Results 21 to 30 of about 2,555,427 (286)
Polynomial decomposition algorithms
Journal of Symbolic Computation, 1985 \textit{M. Fried} and \textit{R. MacRae} [Math. Ann. 180, 220--226 (1969; Zbl 0185.28803)] proved the following theorem: Let \(f,g,p,q\) be univariate polynomials over an arbitrary field \(k\). Then \(p(x)-q(z)\) divides \(f(x)-g(z)\) if and only if there exists a polynomial \(F(t)\) over \(k\) such that \(f(t)=F(p(t))\) and \(g(t)=F(q(t)).\) The ...
David R. Barton, Richard Zippel
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The Extension of the GVW Algorithm to Valuation Domains
Complexity, 2021 The GVW algorithm is an effective algorithm to compute Gröbner bases for polynomial ideals over a field. Combined with properties of valuation domains and the idea of the GVW algorithm, we propose a new algorithm to compute Gröbner bases for polynomial ...
Dongmei Li, Licui Zheng
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Division algorithms for Bernstein polynomials [PDF]
Computer Aided Geometric Design, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Busé, Laurent, Goldman, Ron
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Journal of Mathematical Cryptology, 2022 We investigate the problem of recovering integer inputs (up to an affine scaling) when given only the integer monotonic polynomial outputs. Given nn integer outputs of a degree-dd integer monotonic polynomial whose coefficients and inputs are integers ...
Vivek Srinivas +2 more
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Polynomial decomposition algorithms
Journal of Symbolic Computation, 1989 A polynomial \(f\) over a commutative ring is said to be decomposable if it has a non-trivial functional decomposition \(f=g\circ h\). Previous algorithms to check decomposability were exponential-time in the worst case and only worked over fields of characteristic 0.
Dexter Kozen, Susan Landau 0001
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Algorithmic Computation of Polynomial Amoebas [PDF]
, 2016 We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation of~polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope ...
D. V. Bogdanov +2 more
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IET Control Theory & Applications, 2021 A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second‐order polynomial ...
O. A. Stepanov +4 more
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The Problem of Finding the Maximal Multiple Flow in the Divisible Network and its Special Cases
Моделирование и анализ информационных систем, 2015 In the article the problem of finding the maximal multiple flow in the network of any natural multiplicity k is studied. There are arcs of three types: ordinary arcs, multiple arcs and multi-arcs.
A. V. Smirnov
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Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems [PDF]
Quantum, 2023 Recently Chen and Gao \cite{ChenGao2017} proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems.
Jintai Ding +4 more
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A polynomial algorithm for packing unit squares in a hypograph of a piecewise linear function
Open Engineering, 2017 We consider the problem of packing the maximal number of unit squares in a hypograph of a function. A polynomial time algorithm is described to solve this problem for a piecewise linear function.
Arslanov Marat +2 more
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