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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<link rel="stylesheet" type="text/css" href="html.css" />
<title>JAS Project</title>
</head>
<body class="main">
<h1>Java Algebra System (JAS) Project </h1>
<p><strong>Introduction.</strong>
The Java Algebra System (JAS) is an object oriented, type safe and
multi-threaded approach to computer algebra.
JAS provides a well designed software library using generic types
for algebraic computations implemented in the Java programming language using the JVM runtime infrastructure.
The library can be used as any other Java software package or it can be
used interactively or interpreted through a jython (Java Python) or jruby (Java Ruby) front end,
there is also an Android App based on Ruboto (jruby for Android).
The focus of JAS is at the moment on commutative, solvable and non-commutative polynomials,
power series, Groebner bases, factorization, real and complex roots and applications.
By the use of Java as implementation language JAS is 64-bit and multi-core CPU
ready and can make use of mutiple CPUs where available.
</p>
<p>
The library contains at the moment of the following
<a name="package">packages</a>:
</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>
</dl>
<p>
This page contains documentation and the implementation for the new version
which is designed using type parameters and requires at least Java 6 (JDK 1.6).
It will also compile on Java 7 (JDK 1.7).
Older versions (no more supported) can be found here:
<a href="../jas-2.4">JAS 2.4</a>,
<a href="../jas-2.3">JAS 2.3</a>,
<a href="../jas-2.2">JAS 2.2</a>,
<a href="../jas-2.1">JAS 2.1</a>,
<a href="../jas-2.0">JAS 2.0</a>,
<a href="../jas.j15">JAS using JDK 1.5</a> and
<a href="../jas.j14">JAS using JDK 1.4</a>.
</p>
<h2><a name="docu">Documentation</a></h2>
<p>
For informations on how to get started with JAS see the <a href="guide.html" >users guide</a>.
For frequently asked question see <a href="faq.html" >FAQ</a>.
There is an <a href="gb-book.html">index of algorithms</a> for the book
<a href="http://www.springer.com/mathematics/book/978-0-387-97971-7" target="gbb">Gröbner bases</a>
and their JAS equivalents.
An <a href="algo-ca-book.html">index of algorithms</a> for the book
<a href="http://www.springer.com/computer/theoretical+computer+science/book/978-0-7923-9259-0"
target="gbb">Algorithms for Computer Algebra</a>
and their JAS equivalents is also available.
</p>
<p>
The JAS <a href="design.html" target="main" >API guide</a>
describes the interface and class design considerations and contains
an overview of the most important classes and methods. An online
Javadoc documentation of the API together with source code is
contained in the
<a href="doc/index.html" target="main" >API documentation</a>
(also available as <a href="jas-doc.jar" target="doc">jas-doc.jar</a>).
Some <a href="problems.html" target="main" >design
considerations</a> for the new generic version.
</p>
<p><a href="README" target="main" >README</a>
and
<a href="COPYING.jas" target="copy" >COPYING.jas</a> (GPL)
or
<a href="COPYING.lgpl.jas" target="copy" >COPYING.lgpl.jas</a> (LGPL)
</p>
<h3>Published papers and talks about JAS</h3>
<p>Design and experiences using MPJ and high speed InfiniBand networking for
algebraic computations are described in
<a nohref="" target="aina"
>Heinz Kredel,
<i>Distributed Gröbner bases computation with MPJ</i></a>,
to appear in proceedings of the EOOPS Workshop at
<a href="http://www.aina-conference.org/2013/">AINA-2013</a>,
March 25-28, 2013, Barcelona, Spain
(<a href="kredel/jas-gb-mpj-aina2013-slides.pdf" target="isc">slides</a>)
</p>
<p>Some ideas on categories and mixin composition in ScAS and JAS are presented in the poster
<a href="kredel/com-casc2012-poster.pdf" target="casc"
>Raphael Jolly, Heinz Kredel,
<i>Categories as classes and mixin composition</i></a>,
Poster at
<a href="http://www14.in.tum.de/CASC2012/">CASC 2012</a>,
September 3-6, 2012, Maribor, Slovenia
</p>
<p>A comparison of API interfaces for computer algebra is presented in the paper
<a href="http://doi.ieeecomputersociety.org/10.1109/WAINA.2012.158" target="aina"
>Heinz Kredel,
<i>Fostering Interoperability in Java-Based Computer Algebra Software</i></a>,
Proceedings FINA Workshop
<a href="http://www.aina-conference.org/2012/">AINA-2012</a>,
March 26-29, 2012, Fukuoka, Japan
(<a href="kredel/cas-inter-aina2012-slides.pdf" target="aina">slides</a>)
</p>
<p>The design of algebraic extension structures in JAS and ScAS is presented in the talk
<a href="http://www.springerlink.com/content/978-3-642-23567-2/#section=950349" target="casc"
>Raphael Jolly, Heinz Kredel,
<i>Algebraic Structures as Typed Objects</i></a>,
at the Workshop on Computer Algebra in Scientific Computing
<a href="http://www14.in.tum.de/CASC2011/">CACS 2011</a>,
Kassel, Germany, 2011.
