For a detailed list of the latest changes see the Git change log.
BigQuaternion polynomial coefficients.
Fixed a left-right bug in solvable polynomials monic()
method. (left and right monic must be distinguished although the
inverse of the leading base coefficient is a left and right inverse.)
Fix to leftMonic() where required.
Adjust polynomial reverse() method with using
conjugate() on coefficients. More tests for Ore
conditions for polynomials with quaternion coefficients.
Fixed default implementations in interface MonoidElem for
left, right and two-sided operations by throwing exceptions when not
correctly overriden.
inner*Product() to interior*Product()
since this seems to be the correct translation. Remove and cleanup
unsued experimental code and small bug fixes. Add file with simple
NCSS report summary.
GenExteriorPolynomial and
GenExteriorPolynomialRing. With exterior multiplication
and inner left / right multiplication methods. Also included are
determinant and resultant methods via exterior algebra algorithms.
Add new characteristic polynomial method charPolynomial()
using Faddeev-LeVerrier algorithm in class
GenPolynomialRing. Add trace()method in
class GenMatrix. Fixed many spelling errors, small bug
fixes and cleanups.
SolvableIdeal to represent such ideals. Time-limited
stop for long running or infinite word Groebner Base
computations. Additionally counter stop configuration for long
running Kronecker factorization algorithm cases, using Pull
request 32.
Fix bugs in ExpVector subclasses, in methods
setVal(), this resolves issue
30. Fix in SquarefreeFieldCharP for polynomial
1. Fixes in SquarefreeFieldChar0 and
SquarefreeRingChar0 for recursion to polynomial content.
Fix in PolyUfdUtilTest of
evaluationPoints() to ensure squarefree input.
Added more unit test cases to improve code coverage of statement and
expression tests. Further cleanups and bug fixes (see Git log).
Gen*PolynomialRing constructors
and method getZERO() with respect to Java memory model
for problems appearing with Java OpenJDK version "11.0.15",
2022-04-19 and still in "17.0.4", 2022-07-22. Added some unit tests
to improve test coverage, for example RunGB,
RunSGB, IntegerProgram,
StandardBaseSeq, jas.kern utilities or
GenMatrix and more. Added selectable
Quotient normalizations, but only
QuoNorm.normDenLead works in other parts of JAS. Other
normalizations must be checked and code fixed (see issue
29). Fix bug in UnivPowerSeries method
reductum(). Fix bug in ExpVector
constructor with respect to hashCode(). Verified again
that JAS can be compiled and run with Java 17(.0.3) and jruby 9.2.14
and jython 2.7.2.
derivative methods. Taylor
series expansion for polynomial quotients. Some code moved from
edu.jas.ps and edu.jas.vector to
edu.jas.ufd to clear package dependency cycles. Pade
approximation from Taylor series, in particular for polynomial
quotients.
extGB() and inverse() for d-
and e-Groebner Bases in classes DGroebnerBaseSeq and via
new reduction methods automatically in
EGroebnerBasesSeq. Tests can reuse methods
isReductionMatrix() and
isMinReductionMatrix() from
GroebnerBaseAbstract. Added missing methods for
normalform, S-polynomial, G-Polynomial with recording in
DReduction, EReduction interfaces and
DReductionSeq, EReductionSeq classes. For
scripting the respective methods eExtGB,
iseExtGB, eInverse and
iseInverse have been added to Ideal
respectively SimIdeal. JAS can be compiled and run with
Java 17, but no switch to Java 17 class files at the moment. The JAS
debian package is build on Debian 11 bullseye with Java 17 and Jython
2.7.2, so jas.py and jas -py scripts can be
used again in Debian.
ComplexRootsAbstract. complexRoots(). Revisit recursive
solvable polynomial algorithms and activate some missing test cases,
resolve commutator table related todos, add missing right-multiply
using methods from to do list
(SolvablePseudoReduction. rightNormalform,
rightNormalformRecursive,
rightNormalformFactor). Related fixes and extensions in
scripting frameworks. Update and revision of JAS web documentation.
ufd.PolyUfdUtil and
ufd.FactorModularBerlekamp and are called
contructQmatrix and baseFactorsSquarefree.
