Continued fractions and number-theoretic computations. (English) Zbl 0594.12003

Williams, Hugh C.

Rocky Mt. J. Math. 15, 621-655 (1985).

This mostly expository paper shows how to use certain continued fraction algorithms to carry out various calculations in the theory of real quadratic and complex cubic fields. Topics covered include reduced ideals and lattices, testing whether or not an ideal is principal, and factorization of integers.

Reviewer: L.Washington

MSC:

11R11	Quadratic extensions
11R16	Cubic and quartic extensions
11A55	Continued fractions
12-04	Software, source code, etc. for problems pertaining to field theory

Keywords:

computational number theory; real quadratic fields; complex cubic; fields; continued fraction; algorithm; complex cubic fields; factorization of integers