Selected Citations

1. M. Mignotte, D. Stefanescu: Linear recurrent sequences and polynomial roots, J. Symbolic Computation, 35, 637-649 (2003).
   1. H. Hong: Note on Jacobi's method for approximating dominant roots, J. Symb. Comput., vol. 37 (4), 449-454 (2004). [doua citari].

2. M. Mignotte, D. Stefanescu: La première méthode générale de factorisation des polynômes. Autour d'un mémoire de F. T. Schubert, Revue d'histoire des mathématiques, 7, 101-123 (2001).
   1. M. Galuzzi: The concept of irreducible polynomial from Descartes to Galois, TR, Università di Milano (2003).

   2. D. E. Knuth: The Art of Computer Programming, vol. 2 Seminumerical Algorithms, 3rd Edition, 13th printing, Addison-Wesley (2003).

3. M. Mignotte, D. Stefanescu: Estimates for polynomial roots, Appl. Alg. Eng. Comm. Comp., 12, 437-453 (2001).
   1. H. Hong: Note on Jacobi's method for approximating dominant roots, J. Symb. Comput., vol. 37 (4), 449-454 (2004). [doua citari].

4. L. Panaitopol, D. Stefanescu: On the generalized difference polynomials, Pacific Journal of Mathematics 143, 341-348 (1990).
   1. M. Ayad: The polynomials $F(X,Y)$ such that $K[F]$ is integrally closed in $K[X,Y]$, Acta Arith., vol. 105 (1): 9-28 (2002).

   2. S. Bathia, S. Khanduja: Difference polynomials and their generalizations, Mathematika, 48, 293-299 (2001).
   3. S. D. Cohen, A. Movahhedi, A. Salinier: Factorization over local fields and the irreducibility of generalized difference polynomials, Mathematika, vol. 47 (93-94): 173-196 Part 1-2 (2000).

5. L. Panaitopol, D. Stefanescu: A class of polynomials in positive characteristic, Bull. Math. Soc. Sc. Math. Roumanie 33 (81), 343-346 (1989).
   1. I. E. Shparlinski: Finite fields: theory and computation, Kluwer Academic Publishers, Dordrecht(1999).
   2. I. E. Shparlinski: Computational and Algorithmic Problems in Finite Fields, Kluwer Academic Publishers, Dordrecht (1992).

6. L. Panaitopol, D. Stefanescu: A resultant condition for the irreducibility of the polynomials, Journal of Number Theory 25, 107-111 (1987).
   1. M. Filaseta: Graduate course Math/788F Univ.of South Carolina (2002)

   2. N. Boja, D. Daianu: Elemente algebrice si topologice în teoria corpurilor, Univ. Timisoara, Mathematical Monographs, 30 (1988).

7. L. Panaitopol, D. Stefanescu: Some criteria for the irreducibility of polynomials, Bull. Math. Soc. Sc. Math. Roumanie 29 (77), 69-74 (1985).
   1. G. Angermüller: A generalization of Ehrenfecht's irreducibility criterion, Preprint Univ. Erlangen-Nürnberg (1985);
      J. Number Theory, 36, 80-84 (1990).

8. D. Stefanescu: Algebraic independence of general power series, Abstr. Amer. Math. Soc. 5, 272 (1984).
   1. A. Benhissi: Les corps de séries formelles généralisées, Thèse, Université de Provence. Centre Saint-Charles, Marseille, (Juin 1988).

9. D. Stefanescu: On meromorphic formal power series, Bull. Math. Soc. Sc. Math. Roumanie 27(75), 169-178 (1983).
   1. McDonald, John: Fractional power series solutions for systems of equations. (English) [J] Discrete Comput. Geom. 27, No.4, 501-529 (2002). [ISSN 0179-5376]

   2. Kiran S. Kedlaya: The algebraic closure of the power series field in positive characteristic, Proc. Amer. Math. Soc., vol. 129, no 12, 3461-3470 (2001)

   3. A. Benhissi: La clôture algèbrique du corps des séries formelles, Anal. de Math. Blaise Pascal, nouvelle série, 2, n. 2, 1-14 (1995).

   4. P. Ribenboim: Fields: algebraically closed and others, Manuscr. Math., 75, 115-150 (1992).

   5. A. Benhissi: Les corps de séries formelles généralisées, Thèse, Université de Provence. Centre Saint-Charles, Marseille, (Juin 1988).

