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CoCoA System
Computations in Commutative Algebra
Research and Education
using CoCoA

Currently CoCoA is used by researchers in several countries. Most of them are Commutative Algebraists and Algebraic Geometers, but people working in different areas like Analysis and Statistics have also benefitted from our system.
Some articles which refer to CoCoA.

CoCoA is also used as the main system for teaching advanced courses in several Universities and is mentioned in some of the most used textbooks on Computational Algebra.

If you have used CoCoA for your research, please remember to cite CoCoA


Some articles which refer to CoCoA

(if you would like to add to this list, please fill in this
form)

2003

S.Bistarelli, G.Boffi, F.Rossi
Computer Algebra for Fingerprint Matching
Lecture Notes in Computer Science, 2657, 811--820 (2003)
F. Botana and J.L. Valcarce
A software tool for the investigation of plane loci
Mathematics and Computers in Simulation, 61, 139-152 (2003)
F. Botana
A Web-based intelligent system for geometric discovery
Proc. of ICCS 2003, LNCS-Springer, 2657, 801-810 (2003)

2002

A.M. Bigatti, A.V. Geramita
Level Algebras, Lex Segments and Minimal Hilbert Functions
Communications in Algebra, To appear
Francisco Botana
Interactive versus Symbolic Approaches to Plane Loci Generation in Dynamic Geometry Environments
Lecture Notes in Computer Science, 2330, 211-218 (2002)

2001

G.Boffi,F.Rossi
Lexicographic Gröbner bases of 3-dimensional transportation problems
Contemp. Math., 286, 145--168 (2001)
F. Rapallo
Algebraic Markov Bases and MCMC for Two-Way Contingency Tables
Scand. J. Statist., To appear, (2001)

2000

W.W. Adams, C.A. Berenstein, P. Loustaunau, I. Sabadini, D.C. Struppa
Regular functions of several quaternionic variables and the Cauchy--Fueter Complex
Journal of Geometric Analysis, To appear
W. W. Adams, P. Loustaunau
Analysis of the module determining the properties of regular functions of several quaternionic variables
Pacif. Jour., To appear
L. Bazzotti, G. Dalzotto, L. Robbiano
Some Remarks on Theorem Proving
-, Preprint
F. Colombo, I. Sabadini, D.C. Struppa
Dirac equation in octonionic algebra
Contemp. Math. AMS., To appear
T. Dana-Picard
Rays of light trapped by conics
Int. J. of Math. Educ. in Science and Techn., 31 (5), 758-773 (2000)
L.M. Laita, L. de Ledesma, E. Roanes Lozano, A. Pérez, A. Brunori
Boole's Logic Revisited from Computer Algebra
Mathematics and Computers in Simulation, 51 Special Volume: Non-Standard Applications of Computer Algebra II, 419-439 (2000)
L.M. Laita, E. Roanes Lozano, M.A. Henares, A. Esteban, L. de Ledesma, E. Roanes-Macías
An Algebraic Approach to KBS. Application to Computer Network Selection
Procedings of ES99, , 315-327 (2000)
E. Roanes Lozano, L.M. Laita, E. Roanes Macías, V. Maojo, S. Corredor, A. de la Vega, A. Zamora
A Gröbner Bases-Based Shell for Rule-Based Expert Systems Development
Expert Systems with Applications, 18, 221-230 (2000)
D. Napoletani, I. Sabadini, D.C. Struppa
Variations on a theorem of Severi
Operator Theory: adv. and appl., Birkhäuser, 114, 197--206 (2000)
I. Sabadini, F. Sommen
Special first order systems and their resolutions
-, Preprint
I. Sabadini, D.C. Struppa, M. Shapiro
Algebraic analysis of the Moisil--Theodorescu system
Complex Variables, To appear
I. Sabadini, D.C. Struppa, F. Sommen, P. Van Lancker
Complexes of Dirac Operators in Clifford Algebras
Math. Z., To appear

