Brandt, Alexander; Moreno Maza, Marc On the complexity and parallel implementation of Hensel’s lemma and Weierstrass preparation. (English) Zbl 1506.13001 Boulier, François (ed.) et al., Computer algebra in scientific computing. 23rd international workshop, CASC 2021, Sochi, Russia, September 13–17, 2021. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 12865, 78-99 (2021). Reviewer: Amir Hashemi (Isfahan) MSC: 13-04 13F25 68W30 PDFBibTeX XMLCite \textit{A. Brandt} and \textit{M. Moreno Maza}, Lect. Notes Comput. Sci. 12865, 78--99 (2021; Zbl 1506.13001) Full Text: DOI arXiv
Gutnik, S. A.; Sarychev, V. A. Symbolic-analytic methods for studying equilibrium orientations of a satellite on a circular orbit. (English. Russian original) Zbl 1476.70083 Program. Comput. Softw. 47, No. 2, 119-123 (2021); translation from Programmirovanie 47, No. 2, 28-33 (2021). MSC: 70M20 70G55 13P10 68W30 PDFBibTeX XMLCite \textit{S. A. Gutnik} and \textit{V. A. Sarychev}, Program. Comput. Softw. 47, No. 2, 119--123 (2021; Zbl 1476.70083); translation from Programmirovanie 47, No. 2, 28--33 (2021) Full Text: DOI
Nagasaka, Kosaku Toward the best algorithm for approximate GCD of univariate polynomials. (English) Zbl 1475.13050 J. Symb. Comput. 105, 4-27 (2021). MSC: 13P05 68W30 PDFBibTeX XMLCite \textit{K. Nagasaka}, J. Symb. Comput. 105, 4--27 (2021; Zbl 1475.13050) Full Text: DOI
Bourne, Martin; Winkler, Joab R.; Su, Yi The computation of the degree of the greatest common divisor of three Bernstein basis polynomials. (English) Zbl 1442.13090 J. Comput. Appl. Math. 373, Article ID 112373, 15 p. (2020). MSC: 13P15 33C45 65F99 65H14 PDFBibTeX XMLCite \textit{M. Bourne} et al., J. Comput. Appl. Math. 373, Article ID 112373, 15 p. (2020; Zbl 1442.13090) Full Text: DOI Link
Giesbrecht, Mark; Haraldson, Joseph; Kaltofen, Erich Computing approximate greatest common right divisors of differential polynomials. (English) Zbl 1522.13037 Found. Comput. Math. 20, No. 2, 331-366 (2020). Reviewer: Salah Najib (Khouribga) MSC: 13N10 12-08 13P05 49M15 65L99 PDFBibTeX XMLCite \textit{M. Giesbrecht} et al., Found. Comput. Math. 20, No. 2, 331--366 (2020; Zbl 1522.13037) Full Text: DOI arXiv
Lichtblau, Daniel Approximate polynomial GCD by approximate syzygies. (English) Zbl 1474.13053 Math. Comput. Sci. 13, No. 4, 517-532 (2019). MSC: 13P05 13P10 68W30 68W25 PDFBibTeX XMLCite \textit{D. Lichtblau}, Math. Comput. Sci. 13, No. 4, 517--532 (2019; Zbl 1474.13053) Full Text: DOI
Jia, Xiaohong; Shi, Xiaoran; Chen, Falai Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces. (English) Zbl 1388.13035 J. Comput. Appl. Math. 329, 2-23 (2018). Reviewer: Carlos Hermoso Ortíz (Madrid) MSC: 13D02 13P10 14Q05 14Q10 65D17 68U05 68U07 PDFBibTeX XMLCite \textit{X. Jia} et al., J. Comput. Appl. Math. 329, 2--23 (2018; Zbl 1388.13035) Full Text: DOI
Gutnik, S. A.; Sarychev, V. A. Application of computer algebra methods for investigation of stationary motions of a gyrostat satellite. (English. Russian original) Zbl 1455.70013 Program. Comput. Softw. 43, No. 2, 90-97 (2017); translation from Programmirovanie 43, No. 2, 35-44 (2017). MSC: 70M20 68W30 70-08 13P10 PDFBibTeX XMLCite \textit{S. A. Gutnik} and \textit{V. A. Sarychev}, Program. Comput. Softw. 43, No. 2, 90--97 (2017; Zbl 1455.70013); translation from Programmirovanie 43, No. 2, 35--44 (2017) Full Text: DOI