(<a href="http://krum.rz.uni-mannheim.de/kredel/to-cas-casc2011-slides.pdf" target="casc">slides</a>)
</p>
<p>An early description of the JAS package for unique factorization domains
(greatest common divisors, square-free decomposition, factorization)
is contained in the article
<a href="http://dx.doi.org/10.1007/978-3-642-21046-4_5" target="adg"
>Heinz Kredel,
<i>Unique Factorization Domains in the Java Computer Algebra System</i></a>,
Special issue on Automated Deduction in Geometry,
Lecture Notes in Computer Science volume 6301, pages 86-115,
Springer, 2011
</p>
<p>The design of JAS and ScAS is presented together with examples in the talk
<a href="http://dx.doi.org/10.1007/978-3-642-15274-0_14" target="casc"
>Raphael Jolly, Heinz Kredel,
<i>Generic, Type-safe and Object Oriented Computer Algebra Software</i></a>,
at the Workshop on Computer Algebra in Scientific Computing
<a href="http://www14.in.tum.de/CASC2010/">CACS 2010</a>,
Tsakhkadzor, Armenia, 2010.
(<a href="http://krum.rz.uni-mannheim.de/kredel/oocas-casc2010-slides.pdf" target="casc">slides</a>)
</p>
<p>Performance meassurements for the distributed hybrid Gröbner
bases implementation are contained in the paper
<a href="http://arxiv.org/abs/1008.0011" target="arxiv"
><i>Parallel and distributed Gröbner bases computation in JAS</i></a>,
avaliable as
<a href="http://arxiv.org/abs/1008.0011" target="arxiv"
>arxiv:1008.0011</a>, 2010.
</p>
<p>The new distributed hybrid Gröbner bases implementation
is explained in the talk
<a href="http://doi.ieeecomputersociety.org/10.1109/CISIS.2010.26" target="ecds"
><i>Distributed hybrid Groebner bases computation</i></a>,
at the
<a href="http://www.cisis-conference.eu/" target="ecds">CISIS 2010</a>
Workshop on
<a href="http://voyager.ce.fit.ac.jp/conferences/ecds2010/" target="ecds"
>Engineering Complex Distributed Systems (ECDS 2010)</a>, Krakow.
(<a href="http://krum.rz.uni-mannheim.de/kredel/jas-ecds2010-slides.pdf" target="ecds">slides</a>)
</p>
<p>A description of the JAS comprehensive Gröbner bases package is be
contained in the talk
<a href="http://krum.rz.uni-mannheim.de/kredel/jas-ascm2009-slides.pdf" target="ascm"
><i>Comprehensive Gröbner bases in a Java Computer Algebra System</i></a>,
at the
<a href="http://gcoe.math.kyushu-u.ac.jp/ascm-macis2009/" target="ascm"
>Asian Symposium on Computers and Mathematics (ASCM 2009)</a>,
Fukuoka.
</p>
<p>Some unique factorization domain algorithms in JAS are contained
in the seminar presentation
<a href="http://krum.rz.uni-mannheim.de/kredel/ca-sem-2009.pdf" target="fmi"
>Tools for the integration of rational functions in Java</a>,
during the Computer-Algebra Seminar, University of Mannheim, FMI 2009
</p>
<p>More background information on the python scripting interface
for JAS and ScAS can be found in the article
<a href="http://de.arxiv.org/abs/0906.2315" target="arxivascm"
>Raphael Jolly, Heinz Kredel,
<i>Symbolic Script Programming for Java</i></a>,
avaliable as
<a href="http://de.arxiv.org/abs/0906.2315" target="arxivascm"
>arXiv:0906.2315v2</a>, 2009.
</p>
<p>The parallel and distributed Gröbner bases implementations are explained in
the talk
<a href="http://doi.ieeecomputersociety.org/10.1109/CISIS.2009.109" target="ecds"
><i>Distributed parallel Groebner bases computation</i></a>,
at the
<a href="http://www.cisis-conference.eu/" target="ecds">CISIS 2009</a>
Workshop on
<a href="http://voyager.ce.fit.ac.jp/conferences/ecds2009/" target="ecds"
>Engineering Complex Distributed Systems (ECDS 2009)</a>, Fukuoka.
