| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/aclib/gap/ (GAP Algebra Version 4.15.1©) Datei vom 28.7.2025 mit Größe 90 kB |
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Quellcode-Bibliothek crystgrp.gi Sprache: unbekannt |
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Spracherkennung für: .gi vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen] #############################################################################
## #W In this file we prepare functions to loop over the 2,3 or 4 dimensional #W crystallographic groups as matrix groups or pcp groups. ## cryst4params:= [ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 1 ], [ 2, 1, 2, 2 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 2, 1 ], [ 2, 3, 1, 1 ], [ 2, 3, 1, 2 ], [ 2, 3, 1, 3 ], [ 2, 3, 1, 4 ], [ 2, 3, 2, 1 ], [ 2, 3, 2, 2 ], [ 3, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 2, 1 ], [ 3, 1, 2, 2 ], [ 3, 1, 3, 1 ], [ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ], [ 3, 2, 1, 3 ], [ 3, 2, 2, 1 ], [ 3, 2, 2, 2 ], [ 3, 2, 2, 3 ], [ 3, 2, 3, 1 ], [ 4, 1, 1, 1 ], [ 4, 1, 1, 2 ], [ 4, 1, 1, 3 ], [ 4, 1, 1, 4 ], [ 4, 1, 1, 5 ], [ 4, 1, 1, 6 ], [ 4, 1, 1, 7 ], [ 4, 1, 1, 8 ], [ 4, 1, 1, 9 ], [ 4, 1, 1, 10 ], [ 4, 1, 1, 11 ], [ 4, 1, 1, 12 ], [ 4, 1, 1, 13 ], [ 4, 1, 2, 1 ], [ 4, 1, 2, 2 ], [ 4, 1, 2, 3 ], [ 4, 1, 2, 4 ], [ 4, 1, 3, 1 ], [ 4, 1, 3, 2 ], [ 4, 1, 3, 3 ], [ 4, 1, 3, 4 ], [ 4, 1, 3, 5 ], [ 4, 1, 3, 6 ], [ 4, 1, 3, 7 ], [ 4, 1, 3, 8 ], [ 4, 1, 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[ 33, 3, 1, 2 ], [ 33, 4, 1, 1 ], [ 33, 5, 1, 1 ], [ 33, 5, 1, 2 ], [ 33, 5, 1, 3 ], [ 33, 6, 1, 1 ], [ 33, 6, 1, 2 ], [ 33, 7, 1, 1 ], [ 33, 8, 1, 1 ], [ 33, 8, 1, 2 ], [ 33, 9, 1, 1 ], [ 33, 9, 1, 2 ], [ 33, 10, 1, 1 ], [ 33, 10, 1, 2 ], [ 33, 11, 1, 1 ], [ 33, 12, 1, 1 ], [ 33, 12, 1, 2 ], [ 33, 13, 1, 1 ], [ 33, 14, 1, 1 ], [ 33, 14, 2, 1 ], [ 33, 15, 1, 1 ], [ 33, 16, 1, 1 ] ]; cryst3params := [ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 2, 1 ], [ 2, 2, 2, 2 ], [ 2, 3, 1, 1 ], [ 2, 3, 1, 2 ], [ 2, 3, 1, 3 ], [ 2, 3, 1, 4 ], [ 2, 3, 2, 1 ], [ 2, 3, 2, 2 ], [ 3, 1, 1, 1 ], [ 3, 1, 1, 2 ], [ 3, 1, 1, 3 ], [ 3, 1, 1, 4 ], [ 3, 1, 2, 1 ], [ 3, 1, 2, 2 ], [ 3, 1, 3, 1 ], [ 3, 1, 4, 1 ], [ 3, 1, 4, 2 ], [ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ], [ 3, 2, 1, 3 ], [ 3, 2, 1, 4 ], [ 3, 2, 1, 5 ], [ 3, 2, 1, 6 ], [ 3, 2, 1, 7 ], [ 3, 2, 1, 8 ], [ 3, 2, 1, 9 ], [ 3, 2, 1, 10 ], [ 3, 2, 2, 1 ], [ 3, 2, 2, 2 ], [ 3, 2, 2, 3 ], [ 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4, 5, 1, 5 ], [ 4, 5, 1, 6 ], [ 4, 5, 1, 7 ], [ 4, 5, 1, 8 ], [ 4, 5, 2, 1 ], [ 4, 5, 2, 2 ], [ 4, 5, 2, 3 ], [ 4, 5, 2, 4 ], [ 4, 6, 1, 1 ], [ 4, 6, 1, 2 ], [ 4, 6, 1, 3 ], [ 4, 6, 1, 4 ], [ 4, 6, 2, 1 ], [ 4, 6, 2, 2 ], [ 4, 6, 2, 3 ], [ 4, 6, 2, 4 ], [ 4, 6, 3, 1 ], [ 4, 6, 3, 2 ], [ 4, 6, 4, 1 ], [ 4, 6, 4, 2 ], [ 4, 7, 1, 1 ], [ 4, 7, 1, 2 ], [ 4, 7, 1, 3 ], [ 4, 7, 1, 4 ], [ 4, 7, 1, 5 ], [ 4, 7, 1, 6 ], [ 4, 7, 1, 7 ], [ 4, 7, 1, 8 ], [ 4, 7, 1, 9 ], [ 4, 