A Simple Test Qualifying the Accuracy of Horner'S Rule for Polynomials: A simple test qualifying the accuracy of Horner's rule for polynomials

Συγγραφείς: Boldo, Sylvie, Daumas, Marc

Συνεισφορές: Inria, Rapport De Recherche

Πηγή: Numerical Algorithms. 37:45-60

Θεματικοί όροι: evaluation of polynomials, Coq automatic proof checker, error bound, 0211 other engineering and technologies, HORNER'S RULE, 02 engineering and technology, 01 natural sciences, Software, source code, etc. for problems pertaining to field theory, formal proof, Maple, COQ, Computational aspects of field theory and polynomials, IEEE 754 STANDARD, 0101 mathematics, Roundoff error, Horner's rule, FLOATING POINT, [INFO.INFO-OH] Computer Science [cs]/Other [cs.OH], floating point arithmetic, Mechanization of proofs and logical operations, Computation of special functions and constants, construction of tables, IEEE 754 standard, Java, FORMAL PROOF, Theorem proving (deduction, resolution, etc.)

Περιγραφή αρχείου: application/xml; application/pdf

Σύνδεσμος πρόσβασης: https://hal.inria.fr/inria-00071879/file/RR-4707.pdf
https://zbmath.org/2202950
https://doi.org/10.1023/b:numa.0000049487.98618.61
https://inria.hal.science/inria-00071879v1
https://doi.org/10.1023/b:numa.0000049487.98618.61
https://inria.hal.science/inria-00071879v1/document
https://ui.adsabs.harvard.edu/abs/2004NuAlg..37...45B/abstract
https://dialnet.unirioja.es/servlet/articulo?codigo=1052227
https://hal.inria.fr/inria-00071879
https://hal.inria.fr/inria-00071879/document
https://dblp.uni-trier.de/db/journals/na/na37.html#BoldoD04
https://link.springer.com/article/10.1023/B:NUMA.0000049487.98618.61

Merit Factors of Polynomials Formed by Jacobi Symbols: Merit factors of polynomials formed by Jacobi symbols

Συγγραφείς: Peter Borwein, Kwok-Kwong Stephen Choi

Πηγή: Canadian Journal of Mathematics. 53:33-50

Θεματικοί όροι: class number, Turyn polynomials, twin primes, merit factor, 01 natural sciences, character polynomial, maximum modulus of polynomials on the unit circle, Littlewood polynomials, Software, source code, etc. for problems pertaining to field theory, Polynomials and rational functions of one complex variable, Special sequences and polynomials, 11. Sustainability, Jacobi symbols, \(-1\), 1 coefficients, 0101 mathematics, Fekete polynomials

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/1599818
https://doi.org/10.4153/cjm-2001-002-6
https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/merit-factors-of-polynomials-formed-by-jacobi-symbols/F37F5515F0E18CCB4CBC453E39B1795F
https://cms.math.ca/cjm/abstract/pdf/149301.pdf

New primitive $t$-nomials $(t = 3,5)$ over $GF(2)$ whose degree is a Mersenne exponent: New primitive \(t\)-nomials (\(t=3,5\)) over \(\text{GF}(2)\) whose degree is a Mersenne exponent

Συγγραφείς: Hannes Leeb, Yoshiharu Kurita, Toshihiro Kumada, Makoto Matsumoto

Πηγή: Mathematics of Computation. 69:811-815

Θεματικοί όροι: Software, source code, etc. for problems pertaining to field theory, Mersenne exponent, Software, source code, etc. for problems pertaining to number theory, 0102 computer and information sciences, primitive \(t\)-nomials, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Polynomials over finite fields

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/2000-69-230/S0025-5718-99-01168-0/S0025-5718-99-01168-0.pdf
https://ui.adsabs.harvard.edu/abs/2000MaCom..69..811K/abstract
https://www.ams.org/journals/mcom/2000-69-230/S0025-5718-99-01168-0/home.html
https://www.ams.org/mcom/2000-69-230/S0025-5718-99-01168-0/S0025-5718-99-01168-0.pdf
https://doi.org/10.1090/S0025-5718-99-01168-0
https://dblp.uni-trier.de/db/journals/moc/moc69.html#KumadaLKM00

