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C.9 References
The Centre for Computer Algebra Kaiserslautern publishes a series of preprints
which are electronically available at
http://www.mathematik.uni-kl.de/~zca/Reports_on_ca .
Other sources to check are http://symbolicnet.org/ ,
http://www-sop.inria.fr/galaad/ , http://www.bath.ac.uk/~masjpf/CAIN.html ,... and the following list of books.
For references on non-commutative algebras and algorithms, see References (plural).
Text books on computational algebraic geometry
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Adams, W.; Loustaunau, P.: An Introduction to Gröbner Bases. Providence, RI,
AMS, 1996
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Becker, T.; Weisspfenning, V.:
Gröbner Bases - A Computational Approach to Commutative Algebra. Springer, 1993
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Cohen, H.:
A Course in Computational Algebraic Number Theory,
Springer, 1995
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Cox, D.; Little, J.; O'Shea, D.:
Ideals, Varieties and Algorithms. Springer, 1996
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Cox, D.; Little, J.; O'Shea, D.:
Using Algebraic Geometry. Springer, 1998
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Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry.
Springer, 1995
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Greuel, G.-M.; Pfister, G.:
A Singular Introduction to Commutative Algebra. Springer, 2002
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Mishra, B.: Algorithmic Algebra, Texts and Monographs in Computer Science.
Springer, 1993
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Sturmfels, B.: Algorithms in Invariant Theory. Springer 1993
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Vasconcelos, W.: Computational Methods in Commutative Algebra and Algebraic
Geometry. Springer, 1998
Descriptions of algorithms
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Bareiss, E.:
Sylvester's identity and multistep integer-preserving Gaussian elimination.
Math. Comp. 22 (1968), 565-578
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Campillo, A.: Algebroid curves in positive characteristic. SLN 813, 1980
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Chou, S.:
Mechanical Geometry Theorem Proving.
D.Reidel Publishing Company, 1988
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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
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Decker, W.; Greuel, G.-M.; de Jong, T.; Pfister, G.:
The normalisation: a new algorithm,
implementation and comparisons. Preprint, Univ. Kaiserslautern, 1998
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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
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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
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Gräbe, H.-G.: On factorized Gröbner bases, Univ. Leipzig, Inst. für
Informatik, 1994
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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)
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Greuel, G.-M.; Pfister, G.:
Advances and improvements in the theory of standard bases and
syzygies. Arch. d. Math. 63(1995)
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Kemper; Generating Invariant Rings of Finite Groups over Arbitrary
Fields. 1996, to appear in Journal of Symbolic Computation
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Kemper and Steel: Some Algorithms in Invariant Theory of Finite Groups. 1997
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Lee, H.R.; Saunders, B.D.: Fraction Free Gaussian Elimination for
Sparse Matrices. Journal of Symbolic Computation (1995) 19, 393-402
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Schönemann, H.:
Algorithms in SINGULAR,
Reports on Computer Algebra 2(1996), Kaiserslautern
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Siebert, T.:
On strategies and implementations for computations of free resolutions.
Reports on Computer Algebra 8(1996), Kaiserslautern
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Wang, D.:
Characteristic Sets and Zero Structure of Polynomial Sets.
Lecture Notes, RISC Linz, 1989
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