Results 221 to 230 of about 373,144 (279)

Optimization by decoded quantum interferometry. [PDF]

open access: yesNature
Jordan SP   +8 more
europepmc   +1 more source

ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

Mathematics of the USSR-Sbornik, 1985
This paper contains a complete proof of the following theorem. Let \(\alpha\neq 0,1\) be algebraic, let \(\beta\) be algebraic of degree \(d\geq 2\), and let t be the transcendence degree over \({\mathbb{Q}}\) of the field generated by the numbers (*) \(\alpha^{\beta},...,\alpha^{\beta^{d- 1}}\).
openaire   +2 more sources

On Reconstruction of Algebraic Numbers

2000
Let L be a number field and \(\mathfrak{a}\) be an ideal of some order of L. Given an algebraic number α mod \(\mathfrak{a}\) and some bounds we show how to effectively reconstruct a number b if it exists such that b is smaller then the given bound and b ≡a mod \(\mathfrak{a}\).
Claus Fieker, Carsten Friedrichs
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Algebra and Algebraic Number Theory

1992
The 19th century was an age of deep qualitative transformations and, at the same time, of great discoveries in all areas of mathematics, including algebra. The transformation of algebra was fundamental in nature. Between the beginning and the end of the last century, or rather between the beginning of the last century and the twenties of this century ...
I. G. Bashmakova, A. N. Rudakov
openaire   +1 more source

Identification of algebraic numbers

Journal of Algorithms, 1982
We consider the following two questions: (1) If a and /3 are given algebraic numbers, suppose that approximations (Y’ of OL and j3’ of /3 are known, can we decide whether (Y = j3 or not? (2) If 5 is a complex number given by some limit process, suppose that some approximation I’ of 4 has been computed, can we guess that 6 is an algebraic number and ...
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Hall Numbers and the Composition Algebra of the Kronecker Algebra

Algebras and Representation Theory, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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