See algebraic integer on Wiktionary
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"text": "A Gaussian integer z=a+ib is an algebraic integer since it is a solution of either the equation z²+(-2a)z+(a²+b²)=0 or the equation z-a=0."
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"ref": "1984, Alan Baker, A Concise Introduction to the Theory of Numbers, Cambridge University Press, page 62:",
"text": "An algebraic number is said to be an algebraic integer if the coefficient of the highest power of x in the minimal polynomial P is 1. The algebraic integers in an algebraic number field k form a ring R.",
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"text": "1989, Heinrich Rolletschek, Shortest Division Chains in Imaginary Quadratic Number Fields, Patrizia Gianni (editor), Symbolic and Algebraic Computation: International Symposium, Springer, LNCS 358, page 231,\nLet O_d be the set of algebraic integers in an imaginary quadratic number field Q [√],d<0, where d is the discriminant of O_d."
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"ref": "2010, Pierre Moussa, “Localisation of algebraic integers and polynomial iteration”, in Sergiy Kolyada, Yuri Nanin, Martin Möller, Pieter Moree, Thomas Ward, editors, Dynamical Numbers: Interplay Between Dynamical Systems and Number Theory, American Mathematical Society, page 83:",
"text": "We consider the problem of finding all algebraic integers which belong to a bounded subset of the complex plane together with their conjugates.",
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"(algebra, number theory) A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients."
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"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "algebraic number whose minimal polynomial has integer coefficients",
"word": "代數整數"
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"code": "cmn",
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"roman": "dàishù zhěngshù",
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"word": "αλγεβρικός ακέραιος"
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"sense": "algebraic number whose minimal polynomial has integer coefficients",
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"word": "algebraic integer"
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