(<a href="http://krum.rz.uni-mannheim.de/kredel/jas-ecds2009-slides.pdf" target="ecds"
>slides</a>)
</p>
<p>The Gröbner bases implementation of JAS is explained
in the seminar presentation
<a href="http://krum.rz.uni-mannheim.de/kredel/ca-sem-2008.pdf" target="fmi"
>Gröbner bases and applications in Java</a>,
during the Computer-Algebra Seminar, University of Mannheim, FMI 2008
</p>
<p>A description of the JAS greatest common divisor package is contained
in the talk
<a href="http://krum.rz.uni-mannheim.de/kredel/jas-adg2008-slides.pdf" target="adg"
><i>Multivariate Greatest Common Divisors in the Java Computer Algebra System</i></a>,
at the International Workshop on
<a href="http://adg2008.redlog.eu/" target="adg"
>Automated Deduction in Geometry (ADG 2008)</a>, Shanghai.
</p>
<p>Some background information on the python scripting interface
for JAS can be found in the article
<a href="http://de.arxiv.org/abs/0811.1061" target="arxivascm"
>Raphael Jolly, Heinz Kredel,
<i>How to turn a scripting language into a domain specific language for computer algebra</i></a>,
avaliable as
<a href="http://de.arxiv.org/abs/0811.1061" target="arxivascm"
>arXiv:0811.1061v1</a>, 2008.
Previous title was <i>Computer algebra in Java: libraries and scripting</i>.
</p>
<p>A comparison of JAS to other Computer Algebra Systems is contained
in the talk
<a href="http://krum.rz.uni-mannheim.de/kredel/jas-ascm2007-slides.pdf" target="ascm"
><i>Evaluation of a Java Computer Algebra System</i></a>,
at the
<a href="http://www.comp.nus.edu.sg/~ascm2007/" target="ascm"
>Asian Symposium on Computer Mathematics (ASCM 2007)</a>, Singapore.
<br />
It has been published as paper in
<a href="http://dx.doi.org/10.1007/978-3-540-87827-8_10" target="ascm"
>Heinz Kredel,
<i>Evaluation of a Java Computer Algebra System</i></a>,
Special issue <a href="http://dx.doi.org/10.1007/978-3-540-87827-8">Computer Mathematics</a>
of ASCM 2007 Revised and Invited Papers in
Lecture Notes in Computer Science, volume 5081/2008, pages 121-138,
Springer Berlin / Heidelberg
</p>
<p>An article
<a href="http://dx.doi.org/10.1016/j.scico.2007.07.010" target="scico"
><i>On a Java Computer Algebra System, its Performance and Applications</i></a>,
in
<a href="http://www.elsevier.com/wps/find/journaldescription.cws_home/505623/description"
title="http://www.sciencedirect.com/science/journal/01676423" target="scico"
>Science of Computer Programming (2008)</a>.
</p>
<p>At the
<a href="http://www.wifo.uni-mannheim.de/pppj2006/" target="a3l">PPPJ 2006 conference in Mannheim</a>
I presented the design of the JAS types, classes and implementation
"<a href="http://doi.acm.org/10.1145/1168054.1168075"
target="pppj"
>On the Design of a Java Computer Algebra System</a>"
<!--"http://krum.rz.uni-mannheim.de/kredel/jas-pppj2006.pdf"-->
(<a href="http://krum.rz.uni-mannheim.de/kredel/jas-pppj2006-slides.pdf" target="pppj"
>slides</a>).
</p>
<p>At the
<a href="http://www.a3l.org/" target="a3l">A3L conference in Passau, 2005</a>
I gave some background information on the development from MAS to JAS
"<a href="http://krum.rz.uni-mannheim.de/kredel/jas-a3l.pdf" target="a3l"
>A Systems Perspective on A3L</a>"
(<a href="http://krum.rz.uni-mannheim.de/kredel/jas-a3l-slides.pdf" target="a3l"
>slides</a>).
</p>
<p>The history of the JAS project can be found in the
<a href="jas-log.html" target="main">Web-Log</a>.
See also the <a href="related.html" target="main">related projects</a>
and <a href="acknowledge.html" target="main">credits</a>.
</p>
<h2><a name="downlo">Download</a>, installation and unit tests</h2>
<p>
See <a href="download.html" target="main">Download</a> page.
</p>
<h2><a name="eclipse-usage">Usage</a> with the JEclipse IDE</h2>
<p>
See <a href="download.html#eclipse" target="main">Download</a>
page.
</p>
<h2><a name="jython-usage">Usage</a> with the Jython interpreter</h2>
<p>
See <a href="download.html#jython" target="main">Download</a>
and <a href="guide.html" target="main">Users guide</a> pages.
