ACAC Seminar Abstract

ACAC Seminar Abstract

ACAC Seminars

ACAC Seminar Abstract

Quadratic Fields and Quadratic Forms

Speaker: Claus Fieker
Date, Time: Fri, 01 Feb 2008 15:00

The classical theory of binary quadratic forms goes back a long time: already Gauss had the notions of composition and reduction of quadratic forms and knew about cycles of reduced forms. Later a close link between quadratic forms and ideals in quadratic number fields was discovered, providing an explicit model suitable for machine computations. In more recent years an abundance of methods was developed to

  • allow efficient (fast) composition and reduction of forms
  • compute the structure of the finite abelian group of binary quadratic forms up to equivalence
In this talk I aim to explain the correspondence between forms and ideals and to indicate how the class groups of forms or ideals can be computed in sub-exponential time. The algorithms are due to Hafner and McCurley in the imaginary quadratic case and to Buchmann and Cohen, Diaz y Diaz, Oliver in the real case.
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