1999

Jean Assan, Anna M. Perdon
An efficient computation of the solution of the block decoupling problem with coefficients assignment over a ring
Kybernetika, 35, 765-776 (1999)
A. Conca, G. Valla
Hilbert function of powers of ideals of low codimension
Math.Z., 230, 753-784 (1999)
L.M. Laita, E. Roanes Lozano, L. de Ledesma, J.A. Alonso
A computer algebra approach to verification and deduction in many-valued knowledge systems
Soft Computing (Springer), 3, 7-19 (1999)
L.M. Laita, E. Roanes Lozano, Victor Maojo, A. Díaz
A Logic and Computer Algebra Approach to a Decision-making Problem in Medicine
Revista de la Real Academia de Ciencias Exactas, F°sicas y Naturales, 92, 299-306 (1999)
L.M. Laita, E. Roanes Lozano, V. Maojo, L. de Ledesma
Computer Algebra based Verification and Knowledge Extraction in RBS. Application to Medical Fitness Criteria
Collection of papers from EUROVAV'99, , 53-65 (1999)
G. Pistone, H.P. Wynn
Finitely Generated Cumulants
Statistica Sinica, To appear
E. Riccomagno, H.P. Wynn
Groebner bases in experimental design: an overview
Sigsam Bullettin, March, (1999)
R. Thomas
Algebraic methods in integer programming
Encyclopedia of Optimization, To appear

1998

R.A. Bates, B. Giglio, E. Riccomagno, H.P. Wynn
Groebner basis methods in polynomial modelling
Proceedings of COMPSTAT `98, Bristol 24-28th August 1998, 179-184 (1998)
M. Brundu, A. Logar
Parametrization of the orbits of cubic surfaces
Transform. Groups, 3, 209--239 (1998)
M. Caboara
Optimization of basic algorithms in Commutative Algebra
PhdThesis, Univ. Of Pisa (1998)
M. Caboara and E. Riccomagno
An algebraic computational approach to the identifiability of Fourier models
J. Symb. Comput., 26, 245-260 (1998)
F. Colombo, P. Loustaunau, I. Sabadini, D.C. Struppa
Regular Functions of Biquaternionic Variables and Maxwell's Equations
J. Geom. Phys, 26, 183--201 (1998)
A. Conca
Straightening law and powers of determinantal ideals of Hankel matrices
Adv. Math., 138, 263-292 (1998)
D. La Macchia, F. Rossi
On computational Galois theory. An algorithm to solve a cyclic equation
Quaderni matematici Univ. Trieste, II, 432 (1998)
L.M. Laita, E. Roanes Lozano, V. Maojo
Inference and Verification in Medical Appropriateness Criteria Using Gröbner Bases
Lecture Notes in Artificial Intelligence, 1476, 183-194 (1998)
E. Roanes Lozano, L.M. Laita, E. Roanes Macías
A Polynomial Model for Multi-Valued Logics with a Touch of Algebraic Geometry and Computer Algebra
Mathematics and Computers in Simulation, 45. Special Volume: Non-Standard Applications of Computer Algebra, 83-99 (1998)
L. Robbiano
Gröbner Bases and Statistic
Gröbner Bases and Applications (Proc. of the Conf. 33 Years of Gröbner Bases) London Mathematical Society Lecture Notes Series, 251, 179--204 (1998)
L. Robbiano and M.P. Rogantin
Full Factorial Designs and Distracted Fractions
Gröbner Bases and Applications (Proc. of the Conf. 33 Years of Gröbner Bases) London Mathematical Society Lecture Notes Series, 251, 473--482 (1998)

1997

W. W. Adams, P. Loustaunau, V. Palamodov, D.C. Struppa
Hartog's phenomenon for polyregular functions and projective dimension of related modules
Ann. Inst. Fourier, 47, 623--640 (1997)
M. Caboara and L. Robbiano
Families of Ideals in Statistic
Proc. ISSAC '97. ACM Press, , 404--409 (1997)
A. Conca
Hilbert function and resolution of the powers of the ideal of the rational normal curve
J. Pure Appl. Algebra, To appear
S. Guarrera, A. Logar, E. Mezzetti
An algorithm for computing minimal curves
Arch.Math., 68, 1--12 (1997)
T. Holliday, G. Pistone, E. Riccomagno, H.P. Wynn
The Application of Algebraic Geometry to the Analysis of Designed Experiments: a case study
Computational Statistics, 14, 213-231 (1997)