There are sub-methods for the small and big primes algorithm
variants. Berlekamp factorization algorithm is now the default for
polynomials over finite fields (algebraic extensions of prime
fields), defined in FactorFactory for this case.
GenMatrix is equiped with an inverse method
with the help of LinAlg.decomposeLU. The extension field
builder has a new method matrixExtension to provide
matrix extension rings. A sparser form of a given row echelon matrix
is computed by rowEchelonFormSparse. Some other small
fixes and improvements.
decompositionLU, solveLU,
determinantLU, inverseLU,
nullSpaceBasis, rowEchelonForm and
rankRE. They are contained in class
vector.LinAlg. Corresponding methods and examples for
JRuby and Jython created. Methods contFrac and
contFracApprox for continued fraction computation for
JRuby and Jython. Further cleanups, improvements and small bug fixes.
chineseRemainderTheorem,
isChineseRemainder and CRTInterpolation in
class PolyGBUtil for computing Chinese remainders for
polynomials, polynomial interpolation and test. Together with
corresponding methods and examples for JRuby and Jython. New class
SquarefreeFieldChar0Yun with Yun's square-free
decomposition algorithm. This is now the default algorithm in
square-free factory methods since it is slightly faster. Other small
fixes and improvements. Fix github deployment.
factors in class PolyUfdUtil for
rational functions of class Quotient. New methods
subRing and subRingMember in class
PolyGBUtil for computing GB generators for polynomial
subrings and membership tests. Together with analogous methods and
examples for JRuby and Jython. More small improvements and fixes.
excludeZero method. Squarefree part fix in
edu.jas.root. ComplexRootsAbstract.
Delegate compareTo from edu.jas.arith.
BigDecimal to java.math.
BigDecimal. More unit tests for missing cases. Further
code cleanup by Eclipse rules, small fixes and improvements.
mathn module for rational number
input had to be replaced. JavaDoc is now generated in HTML5, tags and
entities in method descriptions fixed. Internal calls to deprecated
PseudoRemainder methods are replaced. Termination
detection in GreatestCommonDivisorModEval was fixed. A
new parsing method for WordPolynomials was added. The
SymbolicData test are deactivated as its servers
have been terminated. Further cleanups, improvements and small bug
fixes.
hashCode, potential int, long overflows and
parameter typos in Javadoc.
Note: From JAS version 2.7 on, the deprecated methods and
classes might be removed.
lintian
errors. Remove Javadoc reserved @usage tag from source
and cleanup comments. Further cleanups and bug fixes.
FF(p,n) in JAS scripting
interfaces.
Update to Jruby 9.1.7 in JRuby interface to JAS. Installation of
configparser necessary, require mathn and
require Matrix in some place. Other small improvements
and bug fixes.
mapOnStream() methods implemented operating on
(parallel) stream map methods of polynomial monomials. Performance
seems to be worse by factors compared to non stream method variants.
Provide a spliterator over monomials for polynomials via a new
spliterator() method and class
PolySpliterator.
Polynomial absolute norm implemented and some improvements for square
roots.
Converted the usages of edu.jas.util.ThreadPool to
java.util.concurrent.ThreadpoolExecutor.
Checked that JAS compiles and runs with Java 11 (without module
definition). Bug fixes and other small improvements.
ModInt and
ModIntRing based on int integers.
Performance improvements for polynomial sum() method for
polynomials with unbalanced size. sqrt()
approximation for BigRational and tests fixed for
complex abs() methods.
Further small improvements and bug fixes.
mylog.jar, nolog.jar and
droidlog.jar are no more working and obsolet.
Add further missing methods for non-commutative
WordIdeal. Small improvements and bug fixes.
edu.mas. Cleanup
todo comments. Improve types of return values. Checked that JAS
compiles and runs with Java 10. Bug fixes and other small
improvements.
FactorRational,
GreatestCommonDivisorModular and
GreatestCommonDivisorModEval. Thanks to Stanislav
Poslavsky from the Redberry project for pointing out these issues.
