Publications on bergman and related topics

This bibliography includes two kinds of publications:

1. Publications of project participants (algebra and computer algebra)

\item V. Ufnarovski, . \emph{,}
Bibliographic data
1975 J. Backelin.
On the rationality of some Hilbert series. 1.
Preprints Univ. Stockholm No.16, 1975.
1978 J. Backelin
La série de Poincaré-Betti d'une algébre graduée de type fini à une relation est rationnelle. /
C. R. Acad. Sci., Paris, Ser. A287, 843-846, 1978.
1980 J. Backelin.
Monomial rings of embedding dimension four have rational Poincaré series.
Rep. Dep. Mat. Univ. Stockholm, No.14, 15, 1980.
1981 J. Backelin.
A distributiveness property of augmented algebras and some realted homological results.
Preprints Univ. Stockholm, 1981.
1991 J. Backelin, R. Fröberg.
How we proved that there are exactly 924 7-roots. /
S.M.Watt, ed. Proceedings of the ISAAC'91. - ACM, 1991. - P. 103-111.
1993 J.-E. Roos.
Commutative non-Koszul algebras having a linear resolution of arbitrarily high order. Applications to torsion in loop space homology.//
C. R. Acad. Sci. Paris Sér. I Math. 316 (1993), no. 11, 1123-1128.
1993 J.-E. Roos.
On computer-assisted research in homological algebra.
Symbolic computation, new trends and developments (Lille, 1993).//
Math. Comput. Simulation 42 (1996), no. 4-6, 475-490.
1994 J.-E. Roos.
A computer-aided study of the graded Lie algebra of a local commutative Nötherian ring. //
Journal of Pure and Applied Algebra, v. 91, 1994. - P. 255-315. 
Bergman relevant pages are 300-302.
1995 J.-E. Roos.
On the characterisation of Koszul algebras. Four counterexamples.//
C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 1, 15-20.
1995 J.-E. Roos.
Roos, Jan-Erik, A description of the homological behavior of families of quadratic forms in 4 variables.
1995 J.-E. Roos.
Koszul and non-Koszul algebras.
1995 S. Cojocaru, V. Ufnarovski.
Noncommutative Gröbner basis, Hilbert series, Anick's resolution and BERGMAN under MS-DOS. //
Computer Science Journal of Moldova, v. 3, Nr. 1(7), 1995. - P. 24-39.
1995 V.A. Ufnarovskij.
Combinatorial and Asymptotic Methods in Algebra. /
A.I. Kostrikin, I.R. Shafarevich, eds. Algebra VI. - Encyclopaedia of Mathematical Sciences, v. 57. - Berlin, Heidelberg, New York: Springer-Verlag, 1995. - P. 1-196.
Full algebraic backgrounds in encyclopedy presentation (results only, no proofs). Advanced bibliography on the topic.
1996 A. Podoplelov.
Constructing the Gröbner basis using Anick's resolution in the noncommutative algebras. /
Computer Science Journal of Moldova, v.4, nr. 3, 1996, pp.428-435.
1997 J.-E. Roos.
Good and bad Koszul algebras.//
Abstracts AMS.
1997 C. Löfwall, J.-E. Roos.
A nonnilpotent 1-2-presented graded Hopf algebra whose Hilbert series converges in the unit circle.//
Adv. Math. 130 (1997), no. 2, 161-200.
1998 V. Ufnarovski.
Introduction to Noncommutative Gröbner Bases Theory. /
In: Gröbner Bases and Applications, London Mathematical Society Lecture Notes Series. 251, pp. 259-280, 1998.
1998 S. Cojocaru, A. Podoplelov, V. Ufnarovski.
Non-Commutative Gröbner Bases and Anick's resolution. /
In: Progress in Mathematics, vol. 173, Birkhaeuser Verlag, Basel (Switzerland), pp.139-159.
1998 J.-E. Roos, B. Sturmfels.
A toric ring with irrational Poincaré-Betti series.
C. R. Acad. Sci. Paris, Sér. I Math. 326 (1998), no. 2, 141-146.
1999 J.-E. Roos.
Homological Properties of quotients of exterior algebras.
1999 R. Fröberg, J.-E. Roos.
An affine monomial curve with irrational Poincaré-Betti series. //
Journal of Pure and Applied Algebra, v. 144(?).
1999 J.-E. Roos.
Some non-Koszul algebras. /
Advances in geometry, 385-389, Progr. Math., 172, Birkhäuser, Boston, MA, 1999.
2003 J. Backelin, S. Cojocaru, V. Ufnarovski.
The Computer Algebra Project Bergman: Current State, in: "Commutative algebra, Singularities and Computer Algebra", eds. J.Herzog and V.Vulutescu, pp. 75-101. - Series II. Mathematics, Physics and Chemistry. Vol. 115, Kluwer Academic Publishers.
2003 J. Backelin, S. Cojocaru, V. Ufnarovski.
BERGMAN. In: Computer Algebra Handbook. J. Grabmeier, E. Kaltofen, V. Weispfenning (Eds.). - Springer, 2003, pp. 349-352.
2005 J. Backelin, S. Cojocaru, V. Ufnarovski.
Mathematical computations using Bergman. - Lund University, Sweden, 2005. - 206 p. - ISBN 91-631-7203-8.
A printed version of the bergman manual.
2005 J. Backelin, S. Cojocaru, A. Colesnicov, L. Malahova, V. Ufnarovski.
Problems in interaction with the Computer Algebra System Bergman. In: Computational Commutative and Non-Commutative Algebraic Geometry, vol. 196, NATO Science Series. Series III: Computer and Systems Sciences. G. Pfister, S. Cojocaru, V. Ufnarovski (Eds.). - IOS Press, 2005, pp. 185-198.
2005 D. Ronnovius, V. Ufnarovski.
Algorithmic Problems in SAGBI Basis Calculations. In: Computational Commutative and Non-Commutative Algebraic Geometry, vol. 196, NATO Science Series. Series III: Computer and Systems Sciences. G. Pfister, S. Cojocaru, V. Ufnarovski (Eds.). - IOS Press, 2005, pp. 244-248.
2005 A. Torstensson, V. Ufnarovski, H. Öfverbeck.
Using resultants for SAGBI basis verification in the univariate polynomial ring. Journal of Symbolic Computation, vol. 40, issue 3, September 2005, pp. 1087-1105.
2005 H. Öfverbeck.
Constructive Methods for SAGBI and SAGBI-Gröbner Bases. Ph.D. thesis, Lund University, 2005.
The corresponding software computing Hilbert Base, SAGBI and SAGBI-Gröbner packages for Maple can be found here.

