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Books and Publications |
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1. |
Polynomial real root
isolation using Descartes' rule of signs. Proceedings of the 1976
ACM |
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2. |
Vincent's theorem and
Akritas' polynomial real root isolation algorithm. Proceedings of
the North Carolina Academy of Sciences. In: Journal of the Elisha
Mitchell Scientific Society, |
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3. |
A new method for polynomial real root isolation. Proceedings of the 16-th annual southeast regional ACM conference, Atlanta, Georgia, 39-43, April 1978. |
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4. |
A correction on a theorem by Uspensky. Bulletin of the Greek Mathematical Society. Vol. 19, 278-285, 1978. |
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5. |
On the forgotten theorem of Mr. Vincent. Historia Mathematica, Vol. 5, 427-435, 1978 (with S. D. Danielopoulos). |
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6. |
A short note on a new method for polynomial real root isolation. ACM-SIGSAM Bulletin, Vol. 12, No. 4, 12-13, 1978. |
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7. |
Vincent's theorem in algebraic manipulation. Ph.D. thesis, Operations Research Program, North Carolina State University, Raleigh, N.C., 1978. |
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8. |
On the solution of polynomial equations using continued fractions. Information Processing Letters, Vol. 9, No. 4, 182-184, 1979. |
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9. |
The two different ways of expressing the Budan-Fourier theorem and their consequences. Lectures of the General Mathematical Seminar of the University of Patras, Vol. 5, 127-146, 1979 (in Greek). |
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10. |
On the complexity of algorithms for the translation of polynomials. Computing, Vol. 24, 51-60, 1980 (with S. D. Danielopoulos). |
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11. |
The fastest exact algorithms for the isolation of the real roots of a polynomial equation. Computing, Vol. 24, 299-313, 1980. |
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12. |
A remark on the
proposed Syllabus for an AMS short course on Computer Algebra. ACM-SIGSAM
Bulletin, Vol. 14, No. 2, 24-25, 1980. |
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13. |
On the Budan-Fourier Controversy. Abstracts of papers presented to the American Mathematical Society, Vol. 1, No. 5, 443, August 1980. |
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14. |
An implementation of Vincent's Theorem. Numerische Mathematik, Vol. 36, 53-62, 1980. |
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15. |
The two different ways of expressing the Budan-Fourier theorem and their consequences. Mathematiki Epitheorisi, Vol. 18, 3-21, 1980 (in Greek). |
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16. |
An unknown theorem for the isolation of the roots of polynomials. Ganita-Bharati (Bulletin of the Indian Society for History of Mathematics), Vol. 2, 41-49, 1980 (with S. D. Danielopoulos). |
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17. |
On the Budan-Fourier Controversy. ACM-SIGSAM Bulletin, Vol. 15, No.1, 8-10, 1981. |
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18. |
Vincent's forgotten theorem, its extension and application. International Journal of Computers and Mathematics with Applications, Vol. 7, 309-317, 1981. |
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19. |
Exact algorithms for the implementation of Cauchy's rule. International Journal of Computer Mathematics, Vol. 9, 323-333, 1981. |
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20. |
Applications of
Vincent's theorem--approximating the real roots of a polynomial equation and
isolating the smallest. Proceedings of the 1982 Colloque AFCET, |
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21. |
Applications of Vincent's Theorem in cryptography, or, one-time pads made practical. Cryptologia, Vol. 6, No. 4, 312-318, 1982. |
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22. |
Reflections on a pair of theorems by Budan and Fourier. Mathematics Magazine, Vol. 55, No. 5, 292-298, 1982. |
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23. |
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24. |
Polynomial real root approximation using continued fractions. International Journal of Computer Mathematics, Vol. 14, 59-71, 1983 (with K. H. Ng). |
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25. |
Computationally efficient algorithms for a one-time pad scheme. International Journal of Computer and Information Sciences, Vol. 12, No. 4, 285-316, 1983 (with S. S. Iyengar and A. A. Rampuria). |
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26. |
Budan's theorem and its consequences. Sciences et Techniques en Perspective, Vol. 4, 1-13, 1984. |
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27. |
A converse rule of signs for polynomials. Computing, Vol. 34, 283-286, 1985 (with S. D. Danielopoulos). |
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28. |
There is no "Uspensky's method". Extended Abstract. Proceedings of the 1986 Symposium on Symbolic and Algebraic Computation, Waterloo, Ontario, Canada, 88-90. |
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29. |
A simple proof of the validity of the reduced prs algorithm. Computing, Vol. 38, 369-372, 1987. |
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30. |
A note on a paper by M. Mignotte. ACM-SIGSAM Bulletin, Vol. 21, No. 4, 23, 1987. |
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31. |
A new method for computing polynomial greatest common divisors and polynomial remainder sequences. Numerische Mathematik 52, 119-127, 1988. |
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32. |
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33. |
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34. |
The role of the Fibonacci
sequence in the isolation of the real roots of polynomial equations.
