#### symmetry.tst1.4 KB Permalink History Raw

 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485 ``````% test symmetry package % implementation of theory of linear representations % for small groups availablegroups(); printgroup(D4); generators(D4); charactertable(D4); characternr(D4,1); characternr(D4,2); characternr(D4,3); characternr(D4,4); characternr(D4,5); irreduciblereptable(D4); irreduciblerepnr(D4,1); irreduciblerepnr(D4,2); irreduciblerepnr(D4,3); irreduciblerepnr(D4,4); irreduciblerepnr(D4,5); rr:=mat((1,0,0,0,0), (0,0,1,0,0), (0,0,0,1,0), (0,0,0,0,1), (0,1,0,0,0)); sp:=mat((1,0,0,0,0), (0,0,1,0,0), (0,1,0,0,0), (0,0,0,0,1), (0,0,0,1,0)); rep:={D4,rD4=rr,sD4=sp}; canonicaldecomposition(rep); character(rep); symmetrybasis(rep,1); symmetrybasis(rep,2); symmetrybasis(rep,3); symmetrybasis(rep,4); symmetrybasis(rep,5); symmetrybasispart(rep,5); allsymmetrybases(rep); % Ritz matrix from Stiefel, Faessler p. 200 m:=mat((eps,a,a,a,a), (a ,d,b,g,b), (a ,b,d,b,g), (a ,g,b,d,b), (a ,b,g,b,d)); diagonalize(m,rep); % eigenvalues are obvious. Eigenvectors may be obtained with % the coordinate transformation matrix given by allsymmetrybases. r1:=mat((0,1,0), (0,0,1), (1,0,0)); repC3:={C3,rC3=r1}; mC3:=mat((a,b,c), (c,a,b), (b,c,a)); diagonalize(mC3,repC3); % note difference between real and complex case on complex; diagonalize(mC3,repC3); off complex; end; ``````