2. Other references (algebra and computer algebra)

Bibliographic data
1965 B. Buchberger.
An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal.
Univ. of Innsbruck, Austria, Math. Inst., Ph. D. Thesis, 1965. - In German.
1976 B. Buchberger.
A Theoretical Basis for the Reduction of Polynomials to Canonical Form. //
ACM SIGSAM Bull. 10/3: 19-29, and 10/4: 19-24, 1976.
1979 B. Buchberger.
A Criterion for Detecting Unnecessary Reductions in the Construction of Gröbner Bases. /
In: Proc. of the EUROSAM 79 Symp. on Symbolic and Algebraic Computation, Marseille, June 26-28, 1979 (Lect. Notes in Comp. Sci. 72, Springer): 3-21.
1986 D. Anick.
On the homology of associative algebras. //
Transactions of the American Mathematical Society, v. 296, Nr. 2, 1986. - P. 87-112.
An article on theoretical backgrounds of Anick's resolution calculation. 

3. Publication of project participants (programming and software engineering)

Bibliographic data
1995 A. Colesnicov, L. Malahova.
The Bergman package shell: an example of interface to the interpreting system. //
Computer Science Journal of Moldova, v. 3, Nr. 2(8), 1995. - P. 111-122.
Software engineering problems of implementing shell for bergman.
1996  A. Colesnicov.
Implementation and usage of the Bergman package shell. //
Computer Science Journal of Moldova, v. 4, Nr. 2(11), 1996. - P. 260-276.
Details and problems on the shell for bergman implemented under MS-DOS.
1996 A. Colesnicov.
Some aspects of shell design and implementation.
Academy of Sciences of Moldova, Institute of Mathematics. Dissertation of the doctor in physics and mathematics, 1996. - 96 p.
Chapter 3 (pp. 46-70) describes new kinds of object interaction and aspects of their implementation using bergman as an example; actually, work over bergman was the source of introduced ideas.
2000 S.Cojocaru, A. Colesnicov, L. Malahova, S. Verlan.
Aspecte de securitate in versiunea Internet a sistemului de calcul simbolic Bergman./
Conferinta corpului didactico-stiintific "Bilantul activitatii stiintifice a USM pe anii 1998/99". Rezumatele comunicarilor, Chisinau. - P. 91-92. - In Romanian. - [Security aspects in the symbolic calculation system Bergman./ Teaching and research personnel conference "Results of scientific research at the State University of Moldova in 1998-1999". Report abstracts. - Kishinev.]
Problems of security in the bergman system is discussed.
2002 S.Cojocaru, A. Colesnicov, L. Malahova.
Network version of the computer algebra system bergman.
Computer Science Journal of Moldova. v.10, Nr.2, 2002, pp.216-222.
Network demo version of the computer algebra system bergman is described.
2005 S.Cojocaru, A. Colesnicov, L. Malahova.
Interfaces to symbolic computation systems: reconsidering experience of Bergman.
Computer Science Journal of Moldova. v.13, Nr.2, 2005, pp.232-244.
2006 S.Cojocaru, L. Malahova, A. Colesnicov.
Providing Modern Software Environments to Computer Algebra Systems.
In: Computer Algebra in Scientific Computing, Proceedings of the 9th International Workshop, CASC 2006, Chisinau, Moldova, September 11-15, 2006. LNCS, Springer, pp.120-140.
2007 S.Cojocaru.
Intelligent interfaces for Computer Algebra Systems.
Dr.Habilitat thesis. Chisinau, 2007 (in Romanian).

4. Other references (programming)

Bibliographic data
1990 G.L. Steele.
Common Lisp the Language. - 2nd edition . -
Woburn, MA: Digital Press, 1990. - 1035 p.
CLTL2 - a book defining Common Lisp. There is a WWW-version of the book.
1994 X3.226:1994. Programming Language Common Lisp [J13] ANSI Standard developed after CLTL2. There is a WWW-version of the standard.