Proceedings of the 3rd International Conference on Fibonacci Numbers and
Their Applications, |
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35. |
Sylvester's form of the
resultant and the matrix-triangularization subresultant prs method.
Proceedings of the Conference on Computer Aided Proofs in Analysis, |
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36. |
The two classical
subresultant prs methods. Proceedings of the IV International
Conference on Computer Algebra in Physical Research, |
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37. |
Symbolic computation. Macmillan Encyclopedia of Computers, Vol. 2, 924-928, 1992. |
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38. |
Various proofs of Sylvester's (determinant) identity--(Extended Abstract). Proceedings of the International IMACS Symposium on Symbolic Computation--New Trends and Developments 228-230, Lille, France, 1993 (with E. K. Akritas and G. I. Malaschonok). Edited by G. Jacob, N. E. Oussous and S. Steinberg. |
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39. |
Sylvester's forgotten form of the resultant. The Fibonacci Quarterly, Vol. 31, 325-332, 1993. |
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40. |
Matrix computations of subresultant
polynomial remainder sequences in integral domains. With E.K. Akritas and
G.I. Malaschonok. Abstracts of the International Conference on Interval
and |
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41. |
Implementation of real
root isolation algorithms in Mathematica. With A. Bocharov
and A. Strzebonski. Abstracts of the International Conference on Interval and
Computer-Algebraic |
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42. |
Floating-Point
Arithmetic: Precision and Accuracy with Mathematica. A
notebook appearing in Mathematica World, April 1994. |
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43. |
Matrix computations of subresultant polynomial remainder sequences in integral domains. Reliable Computing Vol. 1, 375-381, 1995. (With E.K. Akritas and G.I. Malaschonok.) |
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44. |
Various proofs of Sylvester's (determinant) identity (full paper). Mathematics and Computers in Simulation Vol.42, 585-593, 1996 (with E. K. Akritas and G. I. Malaschonok). |
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45. |
The great ideas of Mathematics taught with the
aid of Mathematica (Extended Abstract). International Conference on
the Teaching of Mathematics, pp. 13-15, Samos, Greece, July 3-6, 1998. |
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46. |
Teaching great ideas
of Mathematics with Mathematica. Mathematica in Education and
Research Vol. 7, No. 4, 5-14, 1998. (With Zamir Bavel.) |
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47. |
Classical Mathematics with Mathematica. Vestnik of the University of Tambov, Science Series, Vol. 4, No. 4, 437-451, 1999. (With Zamir Bavel.) |
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48. |
Calculus and the Race Track principle. Abstract. Vestnik of the University of Tambov, Science Series, Vol. 4, No. 4, 436, 1999. |
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49. |
Calculus and Mathematica in Greece. Abstract. Mathematics and New Technologies, p. 3, Aristotle University of Thessaloniki, Greece, June 18-20, 1999. |
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50. |
Teaching Linear Algebra with SVD Analysis.
Abstract. 6th IMACS International Conference on Applications
of Computer Algebra, p. 110, Steklov Institute of Mathematics, St.
