Search Results - polynomials in real AND complex fields: factorization

New resultant inequalities and complex polynomial factorization

Authors: Victor Y. Pan

Source: Lecture Notes in Computer Science ISBN: 3540555536

Subject Terms: computational complexity, parallel computing, polynomials, Analysis of algorithms and problem complexity, randomized algorithms, approximate factorization, 1. No poverty, Polynomials in real and complex fields: factorization, Parallel numerical computation, deterministic algorithm, 0102 computer and information sciences, 01 natural sciences, Complexity and performance of numerical algorithms, monic univariate polynomial, probabilistic estimates, polynomial factorization, 0103 physical sciences, zeros, Computational aspects of field theory and polynomials, complex field, resultant

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Access URL: https://dblp.uni-trier.de/db/conf/istcs/istcs1992.html#Pan92
https://locus.siam.org/doi/abs/10.1137/S0097539792235712
https://link.springer.com/chapter/10.1007/BFb0035172
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp23.html#Pan94
https://rd.springer.com/chapter/10.1007/BFb0035172
https://link.springer.com/content/pdf/10.1007%2FBFb0035172.pdf
https://epubs.siam.org/doi/abs/10.1137/S0097539792235712

Real Factorization of Multivariate Polynomials with Integer Coefficients: Real factorization of multivariate polynomials with integer coefficients

Authors: A. Galligo

Source: Journal of Mathematical Sciences. 108:934-941

Subject Terms: Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, Polynomials, factorization in commutative rings, 0102 computer and information sciences, primality test over \(\mathbb R\), 0101 mathematics, 01 natural sciences, probabilistic

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Access URL: https://link.springer.com/article/10.1023/A:1013580019355
https://link.springer.com/content/pdf/10.1023/A:1013580019355.pdf

Factorization over local fields and the irreducibility of generalized difference polynomials

Authors: Stephen D. Cohen Alain Salinier A. Movahhedi

Source: Mathematika. 47:173-196

Subject Terms: polynomials, factorization, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, 0101 mathematics, valued fields, Valued fields, 01 natural sciences

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Access URL: https://zbmath.org/1845526
https://doi.org/10.1112/s0025579300015801
http://www.journals.cambridge.org/abstract_S0025579300015801
https://www.cambridge.org/core/journals/mathematika/article/factorization-over-local-fields-and-the-irreducibility-of-generalized-difference-polynomials/8FAF486A18FF575F05918D35FBDF7FE7

The Factorization of Dickson Polynomials over Finite Fields: The factorization of Dickson polynomials over finite fields

Authors: Wun-Seng Chou

Source: Finite Fields and Their Applications. 3:84-96

Subject Terms: Algebra and Number Theory, factorization, Applied Mathematics, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, 0101 mathematics, Dickson polynomial, finite field, 01 natural sciences, Engineering(all), Polynomials over finite fields, Polynomials in number theory, Theoretical Computer Science

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Access URL: https://zbmath.org/1199989
https://doi.org/10.1006/ffta.1996.0169
https://www.sciencedirect.com/science/article/pii/S1071579796901690
https://core.ac.uk/display/81137755
https://www.sciencedirect.com/science/article/abs/pii/S1071579796901690

The field of Nash functions and factorization of polynomials

Authors: Stanisław Spodzieja

Source: Annales Polonici Mathematici. 65:81-94

Subject Terms: Nash functions, Field extensions, Holomorphic functions of several complex variables, holomorphic function, factorization of polynomials, Polynomials in real and complex fields: factorization, algebraic closure, 0101 mathematics, 01 natural sciences

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Access URL: https://www.impan.pl/shop/publication/transaction/download/product/109133?download.pdf
https://zbmath.org/988148
https://doi.org/10.4064/ap-65-1-81-94
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-apmv65z1p81bwm
https://www.impan.pl/get/doi/10.4064/ap-65-1-81-94

Number of zero point for a polynomial in real field

Authors: Liang Lin Yirong Liu

Source: Chinese Science Bulletin. 42:886-890

Subject Terms: polynomial, eliminant, Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, 01 natural sciences, number of real zeros, 0105 earth and related environmental sciences

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Access URL: http://ui.adsabs.harvard.edu/abs/1997ChSBu..42..886L/abstract
https://link.springer.com/article/10.1007/BF02882538

Factorization of the Non-Normal Hamiltonian of Reggeon Field Theory in Bargmann Space.

Authors: Intissar, Abdelkader¹ (AUTHOR) abdelkader.intissar@orange.fr

Source: Mathematics (2227-7390). Jan2025, Vol. 13 Issue 1, p31. 12p.

Subject Terms: *HARMONIC oscillators, *FACTORIZATION, *POLYNOMIALS

Sur l'irréductibilité d'une classe des polynômes. I

Authors: Györy, K.