Wu, Wenyuan; Zeng, Zhonggang The numerical factorization of polynomials. (English) Zbl 1454.65031 Found. Comput. Math. 17, No. 1, 259-286 (2017). MSC: 65H04 12-08 13P05 65J20 65F22 PDFBibTeX XMLCite \textit{W. Wu} and \textit{Z. Zeng}, Found. Comput. Math. 17, No. 1, 259--286 (2017; Zbl 1454.65031) Full Text: DOI arXiv
Bourne, Martin; Winkler, Joab R.; Yi, Su The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials. (English) Zbl 1353.65014 Appl. Numer. Math. 111, 17-35 (2017). MSC: 13P15 33C45 65F99 PDFBibTeX XMLCite \textit{M. Bourne} et al., Appl. Numer. Math. 111, 17--35 (2017; Zbl 1353.65014) Full Text: DOI Link
Sendra, J. Rafael; Sendra, Juana Symbolic computation of Drazin inverses by specializations. (English) Zbl 1382.15007 J. Comput. Appl. Math. 301, 201-212 (2016). MSC: 15A09 68W30 13P10 30B10 30D30 PDFBibTeX XMLCite \textit{J. R. Sendra} and \textit{J. Sendra}, J. Comput. Appl. Math. 301, 201--212 (2016; Zbl 1382.15007) Full Text: DOI
Ruatta, Olivier; Sciabica, Mark; Szanto, Agnes Overdetermined Weierstrass iteration and the nearest consistent system. (English) Zbl 1310.65044 Theor. Comput. Sci. 562, 346-364 (2015). MSC: 65F20 13P15 PDFBibTeX XMLCite \textit{O. Ruatta} et al., Theor. Comput. Sci. 562, 346--364 (2015; Zbl 1310.65044) Full Text: DOI arXiv
Li, Zhe; Liu, Qi A heuristic verification of the degree of the approximate GCD of two univariate polynomials. (English) Zbl 1302.68333 Numer. Algorithms 67, No. 2, 319-334 (2014). MSC: 68W30 65H04 13P05 11A05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{Q. Liu}, Numer. Algorithms 67, No. 2, 319--334 (2014; Zbl 1302.68333) Full Text: DOI
Christou, D.; Karcanias, N.; Mitrouli, M. Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials. (English) Zbl 1293.12007 J. Comput. Appl. Math. 260, 54-67 (2014). MSC: 12Y05 13P05 65H99 68W30 PDFBibTeX XMLCite \textit{D. Christou} et al., J. Comput. Appl. Math. 260, 54--67 (2014; Zbl 1293.12007) Full Text: DOI
López, Hiram H.; Villarreal, Rafael H. Computing the degree of a lattice ideal of dimension one. (English) Zbl 1322.13009 J. Symb. Comput. 65, 15-28 (2014). MSC: 13F20 13D40 PDFBibTeX XMLCite \textit{H. H. López} and \textit{R. H. Villarreal}, J. Symb. Comput. 65, 15--28 (2014; Zbl 1322.13009) Full Text: DOI arXiv Link
Fassino, Claudia; Torrente, Maria-Laura Simple varieties for limited precision points. (English) Zbl 1291.65081 Theor. Comput. Sci. 479, 174-186 (2013). MSC: 65D99 68W30 13P15 26C10 PDFBibTeX XMLCite \textit{C. Fassino} and \textit{M.-L. Torrente}, Theor. Comput. Sci. 479, 174--186 (2013; Zbl 1291.65081) Full Text: DOI arXiv
Emiris, Ioannis Z.; Kalinka, Tatjana; Konaxis, Christos; Luu Ba Thang Implicitization of curves and (hyper)surfaces using predicted support. (English) Zbl 1297.68272 Theor. Comput. Sci. 479, 81-98 (2013). Reviewer: Georg Muntingh (Oslo) MSC: 68W30 13P15 14Q05 14Q10 PDFBibTeX XMLCite \textit{I. Z. Emiris} et al., Theor. Comput. Sci. 479, 81--98 (2013; Zbl 1297.68272) Full Text: DOI