Perturbing polynomials with all their roots on the unit circle

Συγγραφείς: Christopher Pinner, Jeffrey D. Vaaler, Michael J. Mossinghoff

Πηγή: Mathematics of Computation. 67:1707-1726

Θεματικοί όροι: Software, source code, etc. for problems pertaining to field theory, perturbations, transfinite diameter, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Mahler measure, Polynomials in real and complex fields: location of zeros (algebraic theorems), Lehmer's problem, 0101 mathematics, cyclotomic polynomials, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01007-2/S0025-5718-98-01007-2.pdf
https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01007-2/S0025-5718-98-01007-2.pdf
https://www.ams.org/journals/mcom/1998-67-224/S0025-5718-98-01007-2/home.html
https://doi.org/10.1090/S0025-5718-98-01007-2
https://dblp.uni-trier.de/db/journals/moc/moc67.html#MossinghoffPV98
https://www.jstor.org/stable/info/2584872
http://ui.adsabs.harvard.edu/abs/1998MaCom..67.1707M/abstract

A cluster-based cylindrical algebraic decomposition algorithm

Συγγραφείς: Dennis S. Arnon

Πηγή: Lecture Notes in Computer Science ISBN: 9783540159841

Θεματικοί όροι: clusters of cells, Computational Mathematics, Software, source code, etc. for problems pertaining to field theory, Algebra and Number Theory, Projective techniques in algebraic geometry, 0102 computer and information sciences, cylindrical algebraic decomposition, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Software, source code, etc. for problems pertaining to algebraic geometry

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4058864
https://doi.org/10.1016/s0747-7171(88)80012-9
https://link.springer.com/chapter/10.1007%2F3-540-15984-3_273
https://rd.springer.com/chapter/10.1007/3-540-15984-3_273
https://dl.acm.org/doi/10.1016/S0747-7171%2888%2980012-9
https://dblp.uni-trier.de/db/journals/jsc/jsc5.html#Arnon88
https://www.sciencedirect.com/science/article/pii/S0747717188800129
https://link.springer.com/content/pdf/10.1007%2F3-540-15984-3_273.pdf
https://dblp.uni-trier.de/db/conf/eurocal/eurocal1985-2.html#Arnon85
https://link.springer.com/chapter/10.1007/3-540-15984-3_273
https://link.springer.com/content/pdf/10.1007%2F3-540-15984-3_273.pdf

GCDHEU: Heuristic polynomial GCD algorithm based on integer GCD computation

Συγγραφείς: Gaston H. Gonnet, Bruce W. Char, Keith O. Geddes

Πηγή: Lecture Notes in Computer Science ISBN: 354013350X

Θεματικοί όροι: Computational Mathematics, Software, source code, etc. for problems pertaining to field theory, Algebra and Number Theory, heuristic methods, Polynomials in real and complex fields: factorization, height of a polynomial, 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, G.C.D. of multivariate polynomials, 01 natural sciences, Polynomials (irreducibility, etc.)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4112727
https://doi.org/10.1016/s0747-7171(89)80004-5
https://link.springer.com/chapter/10.1007%2FBFb0032851
https://dblp.uni-trier.de/db/conf/eurosam/eurosam1984.html#CharGG84
https://dblp.uni-trier.de/db/journals/jsc/jsc7.html#CharGG89
https://www.sciencedirect.com/science/article/abs/pii/S0747717189800045
https://link.springer.com/chapter/10.1007/BFb0032851
https://rd.springer.com/chapter/10.1007/BFb0032851
https://www.sciencedirect.com/science/article/pii/S0747717189800045

A logarithmic Boolean time algorithm for parallel polynomial division

Συγγραφείς: BINI, DARIO ANDREA, Pan V.

Πηγή: Lecture Notes in Computer Science ISBN: 9783540167662

Θεματικοί όροι: triangular Toeplitz matrix inversion, Analysis of algorithms and problem complexity, 4. Education, interpolation by binary segmentation, 0102 computer and information sciences, parallel computational complexity, Direct numerical methods for linear systems and matrix inversion, 01 natural sciences, Boolean circuit complexity, Software, source code, etc. for problems pertaining to field theory, division with remainder, 0101 mathematics, integer polynomials, polynomial division

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4066311
https://doi.org/10.1016/0020-0190(87)90139-6
http://www.sciencedirect.com/science/article/pii/0020019087901396
https://link.springer.com/chapter/10.1007%2F3-540-16766-8_22
https://www.sciencedirect.com/science/article/pii/0020019087901396
https://core.ac.uk/display/54857420
https://rd.springer.com/chapter/10.1007/3-540-16766-8_22
https://dblp.uni-trier.de/db/journals/ipl/ipl24.html#BiniP87
https://link.springer.com/chapter/10.1007%2F3-540-16766-8_22
https://link.springer.com/10.1007%2F3-540-16766-8_22
https://dblp.uni-trier.de/db/conf/awoc/awoc86.html#BiniP86
https://hdl.handle.net/11568/7967

