| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/repndecomp/lib/ (GAP Algebra Version 4.15.1©) Datei vom 12.8.2025 mit Größe 1 kB |
|
Quelle unitary.gd Sprache: Shell |
|||||||||||||||||||||||||
|
#! @Chapter Algorithms for unitary representations #! @Section Unitarising representations #! @Description Unitarises the given representation quickly, #! summing over the group using a base and strong generating set #! and unitarising with <Ref Func="LDLDecomposition" />. #! <P/> #! @InsertChunk Example_UnitaryRepresentation #! <P/> #! @Arguments rho #! @Returns A record with fields basis_change and unitary_rep such that #! <A>rho</A> is isomorphic to unitary_rep, differing by a change of #! basis basis_change. Meaning if $L$ is basis_change and $\rho_u$ is the unitarised <A>rho</A>, #! then $\forall g \in G: \; L \rho_u(g) L^{-1} = \rho(g)$. DeclareGlobalFunction( "UnitaryRepresentation" ); #! @Description #! <P/> #! @InsertChunk Example_IsUnitaryRepresentation #! <P/> #! @Arguments rho #! @Returns Whether <A>rho</A> is unitary, i.e. for all $g \in G$, #! $\rho(g^{-1}) = \rho(g)^*$ (where $^*$ denotes the conjugate #! transpose). DeclareGlobalFunction( "IsUnitaryRepresentation" ); #! @Description #! <P/> #! @InsertChunk Example_LDLDecomposition #! <P/> #! @Arguments A #! @Returns a record with two fields, L and D such that $A = #! L\mbox{diag}(D)L^*$. $D$ is the $1 \times n$ vector which gives the #! diagonal matrix $\mbox{diag}(D)$ (where <A>A</A> is an $n \times n$ #! matrix). DeclareGlobalFunction( "LDLDecomposition" ); #! @Section Decomposing unitary representations #! @Arguments rho #! @Returns a list of irreps in the decomposition of <A>rho</A> #! @Description NOTE: this is not implemented yet. Assumes that #! <A>rho</A> is unitary and uses an algorithm due to Dixon to #! decompose it into unitary irreps. DeclareGlobalFunction( "IrreducibleDecompositionDixon" );
¤ Dauer der Verarbeitung: 0.3 Sekunden ¤*© Formatika GbR, Deutschland |
|
||||||||||||||||||||||||
2026-11-04