   6. A. Benhissi: Les séries de Puiseux et la clôture algébrique de $K((T))$, Preprint (1988).

10. D. Stefanescu: A method to obtain algebraic elements over $k((T))$, Bull. Math. Soc. Sc. Math. Roumanie, 26 (74),77-91 (1982).
    1. J. McDonald: Fractional power series solutions for systems of equations. Discrete Comput. Geom., 27, 501-529 (2002).

    2. Kiran S. Kedlaya: The algebraic closure of the power series field in positive characteristic, Proc. Amer. Math. Soc., vol. 129, no 12, 3461-3470 (2001)

    3. A. Benhissi: La clôture algèbrique du corps des séries formelles, Anal. de Math. Blaise Pascal, nouvelle série, 2, n. 2, 1-14 (1995).

    4. P. Ribenboim: Fields: algebraically closed and others, Manuscr. Math., 75, 115-150 (1992).

    5. J. MacDonald: Fiber polytopes and fractional power series, J. Pure Appl. Algebra, 104, 213-233 (1992).

    6. A. Benhissi: Les corps de séries formelles généralisées, Thèse, Université de Provence. Centre Saint-Charles, Marseille, (Juin 1988).

    7. A. Benhissi: Les séries de Puiseux et la clôture algébrique de $K((T))$, Preprint (1988).

    8. M. M. Kapranov: On cuspidal divisors on the modular varieties of elliptic modules, Math. USSR Izvestiya, 30, 533-547 (1988).

11. C. Calude, S. Marcus, D. Stefanescu: The Creator versus its creation. From Scotus to Gödel, in Collegium Logicum, Annals of the Gödel Society, vol. 3, Prague, 1-10 (1999).
    1. P. Odifreddi: Ultrafilters, Dictators and Gods, in Finite versus Infinite. Mathematical Contributions to an Eternal Dilemma, Springer Verlag, London, 2000.

12. C. Calude, D. Campbell, K. Svozil, D. Stefanescu: Strong determinism vs. computability, in W. Depauli-Schimanovich, E. Koehler, F. Stadler (eds.): The Foundational Debate, Constructivity in Mathematics and Physics, Kluwer, Dordrecht, 115-131 (1995).
    1. P Cotogno: Hypercomputation and the Physical Church-Turing Thesis British Journal for the Philosophy of Science, 54, 181-223 (2003).

13. M. Mignotte, D. Stefanescu: Polynomials-An Algorithmic Approach, 322 pag., Springer Verlag, Singapore, Berlin, 1999.
    1. Y. Chee, L. Chen, L. : A new constructive root bound for algebraic expressions, in Symposium on Discrete Algorithms, Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, Washington, D.C., pp. 496-505 (2001).
    2. Curgus B., Mascionoi V. : A contraction of the Lucas polygon, Proc. Amer. Math. Soc., vol. 132, 2973-2981 (2004).

    3. P. Fleishmann, H. C. Marcus, P. Roelse: The black-box Niederreiter algorithm and its implementation over thebinary field, Mathematics of Computation Volume 72 , Issue 244 , pp.1887 - 1899 (2003).

    4. A. J. Sommese, J. Verschelde, C. W. Wampler: Symmetric functions applied to decomposing solution sets of polynomial systems, SIAM J. Numer. Anal., vol. 40 (6), pp. 2026-2046 (2002).

    5. C. Li: Exact Geometric Computation: theory and applications, PhD Dissertation, New York University (2001).

    6. John Hubbard, Dierk Schleicher, Scott Sutherland: How to find all roots of complex polynomials by Newton's method Inventiones Mathematicae, 146, 1-33 (2001)

    7. C Li, S. Pion, C Yap: Recent progress in exact geometric computation, [to appear in J. of Logic and Algebraic. Programming (2005)], see also C. Li, C. Yap in Proc. DIMACS Workshop on Algorithmic and Quantitative Aspects in Real Algberaic Geometry in Mathematics and Computer Science, 2001.

    8. P Fleischmann, M Holder, P Roelse: The Black-Box Niederreiter Algorithm and its Implementation over the Binary Field, Math. Comput., 72, 1887-1899 (2003).

    9. A Alpers, P Gritzmann : On stability, error correction and noise compensation in discrete tomography, TR, Tech. Univ. München (2004).

    10. M. Moeller: Good nonzeros of polynomials, SIGSAM Bull., 33, 10-11 (1999).

    11. P. Borwein, M. J. Mossinghof, J. D. Vaaler: Generalizations of Goncalves inequality, arXiv: math.CA/0501163, v1 11 Jan 2005 (2005).