</p>
<h4>jython examples</h4>
<p>Commutative:
<a href="examples/trinks.py" target="py">trinks.py</a>,
<a href="examples/katsura.py" target="py">katsura.py</a>
</p>
<p>Solvable:
<a href="examples/wa_32.py" target="py">wa_32.py</a>,
<a href="examples/u_sl_3_prod.py" target="py">u_sl_3_prod.py</a>,
<a href="examples/u_sl_3.py" target="py">u_sl_3.py</a>
</p>
<p>Modules:
<a href="examples/armbruster.py" target="py">armbruster.py</a>,
<a href="examples/syz.py" target="py">syz.py</a>,
<a href="examples/syzy2.py" target="py">syzy2.py</a>
</p>
<h2><a name="jruby-usage">Usage</a> with the JRuby interpreter</h2>
<p>
See <a href="download.html#jruby" target="main">Download</a>.
<!--and <a href="guide.html" target="main">Users guide</a> pages.-->
</p>
<h4>jruby examples</h4>
<p>Commutative:
<a href="examples/trinks.rb" target="rb">trinks.rb</a>,
<a href="examples/all_rings.rb" target="rb">all_rings.rb</a>,
<a href="examples/gbs.rb" target="rb">gbs.rb</a>
</p>
<h2><a name="ruboto-usage">Usage</a> of the Android App</h2>
<p>
See <a href="download.html#ruboto-irb-jas" target="main">Download</a>.
<!--and <a href="guide.html" target="main">Users guide</a> pages.-->
As the Android app is based on Ruboto (jruby IRB for Android) the
usage is the same as with JRuby. There is a "Scripts" button in the
app where all ruby examples can be accessed.
</p>
<p>The main Ruboto screen with the "trinks.rb" example and its output looks as follows.
</p>
<p>
<a href="images/device-2012-11-18-jas-trinks.png"
><img src="images/device-2012-11-18-jas-trinks-thumb.png" /></a>
<a href="images/device-2012-11-18-jas-trinks-out.png"
><img src="images/device-2012-11-18-jas-trinks-out-thumb.png" /></a>
<a href="images/device-2012-11-18-jas-trinks-out-big.png"
><img src="images/device-2012-11-18-jas-trinks-out-big-thumb.png" /></a>
</p>
<h2><a name="rungb">RunGB</a> Examples</h2>
<p>
The following are examples which can be executed with
the class edu.jas.application.RunGB. E.g. <br />
<code>java -cp .:log4j.jar:jas.jar:... edu.jas.application.RunGB <args></code>
</p>
<p>Commutative:
<a href="ring/gbks.jas" target="jas">gbks.jas</a>,
<a href="ring/katsura2.jas" target="jas">katsura2.jas</a>,
<a href="ring/katsura3.jas" target="jas">katsura3.jas</a>,
<a href="ring/katsura4.jas" target="jas">katsura4.jas</a>,
<a href="ring/katsura5.jas" target="jas">katsura5.jas</a>,
<a href="ring/katsura5s.jas" target="jas">katsura5s.jas</a>,
<a href="ring/katsura5w.jas" target="jas">katsura5w.jas</a>,
<a href="ring/katsura6.jas" target="jas">katsura6.jas</a>,
<a href="ring/katsura6w.jas" target="jas">katsura6w.jas</a>,
<a href="ring/katsura7.jas" target="jas">katsura7.jas</a>,
<a href="ring/katsura8.jas" target="jas">katsura8.jas</a>,
<a href="ring/rose.jas" target="jas">rose.jas</a>,
<a href="ring/trinks6.jas" target="jas">trinks6.jas</a>,
<a href="ring/trinks7.jas" target="jas">trinks7.jas</a>,
<a href="ring/vw.jas" target="jas">vw.jas</a>,
</p>
<p>Solvable:
<a href="ring/kw_18.jas" target="jas">kw_18.jas</a>,
<a href="ring/ore_t.jas" target="jas">ore_t.jas</a>,
<a href="ring/sgb.jas" target="jas">sgb.jas</a>,
<a href="ring/u_sl_3.jas" target="jas">u_sl_3.jas</a>,
<a href="ring/wa_1.jas" target="jas">wa_1.jas</a>,
<a href="ring/wa_32.jas" target="jas">wa_32.jas</a>,
<a href="ring/wa_34.jas" target="jas">wa_34.jas</a>,
<a href="ring/wa_39.jas" target="jas">wa_39.jas</a>,
<a href="ring/wa_41.jas" target="jas">wa_41.jas</a>,
<a href="ring/wa_61.jas" target="jas">wa_61.jas</a>
</p>
<hr />
<address><a name="contact"
href="mailto:kredel@at@rz.uni-mannheim.de">Heinz Kredel</a>
</address>
<p>
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