Chen, Rizeng; Li, Haokun; Xia, Bican; Zhao, Tianqi; Zheng, Tao Isolating all the real roots of a mixed trigonometric-polynomial. (English) Zbl 07740058 J. Symb. Comput. 121, Article ID 102250, 33 p. (2024). MSC: 26Dxx 68Wxx 65Hxx PDFBibTeX XMLCite \textit{R. Chen} et al., J. Symb. Comput. 121, Article ID 102250, 33 p. (2024; Zbl 07740058) Full Text: DOI arXiv
Perrucci, Daniel; Roy, Marie-Françoise A new general formula for the Cauchy index on an interval with subresultants. (English) Zbl 1471.12002 J. Symb. Comput. 109, 465-481 (2022). MSC: 12D10 13P15 14P10 26C15 PDFBibTeX XMLCite \textit{D. Perrucci} and \textit{M.-F. Roy}, J. Symb. Comput. 109, 465--481 (2022; Zbl 1471.12002) Full Text: DOI arXiv
Grigoriev, Dima; Radchenko, Danylo On a tropical version of the Jacobian conjecture. (English) Zbl 1471.14128 J. Symb. Comput. 109, 399-403 (2022). MSC: 14T20 14R15 26B40 PDFBibTeX XMLCite \textit{D. Grigoriev} and \textit{D. Radchenko}, J. Symb. Comput. 109, 399--403 (2022; Zbl 1471.14128) Full Text: DOI arXiv Link
Chen, Shiping; Liu, Zhong Automated proof of mixed trigonometric-polynomial inequalities. (English) Zbl 1444.68284 J. Symb. Comput. 101, 318-329 (2020). MSC: 68V15 26D05 PDFBibTeX XMLCite \textit{S. Chen} and \textit{Z. Liu}, J. Symb. Comput. 101, 318--329 (2020; Zbl 1444.68284) Full Text: DOI
Zeng, Xiaoning; Xiao, Shuijing Determining the limits of bivariate rational functions by Sturm’s theorem. (English) Zbl 1426.12001 J. Symb. Comput. 96, 1-21 (2020). MSC: 12D99 12J15 32B20 26C15 68W30 PDFBibTeX XMLCite \textit{X. Zeng} and \textit{S. Xiao}, J. Symb. Comput. 96, 1--21 (2020; Zbl 1426.12001) Full Text: DOI
Kaur, Yashpreet; Srinivasan, Varadharaj R. Integration in finite terms with dilogarithmic integrals, logarithmic integrals and error functions. (English) Zbl 1436.12007 J. Symb. Comput. 94, 210-233 (2019). MSC: 12H05 26A09 12-08 PDFBibTeX XMLCite \textit{Y. Kaur} and \textit{V. R. Srinivasan}, J. Symb. Comput. 94, 210--233 (2019; Zbl 1436.12007) Full Text: DOI
Herman, Aaron; Hong, Hoon; Tsigaridas, Elias Improving root separation bounds. (English) Zbl 1415.26005 J. Symb. Comput. 84, 25-56 (2018). MSC: 26C10 12D10 PDFBibTeX XMLCite \textit{A. Herman} et al., J. Symb. Comput. 84, 25--56 (2018; Zbl 1415.26005) Full Text: DOI HAL
Batra, Prashant; Mignotte, Maurice; Ştefănescu, Doru Improvements of Lagrange’s bound for polynomial roots. (English) Zbl 1358.65028 J. Symb. Comput. 82, 19-25 (2017). MSC: 65H04 26C10 65Y20 PDFBibTeX XMLCite \textit{P. Batra} et al., J. Symb. Comput. 82, 19--25 (2017; Zbl 1358.65028) Full Text: DOI
Herman, Aaron; Hong, Hoon Quality of positive root bounds. (English) Zbl 1332.12002 J. Symb. Comput. 74, 592-602 (2016). MSC: 12D10 26C10 65H04 PDFBibTeX XMLCite \textit{A. Herman} and \textit{H. Hong}, J. Symb. Comput. 74, 592--602 (2016; Zbl 1332.12002) Full Text: DOI
Collins, George E. Continued fraction real root isolation using the Hong root bound. (English) Zbl 1329.65094 J. Symb. Comput. 72, 21-54 (2016). MSC: 65H04 11A55 11Y65 12D10 26C10 30C15 65Y20 68W30 PDFBibTeX XMLCite \textit{G. E. Collins}, J. Symb. Comput. 72, 21--54 (2016; Zbl 1329.65094) Full Text: DOI
Sagraloff, Michael On the complexity of the Descartes method when using approximate arithmetic. (English) Zbl 1321.65080 J. Symb. Comput. 65, 79-110 (2014). MSC: 65H04 65H05 26C10 PDFBibTeX XMLCite \textit{M. Sagraloff}, J. Symb. Comput. 65, 79--110 (2014; Zbl 1321.65080) Full Text: DOI
