Algebraic number
Finding the ring of integers and its algorithms in algebraic number theory
... algorithmic algebraic number theory: given an algebraic number field K, determine its ring of integers ..."small" number fields K, such as number fields that are given ...
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Units in families of totally complex algebraic number fields
... of algebraic number fields F of degree less than or equal to 4, which have at least one real ...complex algebraic number fields, can be considered as a complement of ...
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Relative integral basis for algebraic number fields
... RELATIVE INTEGRAL BASIS FOR ALGEBRAIC NUMBER FIELDS MOHMOOD HAGHIGHI Department of Computer Science Bradley University Peoria, Illinois 61625 U.S.Ao Received January 23, 1985 and in revi[r] ...
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Contributions to algebraic number theory from India: From independence to late 90's
... We begin the report by listing the two major schools in the country where algebraic number theory has been pursued, and in each case list some of the mathematicians from these schools. Limitation of ...
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Codes from algebraic number fields
... The new codes are the analogues, for number fields, of the codes constructed by Goppa and Tsfasman [7, 12] from curves over fimte fields For the analogy between number fields and curves [r] ...
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On the Solvability of the Diophantine Equation $p^x+(p+8)^y=z^2$ when $p>3$ and $p+8$ are Primes
... The study of the solvability of diophantine equations is one of the classic problems in elementary number theory and algebraic number theory.. In recent years, the authors[r] ...
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Ring-LWE Cryptography for the Number Theorist
... Exciting number theory problems often arise from cryptographic appli- ...associated number theoretic ...in number theory; in particular, we investigate the spectral distortion of an algebraic ...
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Lattices with Symmetry
... Abstract. For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic ...
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Diophantine equations and identities
... Some new third and fifth degree combinatorial identities are derived from units in algebraic number fields... KEY WORDS AND PHRASES..[r] ...
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On some power series with algebraic coefficients and Liouville numbers
... complex number ξ and positive integers n, H, let α be an algebraic number with degree at most n and height at most H such that | ξ –α | takes the smallest positive value; Koksma defines ω ∗ n (H, ξ ) ...
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NOT require the Axiom of Choice; for each xA we have constructed an EXPLICIT left inverse to f. — On the other hand, if we had simply said that one should pick some
... an algebraic number α, there is a unique monic rational polynomial p(t) of least (pos- itive) degree such that p(α) = 0 (the existence of a polynomial of least degree follows from the well-ordering of the ...
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Uniform distribution of Hasse invariants
... GREENFIELD, Uniform Distribution in Subgroups of the Brauer Group of an Algebraic Number Field, Pacific J.[r] ...
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Algebraic conversions
... pure algebraic properties of computational type conversion leads to a new generalizations of the concept of a homomorphism for which the term conversion seems ...
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A NEW ALGORITHM TO CONSTRUCT S-BOXES WITH HIGH DIFFUSION
... In his paper Communication Theory of Secrecy Systems", Claude Shannon defines confusion and diffusion as two essential properties for block cipher design. S-Boxes to be used in this cryptographic algorithms require ...
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An Lower Estimate for the Number of Level Crossing of a Random Algebraic Curve when the Coefficients follow Semi-Stable Distribution
... the number of real zeros of the random algebraic equation∑ ( ) ...the number of real roots must ( ⁄ ) , except for a set of measure at most ...
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Some Normal Intuitionistic Fuzzy Heronian Mean
... the Algebraic and Einstein operation, can widely provide a large number of arithmetical operation with respect to uncertainty information, and Heronian mean can deal with correlations of the input arguments ...
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Squares of Random Linear Codes
... The rest of the paper is organized as follows. Section 3 is devoted to proving Proposition 2.4 and Theorem 2.5. Section 4 states the results that we need on quadratic forms, namely the number of forms of a given ...
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Common Errors in Algebraic Expressions: A Quantitative-Qualitative Analysis
... performing algebraic expressions, students may demonstrate errors that are individual ...simplifying algebraic expressions and concluded that all errors are the results of interference from new learning; ...
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ASYMPTOTIC ESTIMATES OF LEVEL CROSSINGS OF A RANDOM ALGEBRAIC POLYNOMIAL
... the mathematical interest , as reported in Edelman and Kostlan [2 ,page 11] these polynomials have some relationship with physics [1]. We prove the following theorems. Theorem 1 was known to Edelman and Kostlan , however ...
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Existence and uniqueness of algebraic function approximations
... It was shown that by defining a "surplus" for the algebraic form and a "deficiency" for the algebraic function, a unique algebraic form could be defined, and a unique branch of the algeb[r] ...
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