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Bug fixes in caching and comparison of Wyckoff positions #45

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merged 8 commits into from
Dec 18, 2023
Merged

Bug fixes in caching and comparison of Wyckoff positions #45

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7e2e230
Fix conjugation of Wyckoff positions
bfield1 Aug 11, 2023
9712f21
Test for conjugation of cached Wyckoff
bfield1 Aug 14, 2023
162d0e6
Fix comparison of Left Wyckoff Positions
bfield1 Aug 14, 2023
2d7aae3
Remove extraneous comment line
bfield1 Oct 6, 2023
63db375
Apply suggestions from code review in cryst.tst
bfield1 Oct 6, 2023
35cabdb
Include link and description in comment on test for #44
bfield1 Oct 6, 2023
981164b
Streamline change of Wyckoff basis in conjugation
bfield1 Oct 6, 2023
f7f55bf
Properly fix comparison of Left Wyckoff positions
bfield1 Nov 20, 2023
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28 changes: 16 additions & 12 deletions gap/cryst.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -256,7 +256,7 @@ InstallOtherMethod( \^,
IsCollsElms, [ IsAffineCrystGroupOnRight, IsMatrix ], 0,
function ( S, conj )

local d, c, C, Ci, gens, i, R, W, r, w;
local d, c, C, Ci, gens, i, R, W, r, w, t;

d := DimensionOfMatrixGroup( S ) - 1;
if not IsAffineMatrixOnRight( conj ) then
Expand All @@ -267,6 +267,7 @@ function ( S, conj )
C := conj;
Ci := conj^-1;
c := C {[1..d]}{[1..d]};
t := C [d+1]{[1..d]}; # Translation

# conjugate the generators of S
gens := ShallowCopy( GeneratorsOfGroup( S ) );
Expand All @@ -284,10 +285,11 @@ function ( S, conj )
if HasWyckoffPositions( S ) then
W := [];
for w in WyckoffPositions( S ) do
r := rec( basis := w!.basis*c,
translation := w!.translation*c,
class := w!.class,
spaceGroup := R );
r := rec( basis := w!.basis,
translation := w!.translation*c + t,
class := w!.class,
spaceGroup := R );
if r.basis <> [] then r.basis := r.basis * c; fi;
ReduceAffineSubspaceLattice( r );
Add( W, WyckoffPositionObject( r ) );
od;
Expand All @@ -302,7 +304,7 @@ InstallOtherMethod( \^,
IsCollsElms, [ IsAffineCrystGroupOnLeft, IsMatrix ], 0,
function ( S, conj )

local d, c, C, Ci, gens, i, R, W, r, w;
local d, c, C, Ci, gens, i, R, W, r, w, t;

d := DimensionOfMatrixGroup( S ) - 1;
if not IsAffineMatrixOnLeft( conj ) then
Expand All @@ -313,6 +315,7 @@ function ( S, conj )
C := conj;
Ci := conj^-1;
c := TransposedMat( C {[1..d]}{[1..d]} );
t := C {[1..d]}[d+1]; # Translation

# conjugate the generators of S
gens := ShallowCopy( GeneratorsOfGroup( S ) );
Expand All @@ -330,12 +333,13 @@ function ( S, conj )
if HasWyckoffPositions( S ) then
W := [];
for w in WyckoffPositions( S ) do
r := rec( basis := w!.basis*c,
translation := w!.translation*c,
class := w!.class,
spaceGroup := R );
ReduceAffineSubspaceLattice( r );
Add( W, WyckoffPositionObject( r ) );
r := rec( basis := w!.basis,
translation := w!.translation*c + t,
class := w!.class,
spaceGroup := R );
if r.basis <> [] then r.basis := r.basis * c; fi;
ReduceAffineSubspaceLattice( r );
Add( W, WyckoffPositionObject( r ) );
od;
SetWyckoffPositions( R, W );
fi;
Expand Down
6 changes: 6 additions & 0 deletions gap/wyckoff.gi
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Expand Up @@ -172,6 +172,9 @@ function( w1, w2 )
gens := Filtered( GeneratorsOfGroup( S ),
x -> x{[1..d]}{[1..d]} <> One( PointGroup( S ) ) );
U := SubgroupNC( S, gens );
if IsAffineCrystGroupOnLeft( U ) then
U := TransposedMatrixGroup( U );
fi;
rep := RepresentativeAction( U, r1, r2, ImageAffineSubspaceLattice );
return rep <> fail;
end );
Expand Down Expand Up @@ -200,6 +203,9 @@ function( w1, w2 )
gens := Filtered( GeneratorsOfGroup( S ),
x -> x{[1..d]}{[1..d]} <> One( PointGroup( S ) ) );
U := SubgroupNC( S, gens );
if IsAffineCrystGroupOnLeft( U ) then
U := TransposedMatrixGroup( U );
fi;
o1 := Orbit( U, r1, ImageAffineSubspaceLattice );
o2 := Orbit( U, r2, ImageAffineSubspaceLattice );
o1 := Set( List( o1, x -> rec( t := x.translation, b := x.basis ) ) );
Expand Down
20 changes: 20 additions & 0 deletions tst/cryst.tst
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Expand Up @@ -181,12 +181,32 @@ gap> C := [ [ 3, 1, 0, 0 ], [ -1, -2, 0, 0 ], [ 2, 0, 1, 0 ], [ 0, 0, 0, 1 ] ];;
gap> IsSpaceGroup( G^C );
true

# The next checks verify that including a translation component in conjugation
# works correctly, as from <https://github.com/gap-packages/cryst/issues/44>.
gap> C := [ [ 3, 1, 0, 0 ], [ -1, -2, 0, 0 ], [ 2, 0, 1, 0 ], [ 1/2, 0, 0, 1 ] ];;
gap> IsSpaceGroup( G^C );
true

# Test that caching of Wyckoff followed by conjugation works as expected
# Use Set because the order of the Wyckoff positions is semi-arbitrary.
gap> Set(WyckoffPositions( G^C )) = Set(WyckoffPositions(SpaceGroupIT(3,183)^C));
true

gap> G := TransposedMatrixGroup( G );
<matrix group with 6 generators>
gap> W := WyckoffPositions(G);;
gap> IsSpaceGroup( G^TransposedMat(C) );
true

gap> Set(WyckoffPositions( G^TransposedMat(C) )) = Set(WyckoffPositions(SpaceGroupOnLeftIT(3,183)^TransposedMat(C)));
true

# Test Wyckoff positions in a case that involves an empty basis (see <https://github.com/gap-packages/cryst/issues/42>).
gap> G := SpaceGroupIT( 3, 12 );;
gap> W := WyckoffPositions(G);;
gap> IsSpaceGroup( G^C );
true

gap> G := SpaceGroupIT( 3, 208 );
SpaceGroupOnRightIT(3,208,'1')
gap> M := MaximalSubgroupClassReps( G, rec( primes := [2,3] ) );
Expand Down
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