Bibliography

ACM SIGSAM Bulletin, Vol 41, No. 2, June 2007

    

In Memoriam
Giuseppa Carrà-Ferro
(1952-2007)

   Giuseppa Carrà-Ferro, born on August 1, 1952 in Catania, Italy, was a pioneer in computational differential algebra. She completed her undergraduate and master (laurea) degrees in mathematics at the University of Catania, graduating magna cum laude in 1974. Soon after graduation, on October 10, 1974, she joined the Department of Mathematics and Computer Science at the University of Catania. She was a visiting researcher at the Department of Mathematics of Columbia University for the academic year 1979–80. Her association with Professor Ellis R. Kolchin at Columbia and his group influenced very much her future scientific activities and she brought into the group her knowledge of computer algebra which she acquired from her collaboration with the Italian scientific community. She was an assistant professor of algebra at the University of Catania until November, 1993 and an associate professor until November, 2003 when she became a full professor of algebra.

   Her scientific activities have been devoted to differential algebra and computational algebra. She published her first paper on the differential spectrum of a differential ring in 1978. This was followed by works on the global sections of the structure sheaf, tangent space on affine differential varieties, and Hilbert and Kolchin schemes. On the computational side, she was the first to generalize Gröbner basis techniques to differential algebra. For differential polynomial ideals, a differential Gröbner basis need not exist or be finite. Despite such difficulties, she developed and applied her theory to compute the dimensions of algebraic and differential algebraic varieties and bound their multiplicities. With G. Gallo and others, she derived a dimension method and introduced notions of validity levels, allowing automated proofs and probabilistic verification of geometric and differential geometric statements. She investigated the differential analogs of resultants and the sheaf approach in algebraic geometry, and compared Gröbner basis with characteristic set methods. With other authors, she made fundamental constributions to super-G-basis of algebraic ideals (L. Robbiano), classification of rankings (W. Sit), extended characteristic sets (V. Gerdt), and involutive monomial division (V. Marotta). More recently, with her student D. Ferrarello, in a series of papers, she expressed and applied computer algebra techniques to compute properties of graphs.

   She was active in promoting computer algebra, helped organizing two international conferences, and taught several courses for undergraduate and graduate students. She was the Italian coordinator for the INTAS projects n.93-30, Computer Algebra, Symbolic and Combinatorial Tools in Differential Algebra and Differential Equations, with impact in Fundamental Physics and Control Theory, and n.99-01222, Involutive Systems of Differential and Algebraic Equations. She was always interested in the most innovative aspects of her field. Besides applying her results to geometric theorem proving, she was keen to use them for other problems in analog circuit design, statistics, and dynamical systems. The originality of her research was a consequence of her mathematical culture which includes commutative, differential and computational algebra, algebraic geometry, differential equations, algorithms, computational complexity, and graph theory.

   Lately she gave a wonderful seminar on Sturmfel’s Tropical Algebra and its Application to Biology. Unfortunately she could not continue this research because she was diagnosed with a pancreatic cancer in April 2004. Her last contribution was a survey paper on differential Gröbner bases, to appear posthumously in the volume Gröbner Bases in Symbolic Analysis, edited by Markus Rosenkranz and Dongming Wang. She delivered her last lecture, completing her course, a few days before she died in peace with God on March 22, 2007. She was a wonderful wife, mother and teacher. She will always be remembered by her students, colleagues, and fellow researchers.

(Communicated by William Sit)

 