Lichtblau, Daniel Approximate Gröbner bases, overdetermined polynomial systems, and approximate GCDs. (English) Zbl 1285.13036 ISRN Comput. Math. 2013, Article ID 352806, 12 p. (2013). Reviewer: Amir Hashemi (Isfahan) MSC: 13P10 65Y04 PDFBibTeX XMLCite \textit{D. Lichtblau}, ISRN Comput. Math. 2013, Article ID 352806, 12 p. (2013; Zbl 1285.13036) Full Text: DOI
Christou, Dimitrios; Karcanias, Nicos; Mitrouli, Marilena; Triantafyllou, Dimitrios Numerical and symbolical methods for the GCD of several polynomials. (English) Zbl 1255.65062 Van Dooren, Paul (ed.) et al., Numerical linear algebra in signals, systems and control. Selected papers based on the presentations at the international workshop, Kharagpur, India, January 9–11, 2007. In honor of Prof. Biswa Nath Datta. New York, NY: Springer (ISBN 978-94-007-0601-9/hbk; 978-94-007-0602-6/ebook). Lecture Notes in Electrical Engineering 80, 123-144 (2011). MSC: 65D20 12Y05 13P05 PDFBibTeX XMLCite \textit{D. Christou} et al., Lect. Notes Electr. Eng. 80, 123--144 (2011; Zbl 1255.65062) Full Text: DOI Link
Galligo, André; Poteaux, Adrien Computing monodromy via continuation methods on random Riemann surfaces. (English) Zbl 1208.14056 Theor. Comput. Sci. 412, No. 16, 1492-1507 (2011). MSC: 14Q05 68W30 13P05 65P99 PDFBibTeX XMLCite \textit{A. Galligo} and \textit{A. Poteaux}, Theor. Comput. Sci. 412, No. 16, 1492--1507 (2011; Zbl 1208.14056) Full Text: DOI Link
Kaltofen, Erich Exact certification in global polynomial optimization via rationalizing sums-of-squares. (English) Zbl 1191.13001 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 219-227 (2009). MSC: 13-02 13P99 12Y05 68W30 65F30 14P99 90C22 PDFBibTeX XMLCite \textit{E. Kaltofen}, in: Approximate commutative algebra. Berlin: Springer. 219--227 (2009; Zbl 1191.13001) Full Text: DOI
Zeng, Zhonggang Regularization and matrix computation in numerical polynomial algebra. (English) Zbl 1191.65036 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 125-162 (2009). MSC: 65F15 68W30 13P15 13P10 PDFBibTeX XMLCite \textit{Z. Zeng}, in: Approximate commutative algebra. Berlin: Springer. 125--162 (2009; Zbl 1191.65036) Full Text: DOI
Monagan, Michael; Vrbik, Paul Lazy and forgetful polynomial arithmetic and applications. (English) Zbl 1260.68483 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 11th international workshop, CASC 2009, Kobe, Japan, September 13–17, 2009. Proceedings. Berlin: Springer (ISBN 978-3-642-04102-0/pbk). Lecture Notes in Computer Science 5743, 226-239 (2009). MSC: 68W30 13P05 PDFBibTeX XMLCite \textit{M. Monagan} and \textit{P. Vrbik}, Lect. Notes Comput. Sci. 5743, 226--239 (2009; Zbl 1260.68483) Full Text: DOI
Corless, Robert M.; Gatermann, Karin; Kotsireas, Ilias S. Using symmetries in the eigenvalue method for polynomial systems. (English) Zbl 1174.14053 J. Symb. Comput. 44, No. 11, 1536-1550 (2009). Reviewer: Gerhard Pfister (Kaiserslautern) MSC: 14Q99 13P10 PDFBibTeX XMLCite \textit{R. M. Corless} et al., J. Symb. Comput. 44, No. 11, 1536--1550 (2009; Zbl 1174.14053) Full Text: DOI
Sekigawa, Hiroshi On real factors of real interval polynomials. (English) Zbl 1188.68369 J. Symb. Comput. 44, No. 7, 908-922 (2009). MSC: 68W30 13P05 11Y05 PDFBibTeX XMLCite \textit{H. Sekigawa}, J. Symb. Comput. 44, No. 7, 908--922 (2009; Zbl 1188.68369) Full Text: DOI
