C.7 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.mcs.kent.edu/,
http://www.can.nl/,... and the following list of books:

Text books on computational algebraic geometry
----------------------------------------------
* Adams, W.; Loustaunau, P.: An Introduction to Gro"bner Bases. Providence, RI,
AMS, 1996

* Becker, T.; Weisspfenning, V.:
Gro"bner 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

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

* Greuel, G.-M.; Pfister, G.: A SINGULAR Introduction to Commuative 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 normalization: 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

* Faug\`ere,
J. C.; Gianni, P.; Lazard, D.; Mora, T.: Efficient computation
of zero-dimensional
Gro"bner bases by change of ordering. Journal of Symbolic Computation, 1989

* Gra"be, H.-G.: On factorized Gro"bner bases, Univ. Leipzig, Inst. fu"r
Informatik, 1994

* Grassmann, H.; Greuel, G.-M.; Martin, B.; Neumann,
W.; Pfister, G.; Pohl, W.; Scho"nemann, 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

* Scho"nemann, 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

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
</font>

</body>
</html>