Bibliography of Giuseppa Carrà-Ferro

  1. G. Carrà-Ferro, A survey on differential Gr¨obner bases. M. Rosenkranz, D. Wang (eds.), Gröbner Bases in Symbolic Analysis, Proc. Special Semester on Gröbner Bases and Related Methods, de Gruyter, to appear, 2007.
  2. G. Carrà-Ferro, and D. Ferrarello, Polynomial ideals and directed graphs. Preprint available at http://arxiv.org/abs/math/0703381.
  3. G. Carrà-Ferro and D. Ferrarello, Cohen-Macaulay graphs arising from digraphs. Preprint available at http://arxiv.org/abs/math/0703417 submitted to Discrete Mathematics.
  4. G. Carrà-Ferro, and D. Ferrarello, Ideals and graphs: Gröbner bases and decision procedures in graphs. Discrete Mathematics (2007), accepted manuscript (May 15, 2007): doi:10.1016/j.disc.2006.11.041.
  5. G. Carrà-Ferro, Ideals, bifiltered modules and bivariate Hilbert polynomials. J. Symbolic Comput. 41(1) (2006), 112–121.
  6. G. Carrà-Ferro, Generalized differential resultant systems of algebraic ODEs and differential elimination theory. D. Wang, Z. Zheng (eds.), Differential Equations with Symbolic Computation, Trends in Math. (Lecture Notes in C. Sc.), Birkhäuser Basel, 2005, 327–341.
  7. G. Carrà-Ferro and V. P. Gerdt, [An] Improved Kolchin-Ritt algorithm. (Russian) Programmirovanie 29(2) (2003), 35–40. Translation in Program. Comput. Software 29(2) (2003), 83–87.
  8. G. Carrà-Ferro and V. Marotta, Involutive division and involutive autoreduction. H. Kredek and W. Seiler (eds.), Proc. 8th RhineWorkshop on Computer Algebra (RWCA’02, Mannheim, Germany), 2002, 115–124.
  9. G. Carrà-Ferro, M. D’Anna, and V. Marotta, A characterization of involutive divisions and its applications. J. Calmet, M. Hausdorf andW. Seiler (eds.), Proc. Workshop on Under-and Overdetermined Systems of Algebraic or Differential Equations (Institute f¨ur Algorithmen und Kognitive Systeme, Universität Karlsruhe), 2002, 19–36.
  10. G. Carrà-Ferro, Hilbert polynomials in two variables and bifiltered ideals. Zero-dimensional Schemes and Applications (Naples, 2000), Queen’s Papers in Pure and Appl. Math. 123 (2002), Queen’s Univ., Kingston, ON., 49–51.
  11. G. Carrà-Ferro and V. Marotta, Neighborhoods of an ordinary linear differential equation. V. G. Ganzha (ed.), Proc. Computer Algebra in Scientific Computing (4th CASC, Konstanz, 2001), Springer, Berlin, 2001, 107–121.
  12. G. Carrà-Ferro, Systems of nonalgebraic nonlinear ODEs. V. F. Edneral, S. Steinberg (eds.), Computer Algebra for Dynamical Systems and Mechanics (4th IMACS-ACA, Prague, 1998; 5th IMACS ACA, El Escorial, 1999). Math. Comput. Simulation 57(3–5) (2001), 197–209.
  13. G. Carrà-Ferro, Gr¨obner bases as characteristic sets. J. Herzog, G. Restuccia (eds.), Geometric and Combinatorial Aspects of Commutative Algebra (Messina, 1999), Lecture Notes in Pure and Appl. Math. 217 (2001), Marcel Dekker, New York, 99–110.

