1\chapter{CALI: Computational Commutative Algebra}
2\label{CALI}
3\typeout{{CALI: Computational Commutative Algebra}}
4
5{\footnotesize
6\begin{center}
7Hans-Gert Gr\"abe \\
8Institut f\"ur Informatik, Universit\"at Leipzig\\
9Augustusplatz 10 -- 11\\
1004109 Leipzig, Germany \\[0.05in]
11e--mail: graebe@informatik.uni-leipzig.de
12\end{center}
13}
14
15\ttindex{CALI}
16
17This package contains algorithms for computations in commutative algebra
18closely related to the Gr\"obner algorithm for ideals and modules.  Its
19heart is a new implementation of the Gr\"obner algorithm that also allows
20for the computation of syzygies.  This implementation is also applicable to
21submodules of free modules with generators represented as rows of a matrix.
22As main topics CALI contains facilities for
23\begin{itemize}
24\item defining rings, ideals and modules,
25
26\item computing Gr\"obner bases and local standard bases,
27
28\item computing syzygies, resolutions and (graded) Betti numbers,
29
30\item computing (now also weighted) Hilbert series, multiplicities,
31independent sets, and dimensions,
32
33\item computing normal forms and representations,
34
35\item computing sums, products, intersections, quotients, stable
36quotients, elimination ideals etc.,
37
38\item primality tests, computation of radicals, unmixed radicals,
39equidimensional parts, primary decompositions etc. of ideals and
40modules,
41
42\item advanced applications of Gr\"obner bases (blowup, associated graded
43ring, analytic spread, symmetric algebra, monomial curves etc.),
44
45\item applications of linear algebra techniques to zero dimensional
46        ideals, as {\em e.g.\ }the FGLM change of term orders, border bases
47        and affine and projective ideals of sets of points,
48
49\item splitting polynomial systems of equations mixing factorisation and
50the Gr\"obner algorithm, triangular systems, and different versions of the
51extended Gr\"obner factoriser.
52
53\end{itemize}
54
55There is more extended documentation on this package elsewhere, which
56includes facilities for tracing and switches to control its behaviour.
57
58