Determining the fundamental unit of a pure cubic field given any unit

Autor:	N. S. Jeans, M. D. Hendy
Rok vydání:	1978
Předmět:	Computational Mathematics Pure mathematics Algebra and Number Theory Integer Base unit (measurement) Applied Mathematics Mathematical analysis Process (computing) Field (mathematics) Cubic field Unit (ring theory) Real number Mathematics
Zdroj:	Mathematics of Computation. 32:925-935
ISSN:	1088-6842 0025-5718
DOI:	10.1090/s0025-5718-1978-0472761-3
Popis:	A number of algorithms which have been used to derive fundamental units for pure cubic fields suffer from the lack of absolute certainty that the units obtained are fundamental. We present here an algorithm which will correct this deficiency. Briefly, if η \eta is any nontrivial unit of a pure cubic field, then for some positive integer N , η 1 / N N, {\eta ^{1/N}} will be a fundamental unit. Our method determines which of the real numbers η 1 / N {\eta ^{1/N}} are integers of the field and, subsequently, will determine the coefficients of the fundamental unit. We illustrate the process with several numerical examples.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::6ecdbe749be76cc57c64caed60d2c894 https://doi.org/10.1090/s0025-5718-1978-0472761-3 Zobrazit plný text záznamu