Publications

Papers in international journals:

E.Fortuna, P.Gianni, B.Trager : Computation of topological invariants for real projective surfaces with isolated singularities,  J. Symbolic Comput. 68 (2015), part 2, 131–166. 14Pxx

E.Fortuna, P.Gianni, B.Trager : Ideals of curves given by points, Computational algebraic and analytic geometry, 71–87, Contemp. Math., 572, Amer. Math. Soc., Providence, RI, 2012. 13P10 (14H99)

E.Fortuna, P.Gianni, B.Trager : Generators of the ideal of an algebraic space curve, J. Symbolic Comput. ,  44 (2009), no. 9, 1234–1254. 13F20 (13E15 14H99)

E.Fortuna, P.Gianni, D.Luminati, P.Parenti : The adjacency graph of a real algebraic surface ,  Appl. Algebra Engrg. Comm. Comput. 16 (2005), no. 5, 271–292.

E.Fortuna, P.Gianni, P.Parenti, Some constructions for real algebraic curves, J. Symbolic Comput. 40(2005), no. 4-5, 1169–1179. 14P05 (13P10 68W30)

E.Fortuna, P.Gianni, B.Trager, Irreducible decomposition of polynomial ideals J. Symbolic Comput. 39(2005), no. 3-4, 305–316. 13F20 (68W30)

E.Fortuna, P.Gianni, D.Luminati, Algorithmical determination of the topology of a real algebraic surface  J. Symbolic Comput. 38 (2004), no. 6, 1551–1567. 14P25

E.Fortuna, P.Gianni, P.Parenti, C.Traverso, Algorithms to compute the topology of orientable real algebraic surfaces, J. Symbolic Comput. 36 (2003), no. 3-4, 343–364. 14Q10 (14P25 68W30)

E.Fortuna, P.Gianni, B.Trager, Derivations and radicals of polynomial ideals over fields of arbitrary characteristic J. Symbolic Comput. 33 (2002), no. 5, 609–625. 13P10 (13N15)

E.Fortuna, P.Gianni, B.Trager, Degree Reduction under Specialization,  J. Pure Appl. Algebra 164 (2001), no. 1-2, 153–163.  13P10 (68W30)

E.Fortuna, P.Gianni, Square-free decomposition in Finite Characteristic: An Application to Jordan Form Computation, SIGSAM Bulletin, Communications in Computer Algebra, 4, vol. 33, 14-, (1999)

P.Gianni, M.Seppala, R.Silhol, B.Trager, Riemann Surfaces, Plane Algebraic Curves and Their Period Matrices J. Symbolic Comput. 26 (1998), no. 6, 789–803. 
14H40 (14H55 30F10 30F30 30F35) 

P.Gianni, B.Trager, Square-free Algorithms in Positive Characteristic Appl. Algebra Engrg. Comm. Comput. 7 (1996), no. 1, 1–14. 13P05 (12Y05)

J.C.Faugere, P.Gianni, D.Lazard, T.Mora, Efficient computation of zero-dimensional Groebner bases by change of ordering Journal of Symbolic Computation, .16,329-344, (1993) J. Symbolic Comput. 16 (1993), no. 4, 329–344. 68Q40

P.Cellini, P.Gianni, C.Traverso, Shape of curves and surfaces : the combinatorics Computer Graphics and Mathematics (B.Falcidieno, I.Herman, C.Pienovi Eds.), Springer, 91 - 100. (1991)

P.Degano, P.Gianni, A normal form for restricted exponential functions, RAIRO Inform. Théor. Appl. 23 (1989), no. 2, 217–231. 68Q50 (03F30) 

P.Gianni, B.M.Trager, G.Zacharias, Groebner Bases and Primary Decomposition of Polynomial  Ideals J. Symbolic Comput. 6 (1988), no. 2-3, 149–167. 68Q40 (13-04 13A17)

C.De Concini, P.Gianni, C.Traverso, Computation of new Schubert Tables for Quadrics and Projectivities, Algebraic groups and related topics (Kyoto/Nagoya, 1983), 515–523, Adv. Stud. Pure Math., 6, North-Holland, Amsterdam, 1985. 14N10

P.Gianni,C.Traverso, Shape Determination for Real Curves and Surfaces,Ann. Univ. Ferrara, Sez.VII--Sc.Mat., Vol XXIX, 87--109, (1984)