Galligo, André Deformation of roots of polynomials via fractional derivatives. (English) Zbl 1261.65046 J. Symb. Comput. 52, 35-50 (2013). MSC: 65H04 65D07 26A33 12D10 65E05 30C15 65H20 68W30 PDFBibTeX XMLCite \textit{A. Galligo}, J. Symb. Comput. 52, 35--50 (2013; Zbl 1261.65046) Full Text: DOI
Cadavid, C.; Molina, S.; Vélez, J. D. Limits of quotients of bivariate real analytic functions. (English) Zbl 1263.68176 J. Symb. Comput. 50, 197-207 (2013). MSC: 68W30 26E05 26-04 PDFBibTeX XMLCite \textit{C. Cadavid} et al., J. Symb. Comput. 50, 197--207 (2013; Zbl 1263.68176) Full Text: DOI
Collins, George E.; Krandick, Werner On the computing time of the continued fractions method. (English) Zbl 1250.65066 J. Symb. Comput. 47, No. 11, 1372-1412 (2012). Reviewer: Costică Moroşanu (Iaşi) MSC: 65H04 11A55 11B39 65Y20 12D10 26C10 30C15 PDFBibTeX XMLCite \textit{G. E. Collins} and \textit{W. Krandick}, J. Symb. Comput. 47, No. 11, 1372--1412 (2012; Zbl 1250.65066) Full Text: DOI
Yu, Zhiheng; Yang, Lu; Zhang, Weinian Discussion on polynomials having polynomial iterative roots. (English) Zbl 1254.12002 J. Symb. Comput. 47, No. 10, 1154-1162 (2012). Reviewer: Piroska Lakatos (Debrecen) MSC: 12D10 26C10 39B12 68W30 PDFBibTeX XMLCite \textit{Z. Yu} et al., J. Symb. Comput. 47, No. 10, 1154--1162 (2012; Zbl 1254.12002) Full Text: DOI
Burr, Michael A.; Krahmer, Felix SqFreeEVAL: An (almost) optimal real-root isolation algorithm. (English) Zbl 1269.65046 J. Symb. Comput. 47, No. 2, 153-166 (2012). MSC: 65H04 26C10 65Y20 PDFBibTeX XMLCite \textit{M. A. Burr} and \textit{F. Krahmer}, J. Symb. Comput. 47, No. 2, 153--166 (2012; Zbl 1269.65046) Full Text: DOI
Mehlhorn, Kurt; Sagraloff, Michael A deterministic algorithm for isolating real roots of a real polynomial. (English) Zbl 1207.65048 J. Symb. Comput. 46, No. 1, 70-90 (2011). Reviewer: Temur Jangveladze (Tbilisi) MSC: 65H04 65Y20 26C10 PDFBibTeX XMLCite \textit{K. Mehlhorn} and \textit{M. Sagraloff}, J. Symb. Comput. 46, No. 1, 70--90 (2011; Zbl 1207.65048) Full Text: DOI
Batra, Prashant; Sharma, Vikram Bounds on absolute positiveness of multivariate polynomials. (English) Zbl 1198.26017 J. Symb. Comput. 45, No. 6, 617-628 (2010). Reviewer: Armin Rainer (Wien) MSC: 26C10 65H04 68W30 PDFBibTeX XMLCite \textit{P. Batra} and \textit{V. Sharma}, J. Symb. Comput. 45, No. 6, 617--628 (2010; Zbl 1198.26017) Full Text: DOI
Jeronimo, Gabriela; Perrucci, Daniel On the minimum of a positive polynomial over the standard simplex. (English) Zbl 1239.90086 J. Symb. Comput. 45, No. 4, 434-442 (2010). MSC: 90C26 13J30 14P10 26C99 PDFBibTeX XMLCite \textit{G. Jeronimo} and \textit{D. Perrucci}, J. Symb. Comput. 45, No. 4, 434--442 (2010; Zbl 1239.90086) Full Text: DOI arXiv Link
Fassino, Claudia Almost vanishing polynomials for sets of limited precision points. (English) Zbl 1203.13029 J. Symb. Comput. 45, No. 1, 19-37 (2010). Reviewer: Alyson Reeves (Bowie) MSC: 13P10 65H10 14Q99 26C10 PDFBibTeX XMLCite \textit{C. Fassino}, J. Symb. Comput. 45, No. 1, 19--37 (2010; Zbl 1203.13029) Full Text: DOI arXiv
Krandick, Werner; Mehlhorn, Kurt New bounds for the Descartes method. (English) Zbl 1158.12001 J. Symb. Comput. 41, No. 1, 49-66 (2006). MSC: 12D10 26C10 PDFBibTeX XMLCite \textit{W. Krandick} and \textit{K. Mehlhorn}, J. Symb. Comput. 41, No. 1, 49--66 (2006; Zbl 1158.12001) Full Text: DOI