Elementary and Liouvillian solutions of linear differential equations

Συγγραφείς: James H. Davenport, Michael F. Singer

Πηγή: Lecture Notes in Computer Science ISBN: 9783540159841

Θεματικοί όροι: Computational Mathematics, Abstract differential equations, Software, source code, etc. for problems pertaining to field theory, algorithm, Algebra and Number Theory, Explicit solutions, first integrals of ordinary differential equations, differential field, linear differential equation, 0101 mathematics, Differential algebra, Liouvillian solution, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4063225
https://doi.org/10.1016/s0747-7171(86)80026-8
https://link.springer.com/chapter/10.1007%2F3-540-15984-3_335
https://dblp.uni-trier.de/db/conf/eurocal/eurocal1985-2.html#SingerD85
https://rd.springer.com/chapter/10.1007/3-540-15984-3_335
http://www4.ncsu.edu/~singer/papers/singer_davenport.pdf
https://link.springer.com/content/pdf/10.1007%2F3-540-15984-3_335.pdf
https://dblp.uni-trier.de/db/journals/jsc/jsc2.html#Davenport86
https://www.sciencedirect.com/science/article/abs/pii/S0747717186800268
https://www.sciencedirect.com/science/article/pii/S0747717186800268
https://dl.acm.org/citation.cfm?id=7245
https://dl.acm.org/doi/10.1016/S0747-7171%2886%2980026-8

Effective Hilbert irreducibility

Συγγραφείς: Erich Kaltofen

Πηγή: Lecture Notes in Computer Science ISBN: 354013350X

Θεματικοί όροι: Software, source code, etc. for problems pertaining to commutative algebra, Software, source code, etc. for problems pertaining to field theory, polynomial factorization, Polynomials in real and complex fields: factorization, effective version of Hilbert irreducibility theorem, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Engineering(all), Polynomials (irreducibility, etc.), Polynomials over finite fields, probabilistic irreducibility criterion

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.sciencedirect.com/science/article/abs/pii/S0019995885800565
https://dblp.uni-trier.de/db/journals/iandc/iandc66.html#Kaltofen85
https://www.sciencedirect.com/science/article/pii/S0019995885800565
https://dblp.uni-trier.de/db/conf/eurosam/eurosam1984.html#Kaltofen84
https://link.springer.com/content/pdf/10.1007%2FBFb0032850.pdf
https://rd.springer.com/chapter/10.1007/BFb0032850
https://link.springer.com/chapter/10.1007%2FBFb0032850

An adjacency algorithm for cylindrical algebraic decompositions of three-dimensional space: An adjacency algorithm for cylindrical algebraic decompositions of three- dimensional space

Συγγραφείς: Dennis S. Arnon, George E. Collins, Scott McCallum

Πηγή: Lecture Notes in Computer Science ISBN: 9783540159841

Θεματικοί όροι: Computational Mathematics, Software, source code, etc. for problems pertaining to field theory, Algebra and Number Theory, Projective techniques in algebraic geometry, three-dimensional Euclidean space, 0102 computer and information sciences, cylindrical algebraic decomposition, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Software, source code, etc. for problems pertaining to algebraic geometry

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4058863
https://doi.org/10.1016/s0747-7171(88)80011-7
https://link.springer.com/chapter/10.1007/3-540-15984-3_272
https://dblp.uni-trier.de/db/conf/eurocal/eurocal1985-2.html#ArnonCM85
https://www.sciencedirect.com/science/article/pii/S0747717188800117
https://www.sciencedirect.com/science/article/abs/pii/S0747717188800117
https://doi.org/10.1016/S0747-7171(88)80011-7
https://rd.springer.com/chapter/10.1007/3-540-15984-3_272
https://link.springer.com/chapter/10.1007/3-540-15984-3_272
https://dblp.uni-trier.de/db/journals/jsc/jsc5.html#ArnonCM88

Factoring multivariate integral polynomials

Συγγραφείς: Arjen K. Lenstra

Πηγή: Lecture Notes in Computer Science ISBN: 3540123172

Θεματικοί όροι: Software, source code, etc. for problems pertaining to field theory, 0102 computer and information sciences, Factorization, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Theoretical Computer Science, Computer Science(all)

