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Rational function decomposition [PDF]
Proceedings of the 1991 international symposium on Symbolic and algebraic computation, 1991 This paper presents a polynomial time algorithm for determining whether a given univariate rational function over an arbitrary field is the composition of two rational functions over that field, and finds them if so.
Richard Zippel, Zippel, Richard
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The neutrosophic integrals by partial fraction [PDF]
Neutrosophic Sets and Systems, 2022 The purpose of this article is to study the neutrosophic integrals by partial fraction, where the neutrosophic fraction function is defined, in addition, four cases of the neutrosophic proper rational function were discussed, also, integral of the ...
Yaser Ahmad Alhasan
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Shape preserving rational bi-cubic function
Egyptian Informatics Journal, 2012 The study is dedicated to the development of shape preserving interpolation scheme for monotone and convex data. A rational bi-cubic function with parameters is used for interpolation.
Malik Zawwar Hussain +2 more
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On the third moment of L(12,χd) I: The rational function field case
Journal of Number Theory, 2019 In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions ∑ d 0 − monic & sq .
A. Diaconu
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MATRICES OF RATIONAL FUNCTIONS [PDF]
Bulletin of the Australian Mathematical Society, 1974 The properties of the degree of a matrix of rational functions are obtained in a simplified way, which enables them to be generalised to matrices whose elements are not necessarily rational functions. On the basis of these results a theory of realisations is developed, which similarly generalises the theory of state space realisations of a matrix of ...
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The Imagery Models of Mathematics Teacher Candidates on Graph of Rational and Irrational Functions
Journal of Research and Advances in Mathematics Education, 2019 Mathematics teacher candidates are required to have both expertise and communication skills. Therefore, they should have a good imagery model. The present study is a descriptive qualitative research that involved the students of mathematics education ...
Darmadi Darmadi
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Resolution of Singularities by Rational Functions
SIAM Journal on Numerical Analysis, 2023 Results on the rational approximation of functions containing singularities are presented. We build further on the ''lightning method'', recently proposed by Trefethen and collaborators, based on exponentially clustering poles close to the singularities.
Herremans, Astrid +2 more
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Reconstructing rational functions with FireFly [PDF]
Computer Physics Communications, 2020 Abstract We present the open-source C++ library FireFly for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use FireFly in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic ...
Jonas Klappert, Fabian Lange
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Hilbert’s 17th problem in free skew fields
Forum of Mathematics, Sigma, 2020 This paper solves the rational noncommutative analogue of Hilbert’s 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of Hermitian matrices in its domain, then it is a sum of Hermitian squares of noncommutative ...
Jurij Volčič
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Simple Equational Specifications of Rational Arithmetic [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 We exhibit an initial specification of the rational numbers equipped with addition, subtraction, multiplication, greatest integer function, and absolute value. Our specification uses only the sort of rational numbers.
Lawrence S. Moss
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