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<?xml version="1.0" encoding="iso-8859-1"?>
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<title>JAS Packages</title>
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<body class="main">
<h2>Java Algebra System (JAS) Packages</h2>
<p>
The JAS software library contains at the moment of the following <a
name="package">packages</a>. The relations and dependencies between
the packages are shown in figure 1.
</p>
<dl>
<dt>edu.jas.structure:</dt>
<dd>
contains interfaces for the most general algebraic structures like
<code>RingElem</code> and <code>RingFactory</code>.
</dd>
<dt>edu.jas.arith:</dt>
<dd>
contains classes for arithmetic in the basic coefficient rings like
<code>BigRational</code>, <code>BigInteger</code>,
<code>ModInteger</code>, <code>BigDecimal</code> or
<code>BigComplex</code>.
</dd>
<dt>edu.jas.poly:</dt>
<dd>
contains classes for commutative polynomial, solvable polynomial and
free non-commutative polynomial arithmetic like
<code>GenPolynomial</code>, <code>GenSolvablePolynomial</code>,
<code>GenWordPolynomial</code> and others such as
<code>AlgebraicNumber</code> and a polynomial parser
<code>GenPolynomialTokenizer</code>.
</dd>
<dt>edu.jas.vector:</dt>
<dd>
contains classes for vectors and lists of polynomials and solvable
polynomials like <code>GenVector</code> or <code>GenMatrix</code>.
</dd>
<dt>edu.jas.gb:</dt>
<dd>
contains classes for polynomial and solvable polynomial reduction,
Gröbner bases over fields and ideal arithmetic as well as
thread parallel and distributed versions of Buchbergers algorithm
like <code>ReductionSeq</code>, <code>GroebnerBaseAbstract</code>,
<code>GroebnerBaseSeq</code>, <code>GroebnerBaseParallel</code> and
<code>GroebnerBaseDistributedHybridEC</code>. There are also Gröbner
bases in polynomial rings over principal ideal domains and Euclidean
domains, so called D- and E-Gröbner bases,
e.g. <code>EGroebnerBaseSeq</code>. New are Gröbner bases in
free non-commutative polynomial rings over (skew) fields,
see <code>WordGroebnerBaseSeq</code>.
</dd>
<dt>edu.jas.gbmod:</dt>
<dd>
contains classes for module Gröbner bases and syzygies over
polynomials and solvable polynomials like
<code>ModGroebnerBase</code> or <code>SolvableSyzygy</code>.
</dd>
<dt>edu.jas.application:</dt>
<dd>
contains classes with applications of Gröbner bases such as ideal
intersections and ideal quotients implemented in <code>Ideal</code>
or <code>SolvableIdeal</code>. Comprehensive Gröbner bases for
polynomial rings over parameter rings are contained in class
<code>ComprehensiveGroebnerBaseSeq</code>. Latest additions are
zero and arbitrary dimensional radical-, irreducible-, prime- and
primary-decomposition implemented in class <code>Ideal</code>.
</dd>
<dt>edu.jas.ufd:</dt>
<dd>
contains classes for unique factorization domains. Like the
interface <code>GreatestCommonDivisor</code>, the abstract class
<code>GreatestCommonDivisorAbstract</code> and various
implementations, e.g. polynomial remainder sequences and modular
algorithms. The package now contains factorization algorithms for
univariate polynomials over several coefficient rings: modulo primes
in class <code>FactorModular</code>, over integers in class
<code>FactorInteger</code>, over rational numbers in class
<code>FactorRational</code> and over algebraic numbers in class
<code>FactorAlgebraic<C></code>.
</dd>
<dt>edu.jas.gbufd:</dt>
<dd>
contains classes for Gröbner base computation using classes
from the <em>edu.jas.ufd</em> package for polynomial
coefficients. The main classes deal with pseudo reduction
<code>PseudoReduction</code>, <code>PseudoReductionSeq</code> and
greatest common divisors computation on coefficients
<code>GroebnerBasePseudoSeq</code>. Multiplicative sets of
polynomials with several simplifications, e.g. maintaining co-prime
factors or co-prime and squarefree factors, are contained in classes
<code>MultiplicativeSet</code>, <code>MultiplicativeSetCoPrime</code>
or <code>MultiplicativeSetSquarefree</code>. Also contained are
Gröbner bases for polynomial rings over regular rings (direct
products of fields or integral domains) in
<code>RGroebnerBaseSeq</code> and <code>RGroebnerBasePseudoSeq</code>.
</dd>
<dt>edu.jas.root:</dt>
<dd>
contains classes for real root computations. Like the
interface <code>RealRoots</code>, the abstract class
<code>RealRootsAbstract</code> and at the moment of a single
implementation based on Sturm sequences <code>RealRootsSturm</code>.
The package further contains an implementation for real algebraic numbers
<code>RealAlgebraicNumber</code> with a corresponding factory
<code>RealAlgebraicRing</code>.
For complex root isolation there are <code>ComplexRoots</code> interface,
<code>ComplexRootsAbstract</code> and <code>ComplexRootsSturm</code> classes.
The implementation provides an exact infallible method which follows
the numeric method of Wilf. It uses Sturm sequences following the
Routh-Hurwitz Method to count the number of complex roots within a
rectangle in the complex plane.
There is also an implementation for complex algebraic numbers
<code>ComplexAlgebraicNumber</code> with a corresponding factory
<code>ComplexAlgebraicRing</code>.
</dd>
<dt>edu.jas.ufdroot:</dt>
<dd>
contains classes for factorization in structures used in root
computation, for example <code>FactorRealAlgebraic</code>.
</dd>
<dt>edu.jas.ps:</dt>
<dd>
contains univariate and multivariate power series arithmetic
in classes <code>UnivPowerSeries</code> and <code>MultiVarPowerSeries</code>.
There is an initial implementation of Mora's tangent cone reduction algorithm
in class <code>ReductionSeq</code> and a standard bases computation in
<code>StandardBaseSeq</code> with method <code>STD()</code>.
</dd>
<dt>edu.jas.integrate:</dt>
<dd>
contains methods for the elementary integration of univariate rational functions.
The main class is <code>ElementaryIntegration</code> with method
<code>integrate()</code>.
</dd>
<dt>edu.jas.util:</dt>
<dd>
contains further utilities for parallel and distributed computations
like <code>ThreadPool</code>, <code>DistThreadPool</code> or
<code>DistHashTable</code>. Part of this package has become obsolete
with JDK 1.5.
</dd>
<dt>edu.jas.fd:</dt>
<dd>
contains classes for solvable polynomials rings as (non-unique)
factorization domains. There are methods for polynomial pseudo
remainder computation over Ore domains in class <code>FDUtil</code>.
Further, methods for common divisors are included, but not yet
finished.
<!-- Methods provided with interface
<code>GreatestCommonDivisor</code> are e.g. greatest common divisors
<code>gcd()</code>, primitive part <code>primitivePart()</code>.-->
</dd>
</dl>
<p align="center">
<!--img src="../images/PackageOverview.png" width="50%" alt="Static package structure overview" /-->
<img src="../images/jas-pack-over.png" width="80%"
alt="Static package and component structure overview" />
<br />
<b>Figure 1:</b> Package and component structure overview
</p>
<hr />
<address><a name="contact"
href="mailto:kredel@at@rz.uni-mannheim.de">Heinz Kredel</a>
</address>
<p>
<!-- Created: Thu Jun 4 23:42:20 CEST 2005 -->
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Last modified: Mon Mar 28 23:49:24 CEST 2016
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