The R-transform as power map and its generalizations to higher degree: The \(R\)-transform as power map and its generalizations to higher degree

Authors: Alp Bassa, Ricardo Menares

Source: Finite Fields and Their Applications. 102:102546

Subject Terms: \(R\)-transform, Computational methods for problems pertaining to field theory, Mathematics - Number Theory, Mathematics - Rings and Algebras, 0102 computer and information sciences, 12Y05, 01 natural sciences, Polynomials over finite fields, Möbius transformations, Rings and Algebras (math.RA), iterative composition, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics

File Description: application/xml

Access URL: http://arxiv.org/abs/1909.02608
https://zbmath.org/7960815
https://doi.org/10.1016/j.ffa.2024.102546

Asymptotic distributions of the number of zeros of random polynomials in Hayes equivalence class over a finite field

Authors: Zhicheng Gao

Source: Finite Fields and Their Applications. 101:102524

Subject Terms: Computational methods for problems pertaining to field theory, Combinatorial probability, polynomial, prescribed coefficients, deep hole, Reed-Solomon code, Exponential sums, Arithmetic theory of polynomial rings over finite fields, ordinary words, Hayes equivalence, Polynomials over finite fields, Linear codes (general theory), distance distribution

File Description: application/xml

Access URL: https://zbmath.org/7960799
https://doi.org/10.1016/j.ffa.2024.102524

Discovering the Roots: Uniform Closure Results for Algebraic Classes Under Factoring: Discovering the roots: uniform closure results for algebraic classes under factoring

Authors: Pranjal Dutta, Nitin Saxena, Amit Sinhababu

Source: Journal of the ACM. 69:1-39

Subject Terms: FOS: Computer and information sciences, Computational methods for problems pertaining to field theory, Computer Science - Computational Complexity, F.1.1, I.1.2, F.1.3, G.1.5, Networks and circuits as models of computation, circuit complexity, Analysis of algorithms and problem complexity, Polynomials in real and complex fields: location of zeros (algebraic theorems), Computational Complexity (cs.CC), Symbolic computation and algebraic computation

File Description: application/xml

Access URL: https://dl.acm.org/doi/pdf/10.1145/3510359
http://arxiv.org/pdf/1710.03214
http://arxiv.org/abs/1710.03214
https://arxiv.org/abs/1710.03214
https://dl.acm.org/doi/pdf/10.1145/3188745.3188760
https://dblp.uni-trier.de/db/journals/corr/corr1710.html#abs-1710-03214

Squarefree Decomposition of Univariate Polynomials Depending on a Parameter. Application to the Integration of Parametric Rational Functions: Squarefree decomposition of univariate polynomials depending on a parameter. Application to the integration of parametric rational functions

Authors: Gema M. Diaz-Toca, Laureano Gonzalez-Vega

Source: Journal of Symbolic Computation. 32:191-209

Subject Terms: Computational methods for problems pertaining to field theory, Computational Mathematics, Algebra and Number Theory, squarefree decomposition, univariate polynomials, Polynomials in real and complex fields: factorization, Polynomials, factorization in commutative rings, 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Bezoutian

File Description: application/xml

Access URL: https://zbmath.org/1656468
https://doi.org/10.1006/jsco.2001.0471
https://www.sciencedirect.com/science/article/pii/S0747717101904717
https://dialnet.unirioja.es/servlet/articulo?codigo=734573
https://dblp.uni-trier.de/db/journals/jsc/jsc32.html#Diaz-TocaG01
https://www.sciencedirect.com/science/article/abs/pii/S0747717101904717
https://doi.org/10.1006/jsco.2001.0471
https://core.ac.uk/display/82496133

An elementary proof of Barnett's theorem about the greatest common divisor of several univarlate polynomials: An elementary proof of Barnett's theorem about the greatest common divisor of several univariate polynomials

Authors: Laureano Gonzalez-Vega

Source: Linear Algebra and its Applications. 247:185-202

Subject Terms: Computational methods for problems pertaining to field theory, Numerical Analysis, algorithm, Algebra and Number Theory, subresultants, greatest common divisor of univariate polynomials, computation of the coefficients, Determinants, permanents, traces, other special matrix functions, 01 natural sciences, Polynomials over commutative rings, Solving polynomial systems, resultants, Discrete Mathematics and Combinatorics, Geometry and Topology, 0101 mathematics, Polynomials in general fields (irreducibility, etc.), integral domain

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/0024379595000992
https://www.sciencedirect.com/science/article/pii/0024379595000992
https://core.ac.uk/display/82503169

Polynomial division with a remainder by means of evaluation and interpolation

Authors: Akimou Sadikou, Victor Y. Pan, Elliot Landowne

Source: Information Processing Letters. 44:149-153

Subject Terms: Computational methods for problems pertaining to field theory, evaluation and interpolation, algorithm, Algorithms for approximation of functions, parallel algorithm, Parallel numerical computation, 0102 computer and information sciences, 0101 mathematics, computational cost, 01 natural sciences, polynomial division