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://ir.cwi.nl/pub/2542/2542D.pdf
https://dblp.uni-trier.de/db/conf/icalp/icalp83.html#Lenstra83
https://link.springer.com/chapter/10.1007/BFb0036929
https://www.narcis.nl/publication/RecordID/oai:cwi.nl:2583
https://rd.springer.com/chapter/10.1007/BFb0036929
https://dblp.uni-trier.de/db/journals/tcs/tcs34.html#Lenstra84
https://www.narcis.nl/publication/RecordID/oai%3Acwi.nl%3A2542
https://core.ac.uk/display/86360714
https://infoscience.epfl.ch/record/149493
https://www.sciencedirect.com/science/article/pii/0304397584901178

Additive Complexity and Zeros of Real Polynomials: Additive complexity and zeros of real polynomials

Συγγραφείς: Jean-Jacques Risler

Πηγή: SIAM Journal on Computing. 14:178-183

Θεματικοί όροι: Software, source code, etc. for problems pertaining to commutative algebra, number of distinct real zeros, Software, source code, etc. for problems pertaining to field theory, Analysis of algorithms and problem complexity, additive complexity, Polynomials in real and complex fields: location of zeros (algebraic theorems), 0102 computer and information sciences, real polynomial, 0101 mathematics, 01 natural sciences, Polynomials over commutative rings

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3895183
https://doi.org/10.1137/0214014
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp14.html#Risler85
https://locus.siam.org/doi/abs/10.1137/0214014
https://doi.org/10.1137/0214014
https://epubs.siam.org/doi/abs/10.1137/0214014

The use of finite-segmentp-adic arithmetic for exact computation: The use of finite-segment p-adic arithmetic for exact computation

Συγγραφείς: Robert T. Gregory

Πηγή: BIT. 18:282-300

Θεματικοί όροι: Software, source code, etc. for problems pertaining to field theory, 0202 electrical engineering, electronic engineering, information engineering, Software, source code, etc. for problems pertaining to number theory, 02 engineering and technology, 0101 mathematics, Algorithms in computer science, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://link.springer.com/article/10.1007%2FBF01930898
https://link.springer.com/content/pdf/10.1007/BF01930898.pdf

Using an Efficient Sparse Minor Expansion Algorithm to Compute Polynomial Subresultants and the Greatest Common Denominator: Using an efficient sparse minor expansion algorithm to compute polynomial subresultants and the greatest common denominator

Συγγραφείς: Griss

Πηγή: IEEE Transactions on Computers. :945-950

Θεματικοί όροι: Sparse Matrices, Software, source code, etc. for problems pertaining to field theory, Polynomial Subresultants, Other matrix algorithms, Greatest Common Denominator, 0202 electrical engineering, electronic engineering, information engineering, Polynomials in real and complex fields: factorization, Sparse Polynomials, Efficient Sparse Minor Expansion Algorithm, 0102 computer and information sciences, 02 engineering and technology, Symbolic computation and algebraic computation, 01 natural sciences

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/3619310
https://doi.org/10.1109/tc.1978.1674974
https://www.computer.org/csdl/journal/tc/1978/10/01674974/13rRUxBa5ml
https://www.infona.pl/resource/bwmeta1.element.ieee-art-000001674974
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000001674974
https://dblp.uni-trier.de/db/journals/tc/tc27.html#Griss78

A characterization of the λ-invariant of a p-adic L-function: A characterization of the \(\lambda\) -invariant of a p-adic L-function

Συγγραφείς: Tauno Metsänkylä

Πηγή: Annales Fennici Mathematici; Vol. 12 No. 2 (1987): Volume 12, 1987; 335-338
Annales Fennici Mathematici; Vol 12 Nro 2 (1987): Volume 12, 1987; 335-338

Θεματικοί όροι: Software, source code, etc. for problems pertaining to field theory, p-adic L-function, Cyclotomic extensions, Zeta functions and \(L\)-functions, \(\lambda \)-invariant, numerical computation, power series representation, Iwasawa theory

Περιγραφή αρχείου: application/pdf; application/xml

Σύνδεσμος πρόσβασης: https://afm.journal.fi/article/view/134610
https://zbmath.org/4017032
https://doi.org/10.5186/aasfm.1987.1225
http://www.acadsci.fi/mathematica/Vol12/vol12pp335-338.pdf

Finite Field Arithmetic on an Array Processor: Finite field arithmetic on an array processor