Pan, Victor Y. Univariate polynomials: Nearly optimal algorithms for numerical factorization and root-finding. (English) Zbl 1004.65061 J. Symb. Comput. 33, No. 5, 701-733 (2002). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{V. Y. Pan}, J. Symb. Comput. 33, No. 5, 701--733 (2002; Zbl 1004.65061) Full Text: DOI
Fortune, Steven An iterated eigenvalue algorithm for approximating roots of univariate polynomials. (English) Zbl 1004.65060 J. Symb. Comput. 33, No. 5, 627-646 (2002). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 65F15 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{S. Fortune}, J. Symb. Comput. 33, No. 5, 627--646 (2002; Zbl 1004.65060) Full Text: DOI
D’Andrea, Carlos; Emiris, Ioannis Z. Hybrid sparse resultant matrices for bivariate polynomials. (English) Zbl 1021.65024 J. Symb. Comput. 33, No. 5, 587-608 (2002). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H10 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{C. D'Andrea} and \textit{I. Z. Emiris}, J. Symb. Comput. 33, No. 5, 587--608 (2002; Zbl 1021.65024) Full Text: DOI
Emiris, Ioannis Z.; Pan, Victor Y. Symbolic and numeric methods for exploiting structure in constructing resultant matrices. (English) Zbl 1017.65049 J. Symb. Comput. 33, No. 4, 393-413 (2002). Reviewer: Nikolai L.Vulchanov (Warszawa) MSC: 65H10 65F30 26C10 12Y05 30C15 68W30 68W40 PDFBibTeX XMLCite \textit{I. Z. Emiris} and \textit{V. Y. Pan}, J. Symb. Comput. 33, No. 4, 393--413 (2002; Zbl 1017.65049) Full Text: DOI
Collins, George E. Polynomial minimum root separation. (English) Zbl 1008.12001 J. Symb. Comput. 32, No. 5, 467-473 (2001). Reviewer: Maurice Mignotte (Strasbourg) MSC: 12D10 26C05 30C20 PDFBibTeX XMLCite \textit{G. E. Collins}, J. Symb. Comput. 32, No. 5, 467--473 (2001; Zbl 1008.12001) Full Text: DOI
Chionh, Eng-Wee Rectangular corner cutting and Dixon \({\mathcal A}\)-resultants. (English) Zbl 0987.65044 J. Symb. Comput. 31, No. 6, 651-669 (2001). Reviewer: B.Döring (Düsseldorf) MSC: 65H10 12Y05 26C10 30C15 68W30 PDFBibTeX XMLCite \textit{E.-W. Chionh}, J. Symb. Comput. 31, No. 6, 651--669 (2001; Zbl 0987.65044) Full Text: DOI
Wang, Dongming Computing triangular systems and regular systems. (English) Zbl 1007.65039 J. Symb. Comput. 30, No. 2, 221-236 (2000). Reviewer: Vilmar Trevisan (Porto Alegre) MSC: 65H10 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{D. Wang}, J. Symb. Comput. 30, No. 2, 221--236 (2000; Zbl 1007.65039) Full Text: DOI
Verschelde, Jan Toric Newton method for polynomial homotopies. (English) Zbl 0992.65048 J. Symb. Comput. 29, No. 4-5, 777-793 (2000). MSC: 65H10 12Y05 26C10 30C15 65H20 PDFBibTeX XMLCite \textit{J. Verschelde}, J. Symb. Comput. 29, No. 4--5, 777--793 (2000; Zbl 0992.65048) Full Text: DOI Link
Ronveaux, A.; Zarzo, A.; Area, I.; Godoy, E. Decomposition of polynomials with respect to the cyclic group of order \(m\). (English) Zbl 0947.65057 J. Symb. Comput. 28, No. 6, 755-765 (1999). Reviewer: J.Illán González (Vigo) MSC: 65H05 65D20 34A30 34A25 12Y05 26C10 PDFBibTeX XMLCite \textit{A. Ronveaux} et al., J. Symb. Comput. 28, No. 6, 755--765 (1999; Zbl 0947.65057)
Yang, Lu Recent advances on determining the number of real roots of parametric polynomials. (English) Zbl 0957.65041 J. Symb. Comput. 28, No. 1-2, 225-242 (1999). Reviewer: H.Kriete (Göttingen) MSC: 65H05 12Y05 26C10 PDFBibTeX XMLCite \textit{L. Yang}, J. Symb. Comput. 28, No. 1--2, 225--242 (1999; Zbl 0957.65041) Full Text: DOI
