Teo Mora

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

Mora's degree is in mathematics from the University of Genoa in 1974.^[1] Mora's publications span forty years; his notable contributions in computer algebra are the tangent cone algorithm^[2][3] and its extension of Buchberger theory of Gröbner bases and related algorithm earlier^[4] to non-commutative polynomial rings^[5] and more recently^[6] to effective rings; less significant^[7] 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,^[8] and was also formerly an editor of the Bulletin of the Iranian Mathematical Society.^[b]

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^[9]
• Solving Polynomial Equation Systems II: Macaulay's paradigm and Gröbner technology, on equations in several variables^[10][9]
• Solving Polynomial Equation Systems III: Algebraic Solving,
• Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond, on the Buchberger algorithm

Mora lives in Genoa.^[11] Mora published a book trilogy in 1977-1978 (reprinted 2001-2003) called Storia del cinema dell'orrore [it] on the history of horror films.^[11] Italian television said in 2014 that the books are an "authoritative guide with in-depth detailed descriptions and analysis."^[12]

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

• Teo Mora (1977). Storia del cinema dell'orrore. Vol. 1. Fanucci. ISBN 978-88-347-0800-2.. "Second". and "third". volumes: ISBN 88-347-0850-4, ISBN 88-347-0897-0. Reprinted 2001.
• George M Bergman (1978). "The diamond lemma for ring theory". Advances in Mathematics. 29 (2): 178–218. doi:10.1016/0001-8708(78)90010-5.
• F. Mora (1982). "An algorithm to compute the equations of tangent cones". Computer Algebra: EUROCAM '82, European Computer Algebra Conference, Marseilles, France, April 5-7, 1982. Lecture Notes in Computer Science. Vol. 144. pp. 158–165. doi:10.1007/3-540-11607-9_18. ISBN 978-3-540-11607-3.
• F. Mora (1986). "Groebner bases for non-commutative polynomial rings". Algebraic Algorithms and Error-Correcting Codes: 3rd International Conference, AAECC-3, Grenoble, France, July 15-19, 1985, Proceedings (PDF). Lecture Notes in Computer Science. Vol. 229. pp. 353–362. doi:10.1007/3-540-16776-5_740. ISBN 978-3-540-16776-1.
• David Bayer; Ian Morrison (1988). "Standard bases and geometric invariant theory I. Initial ideals and state polytopes". Journal of Symbolic Computation. 6 (2–3): 209–218. doi:10.1016/S0747-7171(88)80043-9.
  • also in: Lorenzo Robbiano, ed. (1989). Computational Aspects of Commutative Algebra. Vol. 6. London: Academic Press.
• Teo Mora (1988). "Seven variations on standard bases".
• Gerhard Pfister; T.Mora; Carlo Traverso (1992). Christoph M Hoffmann (ed.). "An introduction to the tangent cone algorithm". Issues in Robotics and Nonlinear Geometry (Advances in Computing Research). 6: 199–270.
• T. Mora (1994). "An introduction to commutative and non-commutative Gröbner bases". Theoretical Computer Science. 134: 131–173. doi:10.1016/0304-3975(94)90283-6.
• Hans-Gert Gräbe (1995). "Algorithms in Local Algebra". Journal of Symbolic Computation. 19 (6): 545–557. doi:10.1006/jsco.1995.1031.
• Gert-Martin Greuel; G. Pfister (1996). "Advances and improvements in the theory of standard bases and syzygies". CiteSeerX 10.1.1.49.1231.
• M.Caboara, T.Mora (2002). "The Chen-Reed-Helleseth-Truong Decoding Algorithm and the Gianni-Kalkbrenner Gröbner Shape Theorem". Journal of Applicable Algebra. 13 (3): 209–232. doi:10.1007/s002000200097. S2CID 2505343.
• M.E. Alonso; M.G. Marinari; M.T. Mora (2003). "The Big Mother of All the Dualities, I: Möller Algorithm". Communications in Algebra. 31 (2): 783–818. CiteSeerX 10.1.1.57.7799. doi:10.1081/AGB-120017343. S2CID 120556267.
• Teo Mora (March 1, 2003). Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy. Encyclopedia of Mathematics and its Application. Vol. 88. Cambridge University Press. doi:10.1017/cbo9780511542831. ISBN 9780521811545. S2CID 118216321.
• T. Mora (2005). Solving Polynomial Equation Systems II: Macaulay's Paradigm and Gröbner Technology. Encyclopedia of Mathematics and its Applications. Vol. 99. Cambridge University Press.
• T. Mora (2015). Solving Polynomial Equation Systems III: Algebraic Solving. Encyclopedia of Mathematics and its Applications. Vol. 157. Cambridge University Press.
• T Mora (2016). Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond. Encyclopedia of Mathematics and its Applications. Vol. 158. Cambridge University Press. ISBN 9781107109636.
• T. Mora (2015). "De Nugis Groebnerialium 4: Zacharias, Spears, Möller". Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15. pp. 283–290. doi:10.1145/2755996.2756640. ISBN 9781450334358. S2CID 14654596.
• Michela Ceria; Teo Mora (2016). "Buchberger–Weispfenning theory for effective associative rings". Journal of Symbolic Computation. 83: 112–146. arXiv:1611.08846. doi:10.1016/j.jsc.2016.11.008. S2CID 10363249.
• T Mora (2016). Solving Polynomial Equation Systems IV: Buchberger Theory and Beyond. Encyclopedia of Mathematics and its Applications. Vol. 158. Cambridge University Press. ISBN 9781107109636.

• 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