Pope, Scott R.; Szanto, Agnes Nearest multivariate system with given root multiplicities. (English) Zbl 1168.65347 J. Symb. Comput. 44, No. 6, 606-625 (2009). MSC: 65H10 13P15 68W30 PDFBibTeX XMLCite \textit{S. R. Pope} and \textit{A. Szanto}, J. Symb. Comput. 44, No. 6, 606--625 (2009; Zbl 1168.65347) Full Text: DOI
Busé, Laurent; Elkadi, Mohamed; Galligo, André A computational study of ruled surfaces. (English) Zbl 1222.14081 J. Symb. Comput. 44, No. 3, 232-241 (2009). MSC: 14J26 14Q10 13D02 PDFBibTeX XMLCite \textit{L. Busé} et al., J. Symb. Comput. 44, No. 3, 232--241 (2009; Zbl 1222.14081) Full Text: DOI Link
Shirayanagi, Kiyoshi; Sekigawa, Hiroshi A new Gröbner basis conversion method based on stabilization techniques. (English) Zbl 1181.68329 Theor. Comput. Sci. 409, No. 2, 311-317 (2008). MSC: 68W30 13P10 PDFBibTeX XMLCite \textit{K. Shirayanagi} and \textit{H. Sekigawa}, Theor. Comput. Sci. 409, No. 2, 311--317 (2008; Zbl 1181.68329) Full Text: DOI
Terui, Akira Recursive polynomial remainder sequence and its subresultants. (English) Zbl 1173.13028 J. Algebra 320, No. 2, 633-659 (2008). Reviewer: Salah Najib (Lille) MSC: 13P05 PDFBibTeX XMLCite \textit{A. Terui}, J. Algebra 320, No. 2, 633--659 (2008; Zbl 1173.13028) Full Text: DOI arXiv
Szanto, Agnes [Chardin, Marc] Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin). (English) Zbl 1132.13312 J. Symb. Comput. 43, No. 1, 46-74 (2008). MSC: 13P99 68W30 PDFBibTeX XMLCite \textit{A. Szanto}, J. Symb. Comput. 43, No. 1, 46--74 (2008; Zbl 1132.13312) Full Text: DOI
Notari, Roberto; Riccomagno, Eva; Rogantin, Maria-Piera Two polynomial representations of experimental design. (English) Zbl 1427.62088 J. Stat. Theory Pract. 1, No. 3-4, 329-346 (2007). MSC: 62K15 13P10 PDFBibTeX XMLCite \textit{R. Notari} et al., J. Stat. Theory Pract. 1, No. 3--4, 329--346 (2007; Zbl 1427.62088) Full Text: DOI arXiv
Beaumont, James C.; Bradford, Russell J.; Davenport, James H.; Phisanbut, Nalina Testing elementary function identities using CAD. (English) Zbl 1142.68618 Appl. Algebra Eng. Commun. Comput. 18, No. 6, 513-543 (2007). MSC: 68W30 13P99 PDFBibTeX XMLCite \textit{J. C. Beaumont} et al., Appl. Algebra Eng. Commun. Comput. 18, No. 6, 513--543 (2007; Zbl 1142.68618) Full Text: DOI
Chèze, Guillaume; Lecerf, Grégoire Lifting and recombination techniques for absolute factorization. (English) Zbl 1130.12007 J. Complexity 23, No. 3, 380-420 (2007). Reviewer: Michael Pohst (Berlin) MSC: 12Y05 68W30 11Y16 12D05 13P05 PDFBibTeX XMLCite \textit{G. Chèze} and \textit{G. Lecerf}, J. Complexity 23, No. 3, 380--420 (2007; Zbl 1130.12007) Full Text: DOI
Karcanias, N.; Fatouros, S.; Mitrouli, M.; Halikias, G. H. Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation. (English) Zbl 1134.65334 Comput. Math. Appl. 51, No. 12, 1817-1830 (2006). MSC: 65D20 12Y05 13P05 PDFBibTeX XMLCite \textit{N. Karcanias} et al., Comput. Math. Appl. 51, No. 12, 1817--1830 (2006; Zbl 1134.65334) Full Text: DOI
Chèze, Guillaume; Galligo, André From an approximate to an exact absolute polynomial factorization. (English) Zbl 1134.13022 J. Symb. Comput. 41, No. 6, 682-696 (2006). Reviewer: Salah Najib (Lille) MSC: 13P05 12D05 12E05 12Y05 68Q25 68W30 68W40 PDFBibTeX XMLCite \textit{G. Chèze} and \textit{A. Galligo}, J. Symb. Comput. 41, No. 6, 682--696 (2006; Zbl 1134.13022) Full Text: DOI
