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Editorial Advances in Computational Imaging: Theory, Algorithms
Editorial Advances in Computational Imaging: Theory, Algorithms

1. Write the equation in logarithmic form. 2. Evaluate the logarithm. 3
1. Write the equation in logarithmic form. 2. Evaluate the logarithm. 3

Zeros of Polynomial Functions
Zeros of Polynomial Functions

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ECE578-Class 6_GD_2010

Automorphism Groups
Automorphism Groups

... Now I have a contradiction, since this putative subgroup has order 4, which does not divide 10. It follows that there must be an element of order 5. On the other hand, could G contain only elements of order 5? Let a have order 5, and let b be an element of order 5 which is not in hai. Since |hai ∩ h ...
Data Structures
Data Structures

on the burnside problem on periodic groups
on the burnside problem on periodic groups

presentation source - Personal Home Pages (at UEL)
presentation source - Personal Home Pages (at UEL)

Nilpotent Jacobians in Dimension Three
Nilpotent Jacobians in Dimension Three

... In [1] Bass, Connell and Wright showed that it suffices to investigate the Jacobian Conjecture for polynomial maps of the form x + H with JH nilpotent (and H homogeneous of degree 3). Studying these maps led various authors to the following problem (see [4], [8], [9], [10]), where k is a field of ch ...
Interactive Formal Verification (L21) 1 Sums of Powers, Polynomials
Interactive Formal Verification (L21) 1 Sums of Powers, Polynomials

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Arithmetic Operations Revisited

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On the exact number of solutions of certain linearized equations

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04-Powers_Roots_and_Logarithms-

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Solve Exponential Equations Using Common Logs

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Endomorphisms The endomorphism ring of the abelian group Z/nZ

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Honors Algebra II Yearlong Mathematics Map

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APPROXIMATE SOLUTIONS OF SINGULAR DIFFERENTIAL

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Number Fields - American Mathematical Society

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8-1 Factors and Greatest Common Factors

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Number Theory

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... of F-valued functions on the c-regular vertices such that the neighbors of each of the d-regular vertices form a subcode word (with respect to a speci ed ordering of the neighbors). The following theorem is a simple consequence of the de nition of expansion [15]. Theorem 1 Let n;c;d be a (c; d)-regu ...
Sublinear Algorithms Course
Sublinear Algorithms Course

... or is it far from satisfying it? • sometimes it is the right question (probabilistically checkable proofs (PCPs)) • as good when the data is constantly changing (WWW) • fast sanity check to rule out inappropriate inputs (airport security questioning) ...
Algebraic Number Theory, a Computational Approach
Algebraic Number Theory, a Computational Approach

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Factorization of polynomials over finite fields

In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.The case of the factorization of univariate polynomials over a finite field, which is the subject of this article, is especially important, because all the algorithms (including the case of multivariate polynomials over the rational numbers), which are sufficiently efficient to be implemented, reduce the problem to this case (see Polynomial factorization). It is also interesting for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.
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