The monodromy group of an algebraic function

Registro completo de metadados
MetadadosDescriçãoIdioma
Autor(es): dc.creatorRytin, Maxim-
Data de aceite: dc.date.accessioned2019-08-21T19:32:42Z-
Data de disponibilização: dc.date.available2019-08-21T19:32:42Z-
Data de envio: dc.date.issued2009-11-05-
Data de envio: dc.date.issued2009-
Data de envio: dc.date.issued2010-04-30-
Data de envio: dc.date.issued2010-04-30-
Data de envio: dc.date.issued2010-04-30-
Fonte completa do material: dc.identifierhttp://objetoseducacionais2.mec.gov.br/handle/mec/13747-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/capes/494305-
Descrição: dc.descriptionEducação Superior::Ciências Exatas e da Terra::Matemática-
Descrição: dc.descriptionThis Demonstration shows the structure of the branches of a multivalued function w(z) defined by a polynomial equation P(w,z)=0, illustrating the transitions between the branches along paths going around a branch point. The actual configuration may depend on the choice of the branch cuts, but the group generated by the branch cycles is always the same. In general this group is a normal subgroup of the Galois group of P(w,z) over Q. A number of important properties of w(z) can be inferred from the structure of the monodromy group: • P(w,z) is absolutely irreducible if and only if the group is transitive; • if P(w,z) is irreducible, w(z) can be expessed in radicals as a function of if and only if the group is solvable; • the genus of P(w,z) can be computed from the branch cycles using the Riemann–Hurwitz formula. If P(w,z) is irreducible and the genus is zero, the integral of w(z) can always be expressed in terms of w(z) and elementary functions. (The converse is not true: it is possible for w(z) to have an elementary antiderivative if the genus is greater than zero.)-
Idioma: dc.languageen-
Publicador: dc.publisherWolfram Demonstrations Project-
Relação: dc.relationTheMonodromyGroupOfAnAlgebraicFunction.nbp-
Direitos: dc.rightsDemonstration freeware using MathematicaPlayer-
???dc.source???: dc.sourcehttp://demonstrations.wolfram.com/TheMonodromyGroupOfAnAlgebraicFunction/-
Palavras-chave: dc.subjectTeoria de grupo-
Palavras-chave: dc.subjectEducação Superior::Ciências Exatas e da Terra::Matemática::Topologia Algébrica-
Título: dc.titleThe monodromy group of an algebraic function-
???dc.description2???: dc.description2Esta demonstração mostra uma estrutura de ramos deuma função w(z) que assume multivalores, definida por uma equação polinomial P(w,z)=0; ilustra algumas transições entre os ramos, ao longo de alguns pontos-
???dc.description3???: dc.description3This demonstration needs the "MathematicaPlayer.exe" to run. Find it in http://objetoseducacionais2.mec.gov.br/handle/mec/4737-
Aparece nas coleções:Repositório Institucional - MEC BIOE

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