File Description: application/xml

Access URL: https://zbmath.org/148037
https://doi.org/10.1016/0020-0190(92)90055-z
https://dblp.uni-trier.de/db/journals/ipl/ipl44.html#PanSL92
https://www.sciencedirect.com/science/article/abs/pii/002001909290055Z
https://doi.org/10.1016/0020-0190(92)90055-Z

Denesting by Bounded Degree Radicals: Denesting by bounded degree radicals

Authors: Blömer, Johannes

Source: Lecture Notes in Computer Science ISBN: 9783540633976
Technical report / Departement Informatik, ETH Zürich, 273

Subject Terms: Data processing, computer science, Computational methods for problems pertaining to field theory, denesting, COMPUTER ALGEBRA + SYMBOLIC COMPUTATION, PROGRAMS AND ALGORITHMS FOR THE SOLUTION OF SPECIAL PROBLEMS, PROGRAMME UND ALGORITHMEN ZUR LÖSUNG SPEZIELLER PROBLEME, COMPUTERALGEBRA + SYMBOLISCHE BERECHNUNG, 0102 computer and information sciences, Parallel algorithms in computer science, 0101 mathematics, 01 natural sciences, Mathematics, Number-theoretic algorithms, complexity

File Description: application/xml; application/application/pdf

Access URL: https://www.research-collection.ethz.ch/bitstream/20.500.11850/69322/1/eth-4315-01.pdf
https://link.springer.com/chapter/10.1007/3-540-63397-9_5
https://www.research-collection.ethz.ch/bitstream/20.500.11850/69322/1/eth-4315-01.pdf
https://core.ac.uk/display/24355931
https://rd.springer.com/chapter/10.1007%2F3-540-63397-9_5
https://www.research-collection.ethz.ch/handle/20.500.11850/69322
https://dblp.uni-trier.de/db/conf/esa/esa97.html#Blomer97
https://link.springer.com/article/10.1007/s004530010028
https://dblp.uni-trier.de/db/journals/algorithmica/algorithmica28.html#Blomer00
http://e-collection.library.ethz.ch/eserv/eth:4315/eth-4315-01.pdf
http://hdl.handle.net/20.500.11850/69322

Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization: Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization

Authors: Erich Kaltofen

Source: SIAM Journal on Computing. 14:469-489

Subject Terms: Computational methods for problems pertaining to field theory, polynomial-time complexity, Hilbert irreducibility theorem, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, Symbolic computation and algebraic computation, integral polynomial, 01 natural sciences, Polynomials over finite fields, polynomial factorization, 0101 mathematics, algorithm analysis, Hensel lemma, multivariate polynomials, Polynomials (irreducibility, etc.), Number-theoretic algorithms, complexity

File Description: application/xml

Access URL: https://core.ac.uk/display/24518882
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp14.html#Kaltofen85
https://epubs.siam.org/doi/abs/10.1137/0214035

Evaluation of polynomials by computer

Authors: Knuth, Donald E.

Source: Communications of the ACM. 5:595-599

Subject Terms: Computational methods for problems pertaining to field theory, Symbolic computation and algebraic computation

File Description: application/xml

Access URL: https://zbmath.org/3173951
https://doi.org/10.1145/355580.369074
https://doi.acm.org/10.1145/355580.369074
http://authors.library.caltech.edu/72079/
https://doi.org/10.1145/355580.369074
https://dl.acm.org/doi/10.1145/355580.369074
https://core.ac.uk/display/77928080
https://dblp.uni-trier.de/db/journals/cacm/cacm5.html#Knuth62a

Comparative study of software for binary polynomial factorization

Authors: Poli, Alain, Rigoni, C.

Subject Terms: Computational methods for problems pertaining to field theory, Software, source code, etc. for problems pertaining to field theory, software, polynomial factorization, experimental results

File Description: application/xml

Access URL: https://zbmath.org/4006369

zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Authors: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Subject Terms: Computational methods for problems pertaining to field theory, Polynomials in real and complex fields: location of zeros (algebraic theorems), Real polynomials: location of zeros

File Description: application/xml

Access URL: https://zbmath.org/3626507

zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Authors: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Subject Terms: Computational methods for problems pertaining to field theory, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Numerical computation of solutions to single equations

File Description: application/xml

Access URL: https://zbmath.org/20779

Efficient factorization of polynomials over local fields

Authors: Chistov, A. L.

Subject Terms: Computational methods for problems pertaining to field theory, local field, polynomial time, Newton polygon, Symbolic computation and algebraic computation, algorithm for factorizing a multivariate polynomial, Polynomials

File Description: application/xml

Access URL: https://zbmath.org/4035950

Some results on computational complexity

Authors: Strassen, Volker

Subject Terms: Computational methods for problems pertaining to field theory, Factorization, Number-theoretic algorithms, complexity

File Description: application/xml

Access URL: https://zbmath.org/3562519