Computational class field theory
نویسندگان
چکیده
Class field theory furnishes an intrinsic description of the abelian extensions of a number field which is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.
منابع مشابه
Applications of the Class Field Theory of Global Fields
Class field theory of global fields provides a description of finite abelian extensions of number fields and of function fields of transcendence degree 1 over finite fields. After a brief review of the handling of both function and number fields in Magma, we give a introduction to computational class field theory focusing on applications: We show how to construct tables of small degree extensio...
متن کاملar X iv : 0 80 2 . 38 43 v 2 [ m at h . N T ] 2 7 Fe b 20 08 COMPUTATIONAL CLASS FIELD THEORY
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.
متن کاملTopics in computational algebraic number theory par
We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the Pari/Gp system.
متن کاملTopics in Computational Algebraic Number Theory
We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the Pari/Gp system.
متن کاملar X iv : 0 80 2 . 38 43 v 1 [ m at h . N T ] 2 6 Fe b 20 08 COMPUTATIONAL CLASS FIELD THEORY
Class field theory furnishes an intrinsic description of the abelian extensions of a number field that is in many cases not of an immediate algorithmic nature. We outline the algorithms available for the explicit computation of such extensions.
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تاریخ انتشار 2008