Khetan, Amit; D’Andrea, Carlos Implicitization of rational surfaces using toric varieties. (English) Zbl 1115.14028 J. Algebra 303, No. 2, 543-565 (2006). Reviewer: Josef Schicho (Linz) MSC: 14J10 14Q10 14M25 13D02 14J26 PDFBibTeX XMLCite \textit{A. Khetan} and \textit{C. D'Andrea}, J. Algebra 303, No. 2, 543--565 (2006; Zbl 1115.14028) Full Text: DOI arXiv
Rupprecht, David Semi-numerical absolute factorization of polynomials with integer coefficients. (English) Zbl 1137.13314 J. Symb. Comput. 37, No. 5, 557-574 (2004). MSC: 13P05 11Y16 PDFBibTeX XMLCite \textit{D. Rupprecht}, J. Symb. Comput. 37, No. 5, 557--574 (2004; Zbl 1137.13314) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Numerical factorization of multivariate complex polynomials. (English) Zbl 1147.13302 Theor. Comput. Sci. 315, No. 2-3, 651-669 (2004). MSC: 13P05 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., Theor. Comput. Sci. 315, No. 2--3, 651--669 (2004; Zbl 1147.13302) Full Text: DOI
Faugère, Jean-Charles; Hering, Milena; Phan, Jeff The membrane inclusions curvature equations. (English) Zbl 1065.92005 Adv. Appl. Math. 31, No. 4, 643-658 (2003). MSC: 92C05 13P10 92C40 PDFBibTeX XMLCite \textit{J.-C. Faugère} et al., Adv. Appl. Math. 31, No. 4, 643--658 (2003; Zbl 1065.92005) Full Text: DOI
Hoffman, J. William; Madden, James J.; Zhang, Hong Pseudozeros of multivariate polynomials. (English) Zbl 1017.65047 Math. Comput. 72, No. 242, 975-1002 (2003). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 14P10 13P05 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{J. W. Hoffman} et al., Math. Comput. 72, No. 242, 975--1002 (2003; Zbl 1017.65047) Full Text: DOI
Rystsova, A. Yu.; Rystsov, I. K. Construction of Gröbner bases for investigation of systems of polynomial equations. (English. Russian original) Zbl 0927.13025 Cybern. Syst. Anal. 33, No. 5, 718-723 (1997); translation from Kibern. Sist. Anal. 1997, No. 5, 134-141 (1997). Reviewer: A.Reeves (Bowie) MSC: 13P10 65H10 68W30 PDFBibTeX XMLCite \textit{A. Yu. Rystsova} and \textit{I. K. Rystsov}, Cybern. Syst. Anal. 33, No. 5, 718--723 (1997; Zbl 0927.13025); translation from Kibern. Sist. Anal. 1997, No. 5, 134--141 (1997) Full Text: DOI
Ioakimidis, N. I.; Anastasselou, E. G. Application of Gröbner bases to problems of movement of a particle. (English) Zbl 0823.70001 Comput. Math. Appl. 27, No. 3, 51-57 (1994). MSC: 70-08 70F05 13P10 68W30 PDFBibTeX XMLCite \textit{N. I. Ioakimidis} and \textit{E. G. Anastasselou}, Comput. Math. Appl. 27, No. 3, 51--57 (1994; Zbl 0823.70001) Full Text: DOI
Chiricota, Yves; Labelle, Gilbert Families of combinatorial solutions of \(y\prime = 1 + y^ 2\) and autonomous differential equations. (Familles de solutions combinatoires de \(y\prime = 1 + y^ 2\) et d’équations différentielles autonomes.) (French) Zbl 0767.34011 Discrete Math. 115, No. 1-3, 77-93 (1993). MSC: 34A99 05A15 05A19 13J05 PDFBibTeX XMLCite \textit{Y. Chiricota} and \textit{G. Labelle}, Discrete Math. 115, No. 1--3, 77--93 (1993; Zbl 0767.34011) Full Text: DOI