PDF-2KEITHCONRAD2.IsometriesanddotproductsUsingtranslations,wecanreducethe
Author : conchita-marotz | Published Date : 2015-08-19
4KEITHCONRADGeometricallythee ectofthesematricesispicturedbelowOntheleftcossinsincosisacounterclockwiserotationbyanglearoundtheoriginOntherightcossinsincosisare ectionacrosstheline
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2KEITHCONRAD2.IsometriesanddotproductsUsingtranslations,wecanreducethe: Transcript
4KEITHCONRADGeometricallythee ectofthesematricesispicturedbelowOntheleftcossinsincosisacounterclockwiserotationbyanglearoundtheoriginOntherightcossinsincosisare ectionacrosstheline. 4KEITHCONRADProof.Letf(T)2OK[T]beEisensteinatsomeprimeideal.Iff(T)isreducibleinK[T]thenf(T)=g(T)h(T)forsomenonconstantg(T)andh(T)inK[T].We rstshowthatgandhcanbechoseninOK[T].Asfismonic,wecanassumegand discf Galoisgroup X3 X 1 23 S3X3 3X 1 81 A3X3 4X 1 229 S3X3 5X 1 473 S3X3 6X 1 837 S3Table1.SomeGaloisgroupsoverQIfacubicpolynomialhasGaloisgroupA3overQ,itsrootsallgeneratethesame eldextensionofQ,soa
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