Teo Mora Explained

Ferdinando 'Teo' Mora is an Italian mathematician, and since 1990 until 2019 a professor of algebra at the University of Genoa.

Life and work

Mora's degree is in mathematics from the University of Genoa in 1974. Mora's publications span forty years; his notable contributions in computer algebra are the tangent cone algorithm^{[1] [2]} and its extension of Buchberger theory of Gröbner bases and related algorithm earlier^[3] to non-commutative polynomial rings^[4] and more recently^[5] to effective rings; less significant^[6] the notion of Gröbner fan; marginal, with respect to the other authors, his contribution to the FGLM algorithm. Mora is on the managing-editorial-board of the journal AAECC published by Springer, and was also formerly an editor of the Bulletin of the Iranian Mathematical Society.

He is the author of the tetralogy Solving Polynomial Equation Systems:

• Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy, on equations in one variable
• Solving Polynomial Equation Systems II: Macaulay's paradigm and Gröbner technology, on equations in several variables
• Solving Polynomial Equation Systems III: Algebraic Solving,
• Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond, on the Buchberger algorithm

Personal life

Mora lives in Genoa. Mora published a book trilogy in 1977-1978 (reprinted 2001-2003) called on the history of horror films. Italian television said in 2014 that the books are an "authoritative guide with in-depth detailed descriptions and analysis."

See also

• • • FGLM algorithm, Buchberger's algorithm Gröbner fan, Gröbner basis Algebraic geometry#Computational algebraic geometry, System of polynomial equations

Further reading

• Book: Storia del cinema dell'orrore. Teo Mora. 1977 . 978-88-347-0800-2. 1. . none. . Web site: Second . none. and Web site: third . none. volumes:, . Reprinted 2001.
• The diamond lemma for ring theory. Advances in Mathematics. 29. 2. 178–218. 1978. George M Bergman. 10.1016/0001-8708(78)90010-5. free. none.
• Book: An algorithm to compute the equations of tangent cones. F. Mora. Computer Algebra: EUROCAM '82, European Computer Algebra Conference, Marseilles, France, April 5-7, 1982. 144. 158–165. 1982 . 10.1007/3-540-11607-9_18. Lecture Notes in Computer Science. 978-3-540-11607-3. none.
• Book: F. Mora. Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3, Grenoble, France, July 15-19, 1985, Proceedings. Groebner bases for non-commutative polynomial rings. 1986. 229. 353–362. 10.1007/3-540-16776-5_740. Lecture Notes in Computer Science. 978-3-540-16776-1. none.
• Standard bases and geometric invariant theory I. Initial ideals and state polytopes. David Bayer. Ian Morrison. Journal of Symbolic Computation. 1988. 6. 2–3. 209–218. 10.1016/S0747-7171(88)80043-9. none. free.
  • also in: Book: Computational Aspects of Commutative Algebra . Lorenzo Robbiano. 1989 . . 6. 2–3 . . none.
• Web site: Seven variations on standard bases. Teo Mora. 1988. none.
• An introduction to the tangent cone algorithm. Gerhard Pfister . T.Mora . Carlo Traverso. 1992. Christoph M Hoffmann. Issues in Robotics and Nonlinear Geometry (Advances in Computing Research). 6. 199–270. none.
• An introduction to commutative and non-commutative Gröbner bases. T. Mora. 1994. Theoretical Computer Science. 134. 131–173. 10.1016/0304-3975(94)90283-6. none. free.
• Algorithms in Local Algebra. Journal of Symbolic Computation. 19. 1995. 6. 545–557. Hans-Gert Gräbe . 10.1006/jsco.1995.1031. none. free.
• News: Advances and improvements in the theory of standard bases and syzygies . Gert-Martin Greuel . G. Pfister. 1996 . 10.1.1.49.1231 . none.
• The Chen-Reed-Helleseth-Truong Decoding Algorithm and the Gianni-Kalkbrenner Gröbner Shape Theorem. M.Caboara, T.Mora. 2002. Journal of Applicable Algebra. 13. 3. 209–232. 10.1007/s002000200097. 2505343. none.
• The Big Mother of All the Dualities, I: Möller Algorithm. M.E. Alonso . M.G. Marinari . M.T. Mora. Communications in Algebra. 2003. 31. 2. 783–818. 10.1081/AGB-120017343. 10.1.1.57.7799. 120556267 . none.
• Book: Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy. Teo Mora. 9780521811545. March 1, 2003. Cambridge University Press. Encyclopedia of Mathematics and its Application. 88. 10.1017/cbo9780511542831. 118216321. none.
• Book: Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gröbner Technology. T. Mora. 2005. Cambridge University Press. Encyclopedia of Mathematics and its Applications. 99. none.
• Book: Solving Polynomial Equation Systems III: Algebraic Solving. T. Mora. 2015. Cambridge University Press. Encyclopedia of Mathematics and its Applications. 157. none.
• Book: Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond. T Mora. 2016. Cambridge University Press. Encyclopedia of Mathematics and its Applications. 158. 9781107109636. none.
• Book: T. Mora. Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15. De Nugis Groebnerialium 4: Zacharias, Spears, Möller. 2015. 283–290. 10.1145/2755996.2756640. 9781450334358. 14654596. none.
• Buchberger–Weispfenning theory for effective associative rings. Journal of Symbolic Computation. 83. 112–146. 2016. Michela Ceria. Teo Mora. 10.1016/j.jsc.2016.11.008. 1611.08846. 10363249. none.
• Book: Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond. T Mora. 2016. Cambridge University Press. Encyclopedia of Mathematics and its Applications. 158. 9781107109636. none.

External links

• Official page
• Teo Mora and Michela Ceria, Do It Yourself: Buchberger and Janet bases over effective rings, Part 1: Buchberger Algorithm via Spear’s Theorem, Zacharias’ Representation, Weisspfenning Multiplication, Part 2: Moeller Lifting Theorem vs Buchberger Criteria, Part 3: What happens to involutive bases?. Invited talk at ICMS 2020 International Congress on Mathematical Software , Braunschweig, 13-16 July 2020

Notes and References

1. [#mora82|An algorithm to compute the equations of tangent cones]
2. Better algorithms due to Greuel-Pfister and Gräbe are currently available.
3. [#mora85|Gröbner bases for non-commutative polynomial rings]
4. Extending the proposal set by George M. Bergman.
5. [#NG4|De Nugis Groebnerialium 4: Zacharias, Spears, Möller]
6. The result is a weaker version of the result presented in the same issue of the journal by Bayer and Morrison.