Fedora 22 Update: gap-pkg-sonata-2.8-1.fc22
updates at fedoraproject.org
updates at fedoraproject.org
Sat Oct 17 22:56:29 UTC 2015
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Fedora Update Notification
FEDORA-2015-fcccd099a2
2015-10-17 18:39:17.810588
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Name : gap-pkg-sonata
Product : Fedora 22
Version : 2.8
Release : 1.fc22
URL : http://www.algebra.uni-linz.ac.at/Sonata/
Summary : GAP package for systems of nearrings
Description :
SONATA stands for "systems of nearrings and their applications". It
provides methods for the construction and the analysis of finite
nearrings. A left nearring is an algebra (N;+,*), where (N,+) is a (not
necessarily abelian) group, (N,*) is a semigroup, and x*(y+z) = x*y + x*z
holds for all x,y,z in N.
As a typical example of a nearring, we may consider the set of all
mappings from a group G into G, where the addition is the pointwise
addition of mappings in G, and the multiplication is composition of
functions. If functions are written on the right of their arguments,
then the left distributive law holds, while the right distributive law
is not satisfied for non-trivial G.
The SONATA package provides methods for the construction and analysis of
finite nearrings.
1. Methods for constructing all endomorphisms and all fixed-point-free
automorphisms of a given group.
2. Methods for constructing the following nearrings of functions on a
group G:
- the nearring of polynomial functions of G (in the sense of
Lausch-NĂ¶bauer);
- the nearring of compatible functions of G;
- distributively generated nearrings such as I(G), A(G), E(G);
- centralizer nearrings.
3. A library of all small nearrings (up to order 15) and all small
nearrings with identity (up to order 31).
4. Functions to obtain solvable fixed-point-free automorphism groups on
abelian groups, nearfields, planar nearrings, as well as designs from
those.
5. Various functions to study the structure (size, ideals, N-groups, ...)
of nearrings, to determine properties of nearring elements, and to
decide whether two nearrings are isomorphic.
6. If the package XGAP is installed, the lattices of one- and two-sided
ideals of a nearring can be studied interactively using a graphical
representation.
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Update Information:
gap-pkg-sonata-2.8-1.fc23 - Corrected bugs in Is1AffineComplete and
IsDistributiveNearring gap-pkg-sonata-2.8-1.fc22 - Corrected bugs in
Is1AffineComplete and IsDistributiveNearring
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This update can be installed with the "yum" update program. Use
su -c 'yum update gap-pkg-sonata' at the command line.
For more information, refer to "Managing Software with yum",
available at https://docs.fedoraproject.org/yum/.
All packages are signed with the Fedora Project GPG key. More details on the
GPG keys used by the Fedora Project can be found at
https://fedoraproject.org/keys
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