Computational Algebraic Number Theory

M.E. Pohst (Autor)

Buch | Softcover

X, 90 Seiten

1993 | 1993
Springer Basel (Verlag)
978-3-7643-2913-6 (ISBN)

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Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction - Topics from finite fields - Arithmetic and polynomials - Factorization of polynomials - Topics from the geometry of numbers - Hermite normal form - Lattices - Reduction - Enumeration of lattice points - Algebraic number fields - Introduction - Basic Arithmetic - Computation of an integral basis - Integral closure - Round-Two-Method - Round-Four-Method - Computation of the unit group - Dirichlet's unit theorem and a regulator bound - Two methods for computing r independent units - Fundamental unit computation - Computation of the class group - Ideals and class number - A method for computing the class group - Appendix - The number field sieve - KANT - References - Index

Intorduction.- Topics from finite field.- Topics from the geometry of number.- Algebraic number field.- Computation of an integral basis.- Computation of the unit group.- Computation of the class group.-
1 The number field sieve.-
2 KANT.- References.

Erscheint lt. Verlag	1.9.1993
Reihe/Serie	Oberwolfach Seminars
Zusatzinfo	X, 90 p. 1 illus.
Verlagsort	Basel
Sprache	englisch
Maße	170 x 244 mm
Gewicht	181 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Naturwissenschaften
	Sozialwissenschaften
Schlagworte	Algebra • coding theory • cryptography • finite field • Geometry • Hardcover, Softcover / Naturwissenschaften allgemein • HC/Naturwissenschaften allgemein • Informatik • Mathematics • Mathematik • Number Theory • Numerische Mathematik
ISBN-10	3-7643-2913-0 / 3764329130
ISBN-13	978-3-7643-2913-6 / 9783764329136
Zustand	Neuware