Singular

C.9 References

The Centre for Computer Algebra Kaiserslautern publishes a series of preprints which are electronically available at https://www.singular.uni-kl.de/reports. Other sources to check are http://symbolicnet.org/, http://www-sop.inria.fr/galaad/,... and the following list of books.

For references on non-commutative algebras and algorithms, see References (plural).

Text books on computational algebraic geometry

• Adams, W.; Loustaunau, P.: An Introduction to Gröbner Bases. Providence, RI, AMS, 1996

• Becker, T.; Weisspfenning, V.: Gröbner Bases - A Computational Approach to Commutative Algebra. Springer, 1993

• Cohen, H.: A Course in Computational Algebraic Number Theory, Springer, 1995

• Cox, D.; Little, J.; O'Shea, D.: Ideals, Varieties and Algorithms. Springer, 1996

• Cox, D.; Little, J.; O'Shea, D.: Using Algebraic Geometry. Springer, 1998

• Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry. Springer, 1995

• Greuel, G.-M.; Pfister, G.: A Singular Introduction to Commutative Algebra. Springer, 2002

• Mishra, B.: Algorithmic Algebra, Texts and Monographs in Computer Science. Springer, 1993
• Sturmfels, B.: Algorithms in Invariant Theory. Springer 1993

• Vasconcelos, W.: Computational Methods in Commutative Algebra and Algebraic Geometry. Springer, 1998

Descriptions of algorithms

• Bareiss, E.: Sylvester's identity and multistep integer-preserving Gaussian elimination. Math. Comp. 22 (1968), 565-578

• Campillo, A.: Algebroid curves in positive characteristic. SLN 813, 1980

• Chou, S.: Mechanical Geometry Theorem Proving. D.Reidel Publishing Company, 1988

• Decker, W.; Greuel, G.-M.; Pfister, G.: Primary decomposition: algorithms and comparisons. Preprint, Univ. Kaiserslautern, 1998. To appear in: Greuel, G.-M.; Matzat, B. H.; Hiss, G. (Eds.), Algorithmic Algebra and Number Theory. Springer Verlag, Heidelberg, 1998

• Decker, W.; Greuel, G.-M.; de Jong, T.; Pfister, G.: The normalisation: a new algorithm, implementation and comparisons. Preprint, Univ. Kaiserslautern, 1998

• Decker, W.; Heydtmann, A.; Schreyer, F. O.: Generating a Noetherian Normalization of the Invariant Ring of a Finite Group, 1997, to appear in Journal of Symbolic Computation

• Faugère,J. C.; Gianni, P.; Lazard, D.; Mora, T.: Efficient computation of zero-dimensional Gröbner bases by change of ordering. Journal of Symbolic Computation, 1989

• Gräbe, H.-G.: On factorized Gröbner bases, Univ. Leipzig, Inst. für Informatik, 1994

• Grassmann, H.; Greuel, G.-M.; Martin, B.; Neumann, W.; Pfister, G.; Pohl, W.; Schönemann, H.; Siebert, T.: On an implementation of standard bases and syzygies in SINGULAR. Proceedings of the Workshop Computational Methods in Lie theory in AAECC (1995)

• Greuel, G.-M.; Pfister, G.: Advances and improvements in the theory of standard bases and syzygies. Arch. d. Math. 63(1995)

• Kemper; Generating Invariant Rings of Finite Groups over Arbitrary Fields. 1996, to appear in Journal of Symbolic Computation

• Kemper and Steel: Some Algorithms in Invariant Theory of Finite Groups. 1997

• Lee, H.R.; Saunders, B.D.: Fraction Free Gaussian Elimination for Sparse Matrices. Journal of Symbolic Computation (1995) 19, 393-402

• Schönemann, H.: Algorithms in SINGULAR, Reports on Computer Algebra 2(1996), Kaiserslautern

• Siebert, T.: On strategies and implementations for computations of free resolutions. Reports on Computer Algebra 8(1996), Kaiserslautern

• Wang, D.: Characteristic Sets and Zero Structure of Polynomial Sets. Lecture Notes, RISC Linz, 1989