Source: Publicationes Mathematicae Debrecen. 18:289-307

Subject Terms: Polynomials in real and complex fields: factorization, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Polynomials in number theory

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Access URL: https://zbmath.org/3396043
https://zbmath.org/3425732

On One Method for Factorization of Algebraic Polynomials: On one method for factorization of algebraic polynomials

Authors: B. M. Podlevs'kyi

Source: Ukrainian Mathematical Journal. 55:1472-1479

Subject Terms: algorithm, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), factorisation, 0103 physical sciences, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Numerical computation of solutions to single equations, multiple root, 0101 mathematics, 01 natural sciences, algebraic polynomial

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Access URL: https://zbmath.org/2210452
https://doi.org/10.1023/b:ukma.0000018008.76465.3e
https://link.springer.com/article/10.1023/B%3AUKMA.0000018008.76465.3e

Effective Fast Algorithms for Polynomial Spectral Factorization: Effective fast algorithms for polynomial spectral factorization

Authors: BINI, DARIO ANDREA G. FIORENTINO GEMIGNANI, LUCA et al.

Source: Numerical Algorithms. 34:217-227

Subject Terms: convergence, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), polynomial factorization, Graeffe method, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Laurent polynomial inversion, Numerical computation of solutions to single equations, spectral factorization, 0101 mathematics, numerical experiments, the Toeplitz matrix, 01 natural sciences

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Access URL: https://dblp.uni-trier.de/db/journals/na/na34.html#BiniFGM03
http://ui.adsabs.harvard.edu/abs/2003NuAlg..34..217B/abstract
https://doi.org/10.1023/B:NUMA.0000005364.00003.ea
https://link.springer.com/article/10.1023/B%3ANUMA.0000005364.00003.ea
https://arpi.unipi.it/handle/11568/187560
https://link.springer.com/content/pdf/10.1023/B:NUMA.0000005364.00003.ea.pdf
https://hdl.handle.net/11568/187560
https://doi.org/10.1023/B:NUMA.0000005364.00003.ea

Bivariate Factorizations via Galois Theory, with Application to Exceptional Polynomials: Bivariate factorizations via Galois theory, with application to exceptional polynomials

Authors: Michael E. Zieve

Source: Journal of Algebra. 210:670-689

Subject Terms: Algebra and Number Theory, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, exceptional polynomials

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Access URL: https://zbmath.org/1251415
https://doi.org/10.1006/jabr.1998.7581
https://core.ac.uk/display/20992929
http://www.math.lsa.umich.edu/~zieve/papers/biv.pdf
https://www.sciencedirect.com/science/article/pii/S0021869398975810
https://www.sciencedirect.com/science/article/abs/pii/S0021869398975810

Compositions of Polynomials with Coefficients in a Given Field: Compositions of polynomials with coefficients in a given field

Authors: Alan Horwitz

Source: Journal of Mathematical Analysis and Applications. 267:489-500

Subject Terms: polynomial, 39B12, Applied Mathematics, iterate, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, field, 01 natural sciences, composition, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, composition of polynomials, Analysis

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Access URL: http://arxiv.org/abs/math/9807027
https://www.sciencedirect.com/science/article/pii/S0022247X01977789
http://www.personal.psu.edu/faculty/a/l/alh4/real.pdf
https://core.ac.uk/display/82140738

Normal factorisation of polynomials and computational issues: Normal factorisation of polynomials and computational issues.

Authors: Karcanias, N. Mitrouli, M.

Source: Computers & Mathematics with Applications. 45:229-245

Subject Terms: numerical examples, Computational Mathematics, algorithm, Computational Theory and Mathematics, Modelling and Simulation, Factorisation, Greatest common divisor, Approximate computations, Polynomials in real and complex fields: factorization, Numerical computation of solutions to single equations, Polynomials, symbolic computation

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Access URL: https://zbmath.org/2017186
https://doi.org/10.1016/s0898-1221(03)80016-0
https://www.sciencedirect.com/science/article/pii/S0898122103800160
https://pergamos.lib.uoa.gr/uoa/dl/object/3065559

On the Malgrange condition for complex polynomials of two variables

Authors: Patrick J. Rabier

Source: manuscripta mathematica. 109:493-509

Subject Terms: asymptotic critical values, Jacobian conjecture, Germs of analytic sets, local parametrization, Malgrange condition, 0211 other engineering and technologies, Polynomials in real and complex fields: factorization, 02 engineering and technology, Jacobian problem, 0101 mathematics, 01 natural sciences, Fibrations, degenerations in algebraic geometry

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Access URL: https://link.springer.com/article/10.1007%2Fs00229-002-0322-8
https://link.springer.com/content/pdf/10.1007/s00229-002-0322-8.pdf
https://link.springer.com/10.1007/s00229-002-0322-8

Approximate factorization of multivariate polynomials and absolute irreducibility testing

Authors: Miroslav Kolár Mutsuko Sasaki Tateaki Sasaki et al.

Source: Japan Journal of Industrial and Applied Mathematics. 8:357-375

Subject Terms: Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, polynomials with approximate complex coefficients, factorization algorithm, absolute irreducibility of multivariate polynomials, Numerical approximation and computational geometry (primarily algorithms)

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Access URL: https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/102227/1/0746-07.pdf
https://zbmath.org/25373
https://doi.org/10.1007/bf03167142
http://ci.nii.ac.jp/naid/110006215192
https://link.springer.com/article/10.1007%2FBF03167142
https://repository.kulib.kyoto-u.ac.jp/dspace/handle/2433/102227
https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/102227/1/0746-07.pdf

Virtual roots of real polynomials

Authors: Gonzalez-Vega, Laureano Lombardi, Henri Mahé, Louis et al.

