Results 241 to 250 of about 268,040 (278)
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2012
This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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This chapter is an introduction to algebraic number fields, which arose from both a generalization of the arithmetic in ℤ and the necessity to solve certain Diophantine equations. After recalling basic concepts from algebra and providing some polynomial irreducibility tools, the ring of integers \(\mathcal {O}_{\mathbb {K}}\) of an algebraic number ...
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1993
An algebraic number field F is a finite extension field of the rational numbers ℚ. It can be generated by a root p of a monic irreducible polynomial $$f(t) = {{t}^{n}} + {{a}_{1}}{{t}^{{n - 1}}} + {\text{ }} \ldots + {{a}_{n}}\epsilon \mathbb{Z}[t]$$ , (27) where n is also called the degree of F.
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An algebraic number field F is a finite extension field of the rational numbers ℚ. It can be generated by a root p of a monic irreducible polynomial $$f(t) = {{t}^{n}} + {{a}_{1}}{{t}^{{n - 1}}} + {\text{ }} \ldots + {{a}_{n}}\epsilon \mathbb{Z}[t]$$ , (27) where n is also called the degree of F.
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Factoring Polynomials over Algebraic Number Fields
SIAM Journal on Computing, 1985The author describes an algorithm for factoring polynomials over arbitrary number fields. This algorithm works as follows. Given a polynomial f, defined over a number field K. We take the norm N f of f to \({\mathbb{Q}}[X]\), and factor N f over \({\mathbb{Q}}\). If N f is square free we derive a factorization of f.
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Algebraic Numbers and Number Fields
1998A number α is called an algebraic number if it satisfies an equation of degree m of the form $${\alpha ^m} + {a_1}{\alpha ^{m - 1}} + {a_2}{\alpha ^{m - 2}} + \cdots + {a_m} = 0$$ where a 1, a 2,..., a m are rational numbers.
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1981
A system of complex numbers is called a number field (or, more briefly, a field) if it contains more than one number and if along with the numbers α and β it always contains α + β, α − β,αβ, and, if β ≠ 0, α/β.
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A system of complex numbers is called a number field (or, more briefly, a field) if it contains more than one number and if along with the numbers α and β it always contains α + β, α − β,αβ, and, if β ≠ 0, α/β.
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Cancer treatment and survivorship statistics, 2022
Ca-A Cancer Journal for Clinicians, 2022Kimberly D Miller +2 more
exaly
Management of glioblastoma: State of the art and future directions
Ca-A Cancer Journal for Clinicians, 2020Aaron Tan, David M Ashley, Giselle Lopez
exaly
High-entropy polymer produces a giant electrocaloric effect at low fields
Nature, 2021Xiao-Shi Qian, Donglin Han, Lirong Zheng
exaly