Rojas, J. Maurice Solving degenerate sparse polynomial systems faster. (English) Zbl 0943.65060 J. Symb. Comput. 28, No. 1-2, 155-186 (1999). Reviewer: Alyson Reeves (Bowie) MSC: 65H10 65Y20 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{J. M. Rojas}, J. Symb. Comput. 28, No. 1--2, 155--186 (1999; Zbl 0943.65060) Full Text: DOI arXiv
Tran, Quoc-Nam A symbolic-numerical method for finding a real solution of an arbitrary system of nonlinear algebraic equations. (English) Zbl 0921.65044 J. Symb. Comput. 26, No. 6, 739-760 (1998). Reviewer: E.L.Allgower (Fort Collins) MSC: 65H10 68W30 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{Q.-N. Tran}, J. Symb. Comput. 26, No. 6, 739--760 (1998; Zbl 0921.65044) Full Text: DOI
Beckermann, Bernhard; Labahn, George A fast and numerically stable Euclidean-like algorithm for detecting relatively prime numerical polynomials. (English) Zbl 0935.65051 J. Symb. Comput. 26, No. 6, 691-714 (1998). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 68W30 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{B. Beckermann} and \textit{G. Labahn}, J. Symb. Comput. 26, No. 6, 691--714 (1998; Zbl 0935.65051) Full Text: DOI Link
Hong, Hoon Bounds for absolute positiveness of multivariate polynomials. (English) Zbl 0913.65013 J. Symb. Comput. 25, No. 5, 571-585 (1998). Reviewer: J.Illán González (Vigo) MSC: 65D20 26C10 12Y05 68W30 PDFBibTeX XMLCite \textit{H. Hong}, J. Symb. Comput. 25, No. 5, 571--585 (1998; Zbl 0913.65013) Full Text: DOI Link
Salvy, Bruno; Shackell, John Symbolic asymptotics: Functions of two variables, implicit functions. (English) Zbl 0937.41015 J. Symb. Comput. 25, No. 3, 329-349 (1998). Reviewer: F.J.Wright (London) MSC: 41A60 68W30 12F20 26A12 PDFBibTeX XMLCite \textit{B. Salvy} and \textit{J. Shackell}, J. Symb. Comput. 25, No. 3, 329--349 (1998; Zbl 0937.41015) Full Text: DOI Link
Hribernig, V.; Stetter, H. J. Detection and validation of clusters of polynomial zeros. (English) Zbl 0910.65030 J. Symb. Comput. 24, No. 6, 667-681 (1997). MSC: 65H05 68W30 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{V. Hribernig} and \textit{H. J. Stetter}, J. Symb. Comput. 24, No. 6, 667--681 (1997; Zbl 0910.65030) Full Text: DOI
Beauzamy, Bernard Products of polynomials and a priori estimates for coefficients in polynomial decompositions: A sharp result. (English) Zbl 0757.30002 J. Symb. Comput. 13, No. 5, 463-472 (1992). Reviewer: Y.Avci (İstanbul) MSC: 30C10 12E05 26D05 PDFBibTeX XMLCite \textit{B. Beauzamy}, J. Symb. Comput. 13, No. 5, 463--472 (1992; Zbl 0757.30002) Full Text: DOI
Richardson, Daniel Computing the topology of a bounded non algebraic curve in the plane. (English) Zbl 0799.68124 J. Symb. Comput. 14, No. 6, 619-643 (1992). MSC: 68W30 26E05 12H20 PDFBibTeX XMLCite \textit{D. Richardson}, J. Symb. Comput. 14, No. 6, 619--643 (1992; Zbl 0799.68124) Full Text: DOI
Shackell, John Growth estimates for exp-log functions. (English) Zbl 0727.26002 J. Symb. Comput. 10, No. 6, 611-632 (1990). Reviewer: F.J.van der Linden (Eindhoven) MSC: 26A12 26-04 26A09 68W30 PDFBibTeX XMLCite \textit{J. Shackell}, J. Symb. Comput. 10, No. 6, 611--632 (1990; Zbl 0727.26002) Full Text: DOI
Cucker, F.; Roy, M.-F. A theorem on random polynomials and some consequences in average complexity. (English) Zbl 0725.12007 J. Symb. Comput. 10, No. 5, 405-409 (1990). Reviewer: F. J. van der Linden (Eindhoven) MSC: 12Y05 12D10 68W30 26C10 PDFBibTeX XMLCite \textit{F. Cucker} and \textit{M. F. Roy}, J. Symb. Comput. 10, No. 5, 405--409 (1990; Zbl 0725.12007) Full Text: DOI