Contributors: Gonzalez-Vega, Laureano Lombardi, Henri Mahé, Louis et al.

Source: Journal of Pure and Applied Algebra. 124:147-166

Subject Terms: virtual root, Algebra and Number Theory, [MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC], Polynomials in real and complex fields: factorization, 14P05 (14Q05), Pierce-Birkhoff conjecture, spline, 01 natural sciences, [MATH.MATH-AC] Mathematics [math]/Commutative Algebra [math.AC], Mathematics - Algebraic Geometry, Spline approximation, Effectivity, complexity and computational aspects of algebraic geometry, semi-algebraic set, FOS: Mathematics, real root, real polynomial, 0101 mathematics, Semialgebraic sets and related spaces, Algebraic Geometry (math.AG)

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Access URL: http://arxiv.org/abs/1712.01952
https://zbmath.org/1121649
https://doi.org/10.1016/s0022-4049(96)00102-8
https://hal.archives-ouvertes.fr/hal-01656686
https://www.sciencedirect.com/science/article/pii/S0022404996001028
https://arxiv.org/pdf/1712.01952.pdf
https://arxiv.org/abs/1712.01952
http://ui.adsabs.harvard.edu/abs/2017arXiv171201952G/abstract

Factorization of polynomials using commuting matrices

Authors: Thomas J. Laffey Eleanor Meehan

Source: Linear Algebra and its Applications. 196:85-103

Subject Terms: Numerical Analysis, Algebra and Number Theory, factorization, factorization of polynomials, Polynomials in real and complex fields: factorization, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, monic polynomial, 01 natural sciences, Factorization of matrices, commuting matrices

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Access URL: https://core.ac.uk/display/82455463
https://www.sciencedirect.com/science/article/pii/0024379594903174
https://www.sciencedirect.com/science/article/abs/pii/0024379594903174

Factoring Rational Polynomials over the Complex Numbers: Factoring rational polynomials over the complex numbers

Authors: John Canny Joe Warren Chanderjit Bajaj et al.

Source: SIAM Journal on Computing. 22:318-331

Subject Terms: multivariate polynomial, Analysis of algorithms and problem complexity, deterministic NC algorithm, squarefree polynomial in two variables, Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, 0102 computer and information sciences, 0101 mathematics, algorithms, 01 natural sciences, irreducible factors

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Access URL: http://www.cs.rice.edu/~jwarren/papers/SJC.factor.pdf
https://zbmath.org/165028
https://doi.org/10.1137/0222024
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp22.html#BajajCGW93
https://doi.org/10.1137/0222024
https://epubs.siam.org/doi/abs/10.1137/0222024
https://dl.acm.org/doi/abs/10.1137/0222024
https://locus.siam.org/doi/abs/10.1137/0222024

Power roots of polynomials over arbitrary fields

Authors: ACCIARO, Vincenzo

Source: Bulletin of the Australian Mathematical Society. 50:327-335

Subject Terms: computable field, power roots of polynomials, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, polynomial in one variable, effective algorithm, 0101 mathematics, Hensel lifting, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Polynomials over finite fields, Polynomials in number theory

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E4AB00C4E97E9330DD1E48D545FF4EB4/S0004972700013782a.pdf/div-class-title-power-roots-of-polynomials-over-arbitrary-fields-div.pdf
http://www.journals.cambridge.org/abstract_S0004972700013782
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/E4AB00C4E97E9330DD1E48D545FF4EB4/S0004972700013782a.pdf/div-class-title-power-roots-of-polynomials-over-arbitrary-fields-div.pdf
https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/power-roots-of-polynomials-over-arbitrary-fields/E4AB00C4E97E9330DD1E48D545FF4EB4
https://hdl.handle.net/11564/154663

Factorization of polynomials over a finite field and the solution of systems of algebraic equations

Authors: D. Yu. Grigor'ev Grigoriev, Dima

Contributors: D. Yu. Grigor'ev Grigoriev, Dima

Source: Journal of Soviet Mathematics. 34:1762-1803

Subject Terms: polynomial complexity, algorithm, Analysis of algorithms and problem complexity, factorization of polynomials, Polynomials in real and complex fields: factorization, [MATH] Mathematics [math], 0102 computer and information sciences, Arithmetic problems in algebraic geometry, Diophantine geometry, 01 natural sciences, Varieties and morphisms, Polynomials over finite fields, variety, Equations in general fields, 0101 mathematics, irreducible components, Polynomials in general fields (irreducibility, etc.)

File Description: application/pdf; application/xml

Access URL: https://hal.science/hal-03053152v1
https://hal.archives-ouvertes.fr/hal-03053152/document
https://hal.archives-ouvertes.fr/hal-03053152
https://link.springer.com/article/10.1007/BF01095638