frieze}\pif\pif, <nr>, <setting>)'.
+
+\> RodGroupIT( <nr> ) F
+\> RodGroupIT( <nr>, <setting> ) F
+
+returns `SubPeriodicGroupIT(\pif\pif{Rod}\pif\pif, <nr>, <setting>)'.
 
+\> LayerGroupIT( <nr> ) F
+\> LayerGroupIT( <nr>, <setting> ) F
 
+returns `SubPeriodicGroupIT(\pif\pif{Layer}\pif\pif, <nr>, <setting>)'.

doc/manual.six

@@ -109,3 +109,16 @@ F 2.11. SpaceGroupOnLeftIT
 F 2.11. SpaceGroupOnLeftIT
 F 2.11. SpaceGroupIT
 F 2.11. SpaceGroupIT
+F 2.11. SubPeriodicGroupSettingsIT
+F 2.11. SubPeriodicGroupOnRightIT
+F 2.11. SubPeriodicGroupOnRightIT
+F 2.11. SubPeriodicGroupOnLeftIT
+F 2.11. SubPeriodicGroupOnLeftIT
+F 2.11. SubPeriodicGroupIT
+F 2.11. SubPeriodicGroupIT
+F 2.11. FriezeGroupIT
+F 2.11. FriezeGroupIT
+F 2.11. RodGroupIT
+F 2.11. RodGroupIT
+F 2.11. LayerGroupIT
+F 2.11. LayerGroupIT

gap/cryst.gi

@@ -283,6 +283,12 @@ function ( S, conj )
 
     # add Wyckoff positions if known
     if HasWyckoffPositions( S ) then
+      # If we have a sub-periodic group and C includes out-of-basis
+      # components, then we must scrap the cached Wyckoffs.
+      # Just to be safe, we'll scrap it without checking C, as there are
+      # too many edge cases.
+      # Scrapping Wyckoffs just means we don't call SetWyckoffPositions
+      if IsSpaceGroup(S) then
         W := [];
         for w in WyckoffPositions( S ) do
             r := rec( basis       := w!.basis,
@@ -294,6 +300,7 @@ function ( S, conj )
             Add( W, WyckoffPositionObject( r ) );
         od;
         SetWyckoffPositions( R, W );
+      fi;
     fi;
 
     return R;
@@ -331,6 +338,11 @@ function ( S, conj )
 
     # add Wyckoff positions if known
     if HasWyckoffPositions( S ) then
+      # Transformations are only unique for space groups.
+      # Sub-periodic groups can lose information if there are out-of-plane
+      # components, which can make the Wyckoff positions inconsistent.
+      # So we'll only keep the cached Wyckoffs if it is a space group.
+      if IsSpaceGroup(S) then
         W := [];
         for w in WyckoffPositions( S ) do
           r := rec( basis       := w!.basis,
@@ -342,6 +354,7 @@ function ( S, conj )
           Add( W, WyckoffPositionObject( r ) );
         od;
         SetWyckoffPositions( R, W );
+      fi;
     fi;
 
     return R;

gap/hom.gd

@@ -25,6 +25,12 @@ DeclareAttribute( "NiceToCryst", IsPointGroup );
 ##
 DeclareGlobalFunction( "NiceToCrystStdRep" );
 
+#############################################################################
+##
+#F  NiceToCrystStdRepSymmetric( P, perm )
+##
+DeclareGlobalFunction( "NiceToCrystStdRepSymmetric" );
+
 #############################################################################
 ##
 #P  IsFromAffineCrystGroupToFpGroup

gap/hom.gi

@@ -73,7 +73,7 @@ end );
 #F  NiceToCrystStdRep( P, perm )
 ##
 InstallGlobalFunction( NiceToCrystStdRep, function( P, perm )
-    local S, m, d, c;
+    local S, m;
     S := AffineCrystGroupOfPointGroup( P );
     m := ImagesRepresentative( NiceToCryst( P ), perm );
     if IsStandardAffineCrystGroup( S ) then
@@ -83,6 +83,29 @@ InstallGlobalFunction( NiceToCrystStdRep, function( P, perm )
     fi;
 end );
 
+#############################################################################
+##
+#F  NiceToCrystStdRepSymmetric( P, perm )
+##
+InstallGlobalFunction( NiceToCrystStdRepSymmetric, function( P, perm )
+    local S, m, d, mat, lconj, rconj;
+    # Uses SymmetricInternalBasis rather than InternalBasis
+    S := AffineCrystGroupOfPointGroup( P );
+    m := ImagesRepresentative( NiceToCryst( P ), perm );
+    d := DimensionOfMatrixGroup( S ) - 1;
+    # Get transformation into standard basis
+    mat := AugmentedMatrix(SymmetricInternalBasis(S), ListWithIdenticalEntries(d, 0));
+    if IsAffineCrystGroupOnRight( S ) then
+      lconj := mat;
+      rconj := mat^-1;
+    else
+      mat := TransposedMat(mat);
+      lconj := mat^-1;
+      rconj := mat;
+    fi;
+    return lconj * m * rconj;
+end );
+
 #############################################################################
 ##
 #M  NaturalHomomorphismByNormalSubgroup( <G>, <N> ) . .  for AffineCrystGroup

gap/wyckoff.gd

@@ -58,6 +58,12 @@ DeclareGlobalFunction( "ImageAffineSubspaceLattice" );
 ##
 DeclareGlobalFunction( "ImageAffineSubspaceLatticePointwise" );
 
+#############################################################################
+##
+#A  SymmetricInternalBasis . .internal basis that respects lattice symmetries
+##
+DeclareAttribute( "SymmetricInternalBasis", IsAffineCrystGroupOnLeftOrRight );
+
 #############################################################################
 ##
 #A  WyckoffStabilizer . . . . . . . . . stabilizer of representative subspace