7, 1, 10 ], [ 4, 7, 1, 11 ], [ 4, 7, 1, 12 ], [ 4, 7, 1, 13 ], [ 4, 7, 1, 14 ], [ 4, 7, 1, 15 ], [ 4, 7, 1, 16 ], [ 4, 7, 2, 1 ], [ 4, 7, 2, 2 ], [ 4, 7, 2, 3 ], [ 4, 7, 2, 4 ], [ 5, 1, 1, 1 ], [ 5, 1, 2, 1 ], [ 5, 1, 2, 2 ], [ 5, 2, 1, 1 ], [ 5, 2, 2, 1 ], [ 5, 3, 1, 1 ], [ 5, 3, 2, 1 ], [ 5, 3, 2, 2 ], [ 5, 3, 3, 1 ], [ 5, 3, 3, 2 ], [ 5, 4, 1, 1 ], [ 5, 4, 1, 2 ], [ 5, 4, 2, 1 ], [ 5, 4, 2, 2 ], [ 5, 4, 3, 1 ], [ 5, 4, 3, 2 ], [ 5, 5, 1, 1 ], [ 5, 5, 1, 2 ], [ 5, 5, 2, 1 ], [ 5, 5, 2, 2 ], [ 5, 5, 3, 1 ], [ 5, 5, 3, 2 ], [ 6, 1, 1, 1 ], [ 6, 1, 1, 2 ], [ 6, 1, 1, 3 ], [ 6, 1, 1, 4 ], [ 6, 2, 1, 1 ], [ 6, 3, 1, 1 ], [ 6, 3, 1, 2 ], [ 6, 4, 1, 1 ], [ 6, 4, 1, 2 ], [ 6, 4, 1, 3 ], [ 6, 4, 1, 4 ], [ 6, 5, 1, 1 ], [ 6, 5, 1, 2 ], [ 6, 5, 1, 3 ], [ 6, 5, 1, 4 ], [ 6, 6, 1, 1 ], [ 6, 6, 1, 2 ], [ 6, 6, 2, 1 ], [ 6, 6, 2, 2 ], [ 6, 7, 1, 1 ], [ 6, 7, 1, 2 ], [ 6, 7, 1, 3 ], [ 6, 7, 1, 4 ], [ 7, 1, 1, 1 ], [ 7, 1, 1, 2 ], [ 7, 1, 2, 1 ], [ 7, 1, 3, 1 ], [ 7, 1, 3, 2 ], [ 7, 2, 1, 1 ], [ 7, 2, 1, 2 ], [ 7, 2, 1, 3 ], [ 7, 2, 2, 1 ], [ 7, 2, 2, 2 ], [ 7, 2, 3, 1 ], [ 7, 2, 3, 2 ], [ 7, 3, 1, 1 ], [ 7, 3, 1, 2 ], [ 7, 3, 1, 3 ], [ 7, 3, 2, 1 ], [ 7, 3, 2, 2 ], [ 7, 3, 3, 1 ], [ 7, 3, 3, 2 ], [ 7, 4, 1, 1 ], [ 7, 4, 1, 2 ], [ 7, 4, 2, 1 ], [ 7, 4, 2, 2 ], [ 7, 4, 3, 1 ], [ 7, 4, 3, 2 ], [ 7, 5, 1, 1 ], [ 7, 5, 1, 2 ], [ 7, 5, 1, 3 ], [ 7, 5, 1, 4 ], [ 7, 5, 2, 1 ], [ 7, 5, 2, 2 ], [ 7, 5, 2, 3 ], [ 7, 5, 2, 4 ], [ 7, 5, 3, 1 ], [ 7, 5, 3, 2 ] ]; cryst2params := [ [ 1, 1, 1, 1 ], [ 1, 2, 1, 1 ], [ 2, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 2, 1, 2, 1 ], [ 2, 2, 1, 1 ], [ 2, 2, 1, 2 ], [ 2, 2, 1, 3 ], [ 2, 2, 2, 1 ], [ 3, 1, 1, 1 ], [ 3, 2, 1, 1 ], [ 3, 2, 1, 2 ], [ 4, 1, 1, 1 ], [ 4, 2, 1, 1 ], [ 4, 2, 2, 1 ], [ 4, 3, 1, 1 ], [ 4, 4, 1, 1 ] ]; NumberSpaceGroups := function( dim ) if dim = 4 then return 4783; fi; if dim = 3 then return 219; fi; if dim = 2 then return 17; fi; end; SpaceGroup := function( dim, nr ) local type; if dim = 4 then type := cryst4params[nr]; return SpaceGroupBBNWZ( 4, type[1], type[2], type[3], type[4] ); elif dim = 3 then type := cryst3params[nr]; return SpaceGroupBBNWZ( 3, type[1], type[2], type[3], type[4] ); elif dim = 2 then type := cryst2params[nr]; return SpaceGroupBBNWZ( 2, type[1], type[2], type[3], type[4] ); else return fail; fi; end; PointGroupByNumber := function( dim, nr ) local type; if dim = 4 then type := cryst4params[nr]; return MatGroupZClass( 4, type[1], type[2], type[3] ); elif dim = 3 then type := cryst3params[nr]; return MatGroupZClass( 3, type[1], type[2], type[3] ); elif dim = 2 then type := cryst2params[nr]; return MatGroupZClass( 2, type[1], type[2], type[3] ); fi; end; SpaceGroupPcpGroup := function( dim, nr ) local G, iso, H, F, n; G := SpaceGroup( dim, nr ); iso := IsomorphismPcpGroup( G ); if IsBool( iso ) then return fail; fi; H := Image( iso ); n := Length( Igs(H) ); F := Subgroup( H, Igs(H){[n-dim+1..n]} ); SetFittingSubgroup( H, F ); return H; end; [0.157QuellennavigatorsProjekt 2026-06-05] |
2026-07-11