P.Gianni, Sulle diseguaglianze di Arnold-Wilson per le curve algebriche reali, Ann. Univ. Ferrara Sez. VII (N.S.) 28 (1982), 115–126 (1983). 14F45 (14G30 14H99)

W.A.Adkins, P.Gianni, A.Tognoli, A Nullstellensatz for an Algebraically Non--Closed Field, Boll. Un. Mat. Ital. B (5) 15 (1978), no. 1, 338–343. 14G05 (03C60 32C05) 

P.Gianni, Morfismi interi delle varieta' algebriche, Boll.U.M.I.(5), 15-A ,187-196 (1978),

Papers in conference proceedings:

E.Fortuna, P.Gianni, P.Parenti, C.Traverso, Computing the topology of real algebraic surfaces, ISSAC 2002 (International Symposium on Symbolic and Algebraic computation), vol. 1, 92-100, Lille, France 2002

P.Gianni, B.Trager, Incremental Decoding,
International Symposium in Honor of Bruno Buchberger's 60th Birthday. Logic, Mathematics and Computer Science: Interactions (LMCS 2002),
vol. 02-60, 138-146, RISC - Linz (Austria) 2002

E.Fortuna, P.Gianni, B.Trager, Computation of the radical of polynomial ideals over fields of arbitrary characteristic, ISSAC 2001 International Symposium on Symbolic and Algebraic computation), vol. 1, 116-, London, Ontario, Canada 2001

P.Gianni, B.Trager, Integral Closure of Noetherian Rings, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), 212–216 (electronic), ACM, New York, 1997. 13B22 (68W30)

R.Corless, P.Gianni, B.Trager, A Reordered Schur Factorization Method for Zero-dimensional Polynomial Systems with Multiple Roots
Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation (Kihei, HI), 133–140 (electronic), ACM, New York, 1997. 65H10 (15-04)

R.M.Corless, P.M.Gianni, B.M.Trager, S.M.Watt, The Singular Value Decomposition for Polynomial Systems, ISSAC '95 (International Symposium on Symbolic and Algebraic Computation), Montreal, Canada

J.H.Davenport, P.Gianni, B.M.Trager, Scratchpad View of Algebra II : A Categorical View of Factorization, ISSAC '91, (S.Watt Ed.), ACM.

P.Cellini, P.Gianni, C.Traverso, Algorithms for the shape of semialgebraic sets. A new approach Applied algebra, algebraic algorithms and error-correcting codes (New Orleans, LA, 1991), 1–18, Lecture Notes in Comput. Sci., 539, Springer, Berlin, 1991. 68Q20 (14P10 68Q40)

P.Gianni, T.Mora, Algebraic Solution of Systems of Polynomial equations using Groebner Bases Applied algebra, algebraic algorithms and error-correcting codes (Menorca, 1987), 247–257, Lecture Notes in Comput. Sci., 356,Springer, Berlin, 1989. 13P10

P.Gianni, V.Miller, B.Trager, Decomposition of Algebras Lecture Notes in Comput. Sci., 358, Springer, Berlin, 1989. 12Y05 (11Y16)

"Computer Algebra Group", Scratchpad II,IBM Research, Yorktown Heights, NY,(1987)

P.Gianni, Properties of Gr\"obner Bases under specializations, EUROCAL '87 (Leipzig, 1987), 293–297,Lecture Notes in Comput. Sci., 378, Springer, Berlin, 1989. 13P10 (12E12 65H10 68Q40)

P.Gianni, B.Trager, GCD's and Factoring Multivariate Polynomials using Groebner bases, EUROCAL '85, Lect. Notes in Comp.Sci., 409-410, Springer 1985

P.Gianni, C.Traverso, La forma delle curve algebriche piane. Realizzazione di un algoritmo Atti del convegno di Geometria Algebrica, Firenze (1981).

Special Issues- Editor:

A.Dickenstein, P.Gianni, T.Recio (Editors) Effective Methods in Algebraic Geometry (MEGA 2005) Journal of Symbolic Computation, .42, (2007)

M.J.Wester, E.A.Arnold, P.Gianni, I.S.Kotsireas, E.Roanes-Lozano, S.Steinberg (Editors) Special Issue: Applications of Computer Algebra  in Science, Engineering, Simulation and Special Software,Mathematics and Computers in Simulation, 1-2, vol. 67, (2004)

P.Gianni(Editor) Symbolic and Algebraic Computation. Proceedings: ISSAC '89, Lect. Notes in Comp.Sci., N.358, Springer, (1989),