1996

W.W. Adams, C.A. Berenstein, P. Loustaunau, I. Sabadini, D.C. Struppa
On compact singularities for regular functions of one quaternionic variable
Complex Variables, 31, 259--270 (1996)
C.A. Berenstein, I. Sabadini, D.C. Struppa
Boundary values of regular functions of a quaternionic variable
Pitman Res. Notes in Math., 347, 220--232 (1996)

Some books which mention CoCoA

(if you would like to add to this list, please fill in this
form)
W. W. Adams, P. Loustaunau
An Introduction to Gröbner Bases
Graduate Studies in Mathematics: Amer. Math. Soc., Providence, R.I. (1994)
 
F. Colombo, I. Sabadini, F. Sommen, D. C. Struppa
Analysis of Dirac Systems and Computational Algebra
Birkhäuser, Progress in Mathematical Physics, 2004.
The main treatment in this work is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems.
 
D. Cox, J. Little, D. O'Shea
Ideals, Varieties, and Algorithms
Springer-Verlag, New York (1992)
 
D. Cox, J. Little, D. O'Shea
Using Algebraic Geometry
Springer-Verlag, New York (1998). (Graduate Texts in Mathematics, 185)
496 pp. Paperback, ISBN 0-3879-8492-5. Hardcover, ISBN 0-3879-8487-9
 
J. Migliore
Introduction to Liaison Theory and Deficiency Modules
Birkhäuser, Progress in Mathematics 165, (1998).
224 pp. Hardcover, ISBN 0-8176-4027-4
 
D. Eisenbud
Commutative Algebra With a View Toward Algebraic Geometry
Springer-Verlag, New York (1994). (Graduate Texts in Mathematics, 150)
785 pp. Paperback, ISBN 0-3879-4269-6
 
M. Kreuzer, L. Robbiano
Computational Commutative Algebra 1
Springer (2000), ISBN 3-540-67733-X
 
M. Kreuzer, L. Robbiano
Computational Commutative Algebra 2
Springer (2005), ISBN 3-540-25527-3
 

Some courses which use CoCoA

(if you would like to add to this list, please fill in this
form)
See some CoCoA lab sessions
Alfred Czogała
Algebra Obliczeniowa
(Silesian University, Katowice (Poland))

 
Arman Shokrollahi
Advanced Commutative Algebra
(University of Madras)

 
Vincenzo Ancona
Matematiche Complementari
(Universita` di Firenze (C.d.L. in Matematica), Italy)
  • Basic exercises on polynomials and ideals of polynomials;
  • computation of Gröbner bases;
  • computation of resultants;
  • exercises on elimination theory;
  • exercises on the Hilbert Nullstellensatz;
  • exercises on the Hilbert polynomial;
  • construction of simple packages on matrices.

 
Alberto Damiano
Computational Algebra
(Chapman University, California)
Groebner bases and appliactions, 1 semester for undergraduate students
 
Joan Elias
Àlgebra Commutativa
(Universitat de Barcelona)

 
Tony Geramita (Tai Ha)
Computer Algebra
(Queen's University, Canada)
1 term, for undergraduates and graduate students.
Gröbner bases and applications to Commutative Algebra.
 
Dina Ghinelli
Istituzioni di Geometria Superiore
(Univ. of Roma 1, Italy)

 
Martin Kreuzer
Ergänzungen zur Computeralgebra
(Universität Regensburg, Germany)

 
Joseph Lipman
Computational Commutative Algebra
(Purdue University, USA)

 
Sandro Logar and Fabio Rossi
Algebra Computazionale
(Univ. di Trieste, Italy)
2 terms, for undergraduates and graduate students.
Gröbner bases and their properties
 
Edward Mosteig
Computational Commutative Algebra
(Tulane University)
1 term, for graduate students Gröbner bases and applications
 
Lorenzo Robbiano (Anna Bigatti)
Algebra Computazionale
(Univ. of Genova, Italy)
2 terms, for undergraduates and graduate students.
Gröbner bases and applications to Commutative Algebra.
 
Marie A. Vitulli
Seminar on Gröbner Bases
(Univ. of Oregon, USA)
2 terms
Gröbner bases and applications to Commutative Algebra.
 

Please send comments or suggestions to cocoa(at)dima.unige.it
Last Update: 9 Apr 2010.