    12. R Bagnara, A Zaccagnini, T Zolo : The Automatic Solution of Recurrence Relations, TR, Univ. Parma (2003).

    13. N. Broaddus: Noncyclic covers of knot complements, arXiv: math.GT

        /0401120, v3 12 May 2004 (2004).

    14. J. Keyser, K. Ouchi, J. M. Rojas: The Exact Rational Univariate Representation and Its Application, to appear in AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science (2005).

    15. J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du: Elimination of Harmonics in a Multilevel Converter Using the Theory of Symmetric Polynomials and resultants, IEEE Trans. Control Systems Technology, 13, no. 2 (2005).

    16. K. Belabas, M. van Hoeij, J. Kluners, A. Steel: Factoring polynomials over global fields, Arxiv: math.NT/0409510, v1 27 Sep 2004 (2004).

    17. W. D. Smith: Complexity of Minimization, TR, Temple University, math.temple.edu

    18. J. Thomann: Calcul Formel ou Calcul Numérique ?, L'Ouvert, no. 98, 23-50 (2000).

    19. S. Akiyama, H. Brunotte, A. Petho, J. M. Thuswaldner: Generalized radix representations and dynamical systems II - Acta Arith, 2006 (2006).

    20. A. Eigenwillig, C. K. Yap: Almost tight recursion tree bounds for the Descartes method - Proceedings of the 2006 international symposium on Symbolic ..., 2006 - portal.acm.org (2006).

    21. A. Ayad: Complexity bound for the absolute factorization of parametric polynomials, - Journal of Mathematical Sciences, vol. 134, no. 5, 2006 - Springer (2006).

    22. I. Z. Emiris, E. P. Tsigaridas: A note on the complexity of univariate root isolation, TR INRIA, Nov. 2006, hal.inria.fr/docs/00/11/72/01/PDF/RR-avg.pdf (2006).

    23. I. Z. Emiris and E. P. Tsigaridas: Univariate polynomial real root isolation: Continued Fractions revisited 14th Annual European Symposium on Algorithms (ESA 2006), [to appear also available at arXiv.org].

    24. Curgus B., Mascionoi V. : A contraction of the Lucas polygon, Proc. Amer. Math. Soc., vol. 132, 2973-2981 (2004).

    25. P. Fleishmann, H. C. Marcus, P. Roelse: The black-box Niederreiter algorithm and its implementation over thebinary field, Mathematics of Computation Volume 72 , Issue 244 , pp.1887 - 1899 (2003).

    26. A. J. Sommese, J. Verschelde, C. W. Wampler: Symmetric functions applied to decomposing solution sets of polynomial systems, SIAM J. Numer. Anal., vol. 40 (6), pp. 2026-2046 (2002).

    27. C. Li: Exact Geometric Computation: theory and applications, PhD Dissertation, New York University (2001).

    28. John Hubbard, Dierk Schleicher, Scott Sutherland: How to find all roots of complex polynomials by Newton's method Inventiones Mathematicae, 146, 1-33 (2001)

    29. C Li, S. Pion, C Yap: Recent progress in exact geometric computation, [to appear in J. of Logic and Algebraic. Programming (2005)], see also C. Li, C. Yap in Proc. DIMACS Workshop on Algorithmic and Quantitative Aspects in Real Algberaic Geometry in Mathematics and Computer Science, 2001.

    30. P Fleischmann, M Holder, P Roelse: The Black-Box Niederreiter Algorithm and its Implementation over the Binary Field, Math. Comput., 72, 1887-1899 (2003).

    31. A Alpers, P Gritzmann : On stability, error correction and noise compensation in discrete tomography, TR, Tech. Univ. München (2004).

    32. P. Borwein, M. J. Mossinghof, J. D. Vaaler: Generalizations of Goncalves inequality, arXiv: math.CA/0501163, v1 11 Jan 2005 (2005).

    33. R Bagnara, A Zaccagnini, T Zolo : The Automatic Solution of Recurrence Relations, TR, Univ. Parma (2003).

    34. N. Broaddus: Noncyclic covers of knot complements, arXiv: math.GT/0401120, v3 12 May 2004 (2004).

    35. J. Keyser, K. Ouchi, J. M. Rojas: The Exact Rational Univariate Representation and Its Application, to appear in AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science (2005).