Συγγραφείς: Redinbo

Πηγή: IEEE Transactions on Computers. :461-471

Θεματικοί όροι: modulo p arithmetic, finite field arithmetic, Finite fields and commutative rings (number-theoretic aspects), array processor, Numerical methods for trigonometric approximation and interpolation, sequence convolutions, 02 engineering and technology, algorithms, Software, source code, etc. for problems pertaining to information and communication theory, Software, source code, etc. for problems pertaining to field theory, fast Fourier transforms, polynomial multiplications, 0202 electrical engineering, electronic engineering, information engineering, signal processing computers, Theory of error-correcting codes and error-detecting codes

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1675390
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.ieee-000001675390
https://www.infona.pl/resource/bwmeta1.element.ieee-art-000001675390
http://ieeexplore.ieee.org/document/1675390/
https://dblp.uni-trier.de/db/journals/tc/tc28.html#Redinbo79

Splitting of quartic polynomials

Συγγραφείς: William W. Adams

Πηγή: Mathematics of Computation. 43:329-343

Θεματικοί όροι: roots, Separable extensions, Galois theory, Polynomials in real and complex fields: factorization, algorithms, 01 natural sciences, Polynomials over finite fields, Software, source code, etc. for problems pertaining to field theory, Galois groups, recurrence relation, Recurrences, splitting of polynomial over finite field, 0101 mathematics, ideal factorization of primes, integral quartic monic polynomial

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/1984-43-167/S0025-5718-1984-0744941-3/S0025-5718-1984-0744941-3.pdf
https://zbmath.org/3877317
https://doi.org/10.2307/2007416
https://www.ams.org/mcom/1984-43-167/S0025-5718-1984-0744941-3/S0025-5718-1984-0744941-3.pdf
https://www.ams.org/journals/mcom/1984-43-167/S0025-5718-1984-0744941-3/home.html

Computation of Class Numbers by an Analytic Method: Computation of class numbers by an analytic method

Συγγραφείς: Carsten Eckhardt

Πηγή: Journal of Symbolic Computation. 4:41-52

Θεματικοί όροι: Computational Mathematics, Software, source code, etc. for problems pertaining to field theory, Algebra and Number Theory, Dedekind zeta- function, regulator, computation of the class number, functional equation, 0101 mathematics, 01 natural sciences, Iwasawa theory

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://zbmath.org/4027608
https://doi.org/10.1016/s0747-7171(87)80052-4
https://www.sciencedirect.com/science/article/pii/S0747717187800524
https://www.sciencedirect.com/science/article/abs/pii/S0747717187800524

An Efficient One-Way Enciphering Algorithm: An efficient one-way enciphering algorithm

Συγγραφείς: C. Forney, F. S. Bader, H. D. Knoble

Πηγή: ACM Transactions on Mathematical Software. 5:97-107

Θεματικοί όροι: Password Verification, Analysis of algorithms and problem complexity, Arithmetic functions, related numbers, inversion formulas, Enciphering Algorithm, Keys, 02 engineering and technology, 01 natural sciences, Primes, Theory of operating systems, Polynomials over finite fields, Multiprecision Integer Arithmetic, Software, source code, etc. for problems pertaining to field theory, Information storage and retrieval of data, 0202 electrical engineering, electronic engineering, information engineering, Software, source code, etc. for problems pertaining to number theory, Evaluate Congruential Polynomials of Very High Degree, 0101 mathematics, Arithmetic theory of polynomial rings over finite fields, One-Way Security Transformation, Computer Security

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://dblp.uni-trier.de/db/journals/toms/toms5.html#KnobleFB79
https://dl.acm.org/doi/10.1145/355815.355822

Quadratic fields with 3-rank equal to 4

Συγγραφείς: Hugh C. Williams, Daniel Shanks, F. Diaz y Diaz

Πηγή: Mathematics of Computation. 33:836-840

Θεματικοί όροι: Quadratic extensions, 3-Rank, Software, source code, etc. for problems pertaining to field theory, Quadratic Field, Computation, 0101 mathematics, 01 natural sciences, Iwasawa theory

Περιγραφή αρχείου: application/xml

Σύνδεσμος πρόσβασης: https://www.ams.org/mcom/1979-33-146/S0025-5718-1979-0521299-4/S0025-5718-1979-0521299-4.pdf
https://www.ams.org/journals/mcom/1979-33-146/S0025-5718-1979-0521299-4/home.html
https://www.ams.org/mcom/1979-33-146/S0025-5718-1979-0521299-4/S0025-5718-1979-0521299-4.pdf
https://www.jstor.org/stable/2006320