Petersburg, Russia, |
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51. |
Fast Matrix Computation of
Subresultant Polynomial Remainder Sequences. Third Workshop on
Computer Algebra in Scientific Computing, CASC 2000, pp. 1-11, Samarkand,
Uzbekistan, |
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52. |
Using Mathematica to illustrate the Race Track Principle in Calculus. Mathematica in Education and Research Vol. 9, No. 2, 87-92, 2000. (With Zamir Bavel.) |
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53. |
Applications of Singular Value Decomposition (SVD). Abstracts of the 8th International Conference on Applications of Computer Algebra, ACA 2002, p. 39, Volos Greece, June 25-28, 2002. (With G. I. Malaschonok.) University of Thessaly Press, Volos, 2002. Edited by: A.G. Akritas and I.S. Kotsireas. |
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54. |
Computations in Modules over Commutative Rings. Abstracts of the 8th International Conference on Applications of Computer Algebra, ACA 2002, pp. 127-128, Volos Greece, June 25-28, 2002. (With G. I. Malaschonok.) University of Thessaly Press, Volos, 2002. Edited by: A.G. Akritas and I.S. Kotsireas. |
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55. |
Effective Real Root Isolation Using Continued Fractions. Abstracts of the 8th International Conference on Applications of Computer Algebra, ACA 2002, pp. 137-138, Volos Greece, June 25-28, 2002. (With A. Strzebonski.) University of Thessaly Press, Volos, 2002. Edited by: A.G. Akritas and I.S. Kotsireas. |
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56. |
Applications of Singular Value Decomposition (SVD). Mathematics and Computers in Simulation, Vol. 67, 15-31, 2004. (With G.I. Malaschonok) Special Issue: Applications of Computer Algebra in Science, Engineering, Simulation and Special Software). |
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57. |
Computations in Modules over Commutative Domains. (With G.I. Malaschonok). Proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, pp. 11 -- 23, Bonn, Germany, September 16-20, 2007. LNCS 4770, Springer Verlag, Berlin. Edited by V. G. Ganzha, E. W. Mayr and E. V. Vorozhtsov. |
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58. |
A Comparative Study of Two Real Root Isolation Methods (With Adam W. Strzebonski.) Nonlinear Analysis: Modelling and Control, Vol. 10, No. 4, 297-304, 2005. |
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59. |
Movements of Slavophones (1912-1930) - The War of Statistics. Book review in Greek, Social Sciences Tribune (To Vima), Vol. 40, 215-218, 2004. |
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60. |
An Introduction to Wavelet Transforms and Data
Compression Using Mathematica manuscript. |
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61. |
On Some Applications of the (Fast) Discrete Fourier Transform. (With Jerry Uhl and P. Vigklas). The Mathematica Journal, Vol. 11, No. 1, 32-48, 2008 |
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62. |
On Some Applications of the (Fast) Discrete Fourier Transform. (With Jerry Uhl and P. Vigklas) . Abstracts of the 11th International Conference on Applications of Computer Algebra, ACA 2005, p. 38, Nara, Japan, July 31- August 3, 2005 |
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63. |
Computation of the Adjoint Matrix (With G.I. Malaschonok) Proceedings of the 6th International Conference on Computational Science (ICCS 2006), Reading, UK, May 28-31, 2006, Part II, Editors: Vassil N. Alexandrov, Geert Dick van Albada, Peter M.A. Sloot, Jack Dongarra, Lecture Notes in Computer Science (LNCS), Springer Verlag Berlin / Heidelberg, Vol. 3992, pp. 486 - 489, 2006. |
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64. |
The SVD-Fundamental Theorem of Linear Algebra. (With G.I. Malaschonok and P.S. Vigklas) Nonlinear Analysis: Modelling and Control, Vol. 11, No. 2, 123-136, 2006. |
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65. |