  14. G. Carrà-Ferro, Computer algebra, nonlinear differential equations and analog circuit design. Proc. InternationalWorkshop on Symbolic Methods and Applications to Circuit Design (SMACD’98, Fraunhofer Institut Techno- und Wirtschaftsmathematik, Kaiserslautern, October 7–9 1998), 130–133.
  15. G. Carrà-Ferro, Triangular matrices, differential resultants and systems of linear homogeneous PDEs. A. D. Bruno, V. F. Edneral, S. Steinberg (eds.), Simplification of Systems of Algebraic and Differential Equations with Applications. Math. Comput. Simulation 45(5–6) (1998), 511–518.
  16. G. Carrà-Ferro, A resultant theory for ordinary algebraic differential equations. T. Mora, H. F. Mattson (eds.), Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-12, Toulouse, 1997), Lecture Notes Comput. Sci. 1255 (1997), Springer, Berlin, 55–65.
  17. G. Carrà-Ferro, A resultant theory for the systems of two ordinary algebraic differential equations. Appl. Algebra Engrg. Comm. Comput. 8(6) (1997), 539–560.
  18. G. Carrà-Ferro, Differential Gr¨obner bases in one variable and in the partial case. Algorithms and Software for Symbolic Analysis of Nonlinear Systems. Math. Comput. Modelling 25(8–9) (1997), 1–10.
  19. G. Carrà-Ferro, G. Gallo, and R. Gennaro, Probabilistic verification of elementary geometry statements. D. Wang (ed.), Selected Papers from the International Workshop on Automated Deduction in Geometry (Toulouse, 1996), Lecture Notes in Computer Science 1360 (1997) (subseries: Lecture Notes in Artificial Intelligence), Springer-Verlag, London, UK, 87–101.
  20. G. Carrà-Ferro, Systems [Symmetries] of nonhomogeneous linear partial differential equations and differential resultants. N. H. Ibragimov, F. M. Mahomed (eds.), Proc. Modern Group Analysis VI: Developments in Theory, Computation and Application (Johannesbury, South Africa, 1996), New Age International, 1996, 401–409.
  21. M. A. Alberti, G. Carrà-Ferro, B. Lammoglia, and M. Torelli, The dimension method in elementary and differential geometry. Ann. Math. Artificial Intelligence 13(1–2) (1995), 47–71.
  22. G. Carrà-Ferro, An extension of a procedure to prove statements in differential geometry. J. Automat. Reason. 12(3) (1994), 351–358.
  23. G. Carrà-Ferro, A resultant theory for systems of linear partial differential equations. Proc. Modern Group Analysis V: Theory and Applications in Mathematical Modelling (Johannesburg, 1994). Lie Groups Appl. 1(1) (1994), 47–55.
  24. G. Carrà-Ferro and W. Y. Sit, On term-orderings and rankings. K. G. Fischer et al. (eds.), Computational Algebra (Fairfax, VA, 1993), Lecture Notes in Pure and Appl. Math. 151 (1994), Marcel Dekker, New York, 31–77.
  25. G. Carrà-Ferro, and S. V. Duzhin, Differential-algebraic and differential-geometric approach to the study of involutive symbols. N. Kh. Ibragimov, M. Torrisi, A. Valenti (eds.), Proc. Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics (Acireale, 1992), Kluwer Acad. Publ., Dordrecht, 1993, 93–99.
  26. G. Carrà-Ferro and L. Robbiano, On super G-bases. J. Pure Appl. Algebra 68(3) (1990), 279–292.

  27. G. Carrà-Ferro, G. Gallo, A procedure to prove statements in differential geometry. J. Automat. Reason. 6(2) (1990), 203–209.
  28. G. Carrà-Ferro, Kolchin schemes. J. Pure Appl. Algebra 63(1) (1990), 13–27.
  29. G. Carrà-Ferro, Some remarks on the differential dimension. T. Mora, (ed.), Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-6, Rome, 1988), Lecture Notes in Comput. Sci. 357 (1989), Springer, Berlin, 152–163.
  30. G. Carrà-Ferro, G. Gallo, A procedure to prove geometrical statements. Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-5, Menorca, 1987), Lecture Notes in Comput. Sci. 356 (1989), Springer, Berlin, 141–150.
  31. G. Carrà-Ferro, Gröbner bases and differential algebra. Proc. Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-5, Menorca, 1987), Lecture Notes in Comput. Sci. 356 (1989), Springer, Berlin, 129–140.
  32. G. Carrà-Ferro, Gröbner bases and Hilbert schemes. I. Computational aspects of commutative algebra. J. Symbolic Comput. 6(2–3) (1988), 219–230.
  33. G. Carrà-Ferro, Some properties of the lattice points and their application to differential algebra. Comm. Algebra 15(12) (1987), 2625–2632.
  34. G. Carrà-Ferro, Some upper bounds for the multiplicity of an autoreduced subset of N^m and their applications. Algebraic Algorithms and Error Correcting Codes (AAECC-3, Grenoble, 1985), Lecture Notes in Comput. Sci. 229 (1985), Springer-Verlag, London, 306–315.
  35. G. Carrà-Ferro, On the tangent space to an affine differential variety at a given point. Bollettino Unione Matematica Italiana, Sezione D. VI (Algebra e Geometria) 4(1) (1985), 1–16.
  36. G. Carrà-Ferro, The ring of global sections of the structure sheaf on the differential spectrum. Rev. Roumaine Math. Pures Appl. 30(10) (1985), 809–814.
  37. G. Carrà-Ferro, Sullo Spettro Differenziale di un Anello Differenziale [On the differential spectrum of a differential ring]. (Italian) Le Matematiche (Univ. Catania) 33(1) (1978), 1–17.