    36. J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, Z. Du: Elimination of Harmonics in a Multilevel Converter Using the Theory of Symmetric Polynomials and resultants, IEEE Trans. Control Systems Technology, 13, no. 2 (2005).

    37. K. Belabas, M. van Hoeij, J. Kluners, A. Steel: Factoring polynomials over global fields, Arxiv: math.NT/0409510, v1 27 Sep 2004 (2004).

    38. W. D. Smith: Complexity of Minimization, TR, Temple University, math.temple.edu

    39. Lecture Notes for Students :
        1. http://www-madlener.informatik.uni-kl.de/ag-madlener/teaching/ws2001-2002/ca/ca.html

        2. http://www.informatik.uni-leipzig.de/ graebe/vorlesungen/polynome.html

        3. http://www.cs.berkeley.edu/ fateman/282/hand1.pdf

        4. http://mate.dm.uba.ar/ krick/ProgEcPol04.pdf

    40. Diploma Theses:
        1. http://www.mathematik.uni-kassel.de/ koepf/Diplome/factor.html

    41. Seminars:
        1. http://homepages.cwi.nl/ schuppen/cwi/semcst2001s.html

    42. Mathematical Encyclopaedia on-line:
        1. http://mathworld.wolfram.com/Polynomial.html

        2. http://www.ericweisstein.com/encyclopedias/books/Polynomials.html

        3. http://perso.wanadoo.fr/jean-paul.davalan/liens/liens_polynomes.html

        4. http://math.fullerton.edu/mathews/c2003/PolyRootComplexBib/

           Links/PolyRootComplexBib_lnk_3.html

        5. http://www.cecm.sfu.ca/ mjm/Lehmer/references.html

        6. http://www.mri.ernet.in/ ntweb/ntw/additions4.html

    43. Forums:
        1. http://www.forum-one.org/new-5172030-4349.html

        2. http://www.math.niu.edu/ rusin/known-math/97/budan_fourier

    44. Data bases:
        1. www.elsevier.com/homepage/sac/cam/mcnamee/2002/

        2. math.fullerton.edu/mathews/c2003/PolyRootComplexBib/ Links/PolyRootComplexBib

        3. http://www.fachgruppe-computeralgebra.de/CAR/CAR25/node15.html

14. D. Stefanescu: Modele Matematice în Fizica, Univ. Bucuresti, 224 pag., 1984.
    1. K. Svozil: Undecidability anewhere?, in J. L. Casti, A. Kirlqvist (Eds.) Boundaries and Barriers, Addison-Wesley, New York, 215-237 (1996).

    2. K. Svozil: Set Theory and Physics, Preprint TU Wien, May 1995;
       Foundations of Physics, 25, 1541-1560 (1995).

    3. K. Svozil: Varieties of Physical Undecidability, Preprint TU Wien, May 1995.

15. C. Calude, D. Campbell, K. Svozil, D. Stefanescu: Strong determinism vs. computability, in W. Depauli-Schimanovich, E. Koehler, F. Stadler (eds.): The Foundational Debate, Constructivity in Mathematics and Physics, Kluwer, Dordrecht, 115-131 (1995).
    1. P Cotogno: Hypercomputation and the Physical Church-Turing Thesis British Journal for the Philosophy of Science, 54, 181-223 (2003).

16. D. Stefanescu: New bounds for positive roots of polynomials, J. Univ. Comp. Sci., 2132-2141 (2005).
    1. A. Akritas, A. Strzebonski, P. Vigklas: Implementations of a New Theorem for Computing Bounds for Positive Roots of Polynomials Journal, Computing, [to appear, version on line available as DOI 10.1007/s00607-006-0186-y] (2006).

    2. A. Akritas, P. Vigklas: A Comparison of Various Methods for Computing Bounds of Positive Roots of Polynomials (TR 2006, submitted to JUCS) (2006).

    3. E. P. Tsigaridas, I. Z. Emiris: Univariate polynomial real root isolation: Continued Fractions revisited - Arxiv preprint cs.SC/0604066, 2006 - arxiv.org, also 14th Annual European Symposium on Algorithms (ESA 2006), [to appear] (2006). (2006)

    4. I. Z. Emiris, E. P. Tsigaridas: A note on the complexity of univariate root isolation, TR INRIA, Nov. 2006, hal.inria.fr/docs/00/11/72/01/PDF/RR-avg.pdf (2006).