Solving the Heat and Wave Equations with the (Fast) Discrete Fourier Transform. (With Jerry Uhl and P. S. Vigklas). International Seminar on Symbolic Computation in Education, Beijing, China, April 12-14, 2006. See pp. 230--245 in: Symbolic Computation and Education, World Scientific, Beijing, 2007. Edited by Shangzhi Li, Dongming Wang, and Zing-Zhong Zhang. |
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66. |
Nikola Obreschkoff's Contribution to the Problem of Isolating Real Roots Using Continued Fractions Presentation devoted to the 110 th anniversary of the Bulgarian mathematician Nikola Obreschkoff. Abstracts of the 12th International Conference on Applications of Computer Algebra, ACA 2006, pp. 5, Varna, Bulgaria, June 26-29, 2006. (With P. S. Vigklas.) Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Varna, 2006. Edited by: Vladimir Gerdt, Margarita Spiridonova and Maria Nisheva-Pavlova. |
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67. |
A Comparison of Various Methods for Computing Bounds for positive Roots of Polynomials. (With P. S. Vigklas) Abstracts of the 12th International Conference on Applications of Computer Algebra, ACA 2006, pp. 32, Varna, Bulgaria, June 26-29, 2006. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Varna, 2006. Edited by: Vladimir Gerdt, Margarita Spiridonova and Maria Nisheva-Pavlova. |
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68. |
A Comparison of Various Methods for Computing Bounds for Positive Roots of Polynomials. (With P. S. Vigklas). Journal of Universal Computer Science, Vol. 13, No. 4, 455-467, 2007. |
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69. |
Implementations of a New Theorem for Computing Bounds for Positive Roots of Polynomials. (With A. W. Strzebonski and P. S. Vigklas). Computing, Vol. 78,355-367, 2006 |
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70. |
Advances on the Continued Fractions Method Using Better Estimations of Positive Root Bounds. (With A. W. Strzebonski and P. S. Vigklas). Proceedings of the 10th International Workshop on Computer Algebra in Scientific Computing, CASC 2007, pp. 24 -- 30, Bonn, Germany, September 16-20, 2007. LNCS 4770, Springer Verlag, Berlin. Edited by V. G. Ganzha, E. W. Mayr and E. V. Vorozhtsov. |
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71. |
There is no Descartes' method. In M.J.Wester and M. Beaudin (Eds), Computer Algebra in Education, AullonaPress, USA, 19--35, 2008. |
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72. |
On the Various Bisection Methods Derived from Vincent's Theorem. (With A. W. Strzebonski and P. S. Vigklas). Serdica Journal of Computing, Vol. 2, 89-104, 2008. |
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73. |
FLQ, the Fastest Quadratic Complexity Bound on the Values of Positive Roots of Polynomials. (With Andreas Argyris and Adam Strzebonski). Serdica Journal of Computing, Vol. 2, 145-162, 2008. |
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74. |
Quadratic Complexity Bounds on the Values of Positive Roots of Polynomials. (With Adam W. Strzebonski and Panagiotis S. Vigklas). Abstracts of the International Conference on Polynomial Computer Algebra, PCA 2008, p. 6, St. Petersburg, Russia, April 4-7, 2008. Euler International Mathematical Institute, Russian Academy of Sciences. |
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75. |
Improving the Performance of the Continued Fractions Method Using new Bounds of Positive Roots. (With Adam W. Strzebonski and Panagiotis S. Vigklas). Nonlinear Analysis: Modelling and Control, Vol. 13, No. 3, 265-279, 2008. |
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76. |
Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials. Journal of Universal Computer Science, Vol. 15, No. 3, 523-537, 2009. |
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77a. |
Vincent's Theorem of 1836: Overview and Recent Developments (ppt). Plenary talk, given at ACA 2008, the International Conference on Applications of Computer Algebra, held at RISC-Linz, Hagenberg, Austria (July 27-30, 2008). |
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77b. |
Vincent's Theorem of 1836: Overview and Recent Developments. Στο: Μιχάλης Ζουμπουλάκης (Επιστημονική Επιμέλεια): επιστημονικά ανάλεκτα, επετειακός τόμος για τα 20 χρόνια του Πανεπιστημίου Θεσσαλίας, σελ. 247-270, Πανεπιστημιακές Εκδόσεις Θεσσαλίας, Βόλος 2010. |
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78a. |
Vincent's Theorem of 1836: Overview and Future Research (beamer). Presentation at PCA 2009, The International Conference on Polynomial Computer Algebra, held at St. Petersburg, Russia (April 8-12, 2009). |
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78b. |
Vincent's Theorem of 1836: Overview and Future Research. In N. N. Vassiliev (Ed.), /Proceedings of the International Conference on Polynomial Computer Algebra/, PCA 2009, 48-51, St. Petersburg, Russia, April 8-12, 2009. Euler International Mathematical Institute, Russian Academy of Sciences. |
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78c. |
Vincent's Theorem of 1836: Overview and Future Research. In Н.Н. Васильев, А.М. Вершик (Eds.) Zap. Nauchnyh Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), Teor. Predst. Din. Sist. Komb. Metody. XVII, V.373, 5-33, 2009. |
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78d. |
Vincent's Theorem of 1836: Overview and Future Research. Journal of Mathematical Sciences, Vol. 168, No. 3, 309-325, 2010. |
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79. |
Counting the Number of Real Roots in an Interval with Vincent's Theorem. (With Panagiotis S. Vigklas). Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, Vol. 53(101), No. 3, 201-211, 2010. |
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80. |
Λογισμικά για Συμβολικούς Υπολογισμούς : ένα Συγκριτικό Τεστ Ελεύθερων και Εμπορικών Λογισμικών (με την Κυρ. Τσιλίκα). Στο Ν. Αλεξανδρής, Π. Βλάμος, Χ. Δουληγέρης, Β. Μπελεσιώτης (Εκδότες) : Proceedings of the 3rd Conference on Informatics in Education 2011, 430-440, Pireas, Greece, October 8-9, 2011. |
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81. |
Budan's theorem. Wikipedia article, http://en.wikipedia.org/wiki/Budan's_theorem. (With my students Apostolopoulou Ifigenia, Kiamili Nikolao and Haritidi Polychroni) 2012. |
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82. |
Vincent's theorem. Wikipedia article, http://en.wikipedia.org/wiki/Vincent's_theorem. (With my students Apostolopoulou Ifigenia, Kiamili Nikolao and Haritidi Polychroni) 2012. |
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83. |
Το σύστημα υπολογιστικής άλγεβρας Xcas ως περιβάλλον Δυναμικής Γεωμετρίας. Στο: Γεωμετρία - Από την Επιστήμη στην Εφαρμογή, σελ 17-18, ΤΕΙ Πειραιά, 1-2 Ιουνίου, 2012. (http://civil.teipir.gr/web/uploads/SYMPOSIO_ABSTRACTS.pdf). |
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84. |
Computing Sturm sequences with matrix triangularization. In: Applications of Computer Algebra, June 25-28, 2012 in Sofia, Bulgaria, (with Ifigenia I. Apostolopoulou and Georgios S. Floros) |
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85. |
Implementation of VAS in iOS. In: Applications of Computer Algebra, June 25-28, 2012 in Sofia, Bulgaria (with Spyros Kehagias) |
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86. |
Gröbner Bases. Translation from Russian of two papers by N. Vasiliev (ВАСИЛЬЕВ НИКОЛАЙ НИКОЛАЕВИЧ: КАК КОМПЬЮТЕР ПОМАГАЕТ УПРОЩАТЬ АЛГЕБРАИЧЕСКИЕ УРАВНЕНИЯ ИЛИ НЕМНОГО О БАЗИСАХ ГРЁБНЕР. КОМПЬЮТЕРНЫЕ ИНСТРУМЕНТЫ В ОБРАЗОВАНИИ, pp. 43 - 51, No 5, 2005Г AND pp. 26 - 33, No 6, 2005Г ). For the examples the computer algebra system Xcas was introduced. 2012. |
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87. |
Το σύστημα υπολογιστικής άλγεβρας Xcas ως περιβάλλον Δυναμικής Γεωμετρίας. Στο: Μαλικούτη Στ. - Λευκαδίτης Γ. επιμ., Γεωμετρία: από την Επιστήμη στην Εφαρμογή, Τμήμα Πολιτικών Δομικών Έργων Τ.Ε.Ι. Πειραιά, Σύγχρονη Εκδοτική: Αθήνα, σελ. 69-82, 2013 (με Κ. Τσιλίκα) |
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88. |
Free Working Environments for Computer Algebra. КОМПЬЮТЕРНЫЕ ИНСТРУМЕНТЫ В ОБРАЗОВАНИИ, 2012, No. 6, pp 35-43. |
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89. |
Implementation of the VAS algorithm in Maxima. In: Abstracts of the International Conference Mathematical Partnership, Parallel Computing and Computer Algebra, Gennadi, Rhodes, Greece, p. 8, August 2013. |
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90. |
Implementation of the VAS algorithm in Reduce. In: Abstracts of the International Conference Mathematical Partnership, Parallel Computing and Computer Algebra, Gennadi, Rhodes, Greece, p. 7, August 2013. |
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91. |
Implementation of the VAS algorithm on Android OS. (With A. Berkakis) In: Abstracts of the International Conference Mathematical Partnership, Parallel Computing and Computer Algebra, Gennadi, Rhodes, Greece, p. 9, August 2013. |
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92. |
On a Theorem by Van Vleck Regarding Sturm Sequences. (With G.I. Malaschonok and P.S. Vigklas). Serdica Journal of Computing, Vol. 7, No 4, 101–134, 2013. |
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93. |
Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences. (With G.I. Malaschonok and P.S. Vigklas). Serdica Journal of Computing, Vol. 8, No 1, 29–46, 2014. |
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94. |
Three New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS’s). Serdica J. Computing 9(1) (2015), 1-26. |
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95. |
On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials. (With G.I. Malaschonok and P.S. Vigklas). Serdica Journal of Computing, 9(2) (2015), 123-138. |
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96. |
A Basic Result on the Theory of Subresultants. (With G.I. Malaschonok and P.S. Vigklas). Serdica Journal of Computing 10 (2016), Νο.1, 31--48. |
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97. |
Subresultant Polynomial Remainder Sequences Obtained by Polynomial Divisions in Q[x] or in Z[x]. (With G.I. Malaschonok and P.S. Vigklas). Serdica Journal of Computing 10 (2016), Νο.3-4, 197-217. |
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98. |
Various New Methods for Computing Subresultant Polynomial Remainder Sequences (PRS's). In Proceedings of: Applications of Computer Algebra, pp 85-90, Kalamata, Greece, July 20-23, 2015. (Caveat: In this beamer presentation slide 23 with frames 87-93 is a "must see."). |
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99. |
Lagrange’s Bound on the Values of the Positive Roots of Polynomials. (With Adam W. Strzebonski and Panagiotis S. Vigklas). Serdica Journal of Computing, 12(4) (2018), 227-246. |
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100. |
Anna Johnson and Her Seminal Theorem of 1917. Computer Tools in Education, No 2, (2016), 13–35. |
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101. |
An Improvement on Lagrange's Quadratic Bound on the Values of the Positive Roots of Polynomials. (With G.I. Malaschonok). To appear in: Abstracts of the International Conference Mathematical Partnership, Parallel Computing and Computer Algebra, Agia Paraskevi, Halkidiki, Greece, August 2016. |
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102. |
On Polynomial Remainder Sequences (PRS's). Invited talk, Department of Mathematics, Computational Mathematics, University of Kassel, Germany, 25-10-2016. |
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103. |
A sympy/sage Module for Computing Polynomial Remainder Sequences. (With G.I. Malaschonok and P.S. Vigklas). In: 23rd Conference on Applications of Computer Algebra, pp. 36-- 39, July 17-21, 2017, Jerusalem, Israel. |
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104. |
On Vincent’s Theorem. Invited talk, Department of Mathematics, Computational Foundry, University of Swansea, Wales, United Kingdom, 25-10-2018. |