Several Findbugs issues have been fixed, for example, insufficient
synchronization. Other bug fixes and small improvements.
MonoidElem
with commutative default implementations. The Ore condition for
StarRingElem classes can be computed. Quaternion classes
are refactored for separate Ring and integral quaternion
classes. Bug fixes and small improvements.
There is now a Maven compatible repository with JAS at
http://krum.rz.uni-mannheim.de/maven-repository/.
java.math. Main method is factors() in
class PrimeInteger.
Cyclotomic polynomial construction and decomposition, similar to
Sympy. Improvements in Gröbner walk implementation to make
source and target term order selectable. Small improvements and bug
fixes.
GroebnerBaseWalk. Extensions to existing code for marked
polynomials used in Gröbner walk.
Bug fixes and small improvements, more use of Java 8 features.
RootFactory methods.
New methods in class
RootFactory to compute both the real and complex
algebraic roots with algebraicRoots(), method
rootsOfUnity() to filter roots of unity, and methods
rootRefine() and decimalRoots() to compute
approximations of real and complex roots. The method
rootReduce() in RootFactoryApp helps to
construct common field extensions via primitive element
computations. The algorithms are also accessible via the scripting
interfaces under the same names.
Dockerfile to construct a standalone JAS scripting application.
edu.jas.fd.
Use (Java 8) method power() from MonoidElem
where possible. Further bug fixes and small improvements.
edu.jas.fd. New class
SGCDFactory with methods getImplementation()
and getProxy() to obtian suitable common divisor
implementations based on the coefficient ring of the polynomials.
New class SGCDParallelProxy to run two common divisor
implementations in parallel and take the result of the first finished
one (compare to GCDProxy).
The solvable left and right common divisor algorithms are now used in
SolvableLocalResidue, SolvableLocal and
SolvableQuotient to reduce the fractions to lower terms.
Refactoring some classes to edu.jas.fd package.
Bug fixes, small improvements and use of more Java 8 features.
GroebnerBaseF5SigSeqIter,
GroebnerBaseGGVSigSeqIter,
GroebnerBaseArriSigSeqIter and are selectable via
GBAlgorithmBuilder methods F5(),
GGV() and Arri(). Some of the new methods
use Java 8 constructions.
GBAlgorithmBuilder expressions can be used in
RunGB using the parameter
build=string. Started with new methods
bitLength() for coefficient arithmetic classes and
polynomials. Some bug fixes and small improvements. Debian package
improved.
GBDist,
GBDistHybrid, GroebnerBaseDistributed,
GroebnerBaseDistributedHybrid, the method
divideAndRemainder of several classes and some other
unused methods. Code cleanup and unified logger declaration.
New class IntegerProgram to solve integer optimization
problems via Gröbner bases. Tests and some fixes for
compatibility of term orders with Sage, Singular and
Mathematica. Several small bug fixes and improvements. Print JAS
version in jython and jruby modules. Iterative Gröbner base
algorithms selectable in GBAlgorithmBuilder.
GreoebnerBaseParIter. Names for Sage, Singular and
Mathematica term orders defined in class
TermOrderByName. Better separation of ExpVector from
TermOrder. Missing polynomial methods weightDegree()
and leadingWeightPolynomial() added.
Switched to Junit 4.12 and use the timeout option on long running
tests. Small improvements, changes and bug fixes.
GreoebnerBaseSeqIter. Term orders with weight matrix are
now usable from jython and jruby via the PolyRing
constructors. More names for defined and implemented term orders in
class TermOrderByName.
Improved unit tests and further small changes and bug fixes.
edu.jas.gbmod to the packages edu.jas.gb
and edu.jas.gbufd to cut the package dependency cycles.
Changes to the organization and contents of the Web pages.
Note: The next release will eventually use Java 8 features and
drop Java 7 support, moreover many deprecated methods and classes
may be removed.
valueOf methods in polynomial ring classes to
construct polynomials from coefficients and exponents or words. Check
for missing Ore condition usage in solvable reduction algorithms. Use
Ore condition in solvable pseudo reduction algorithms for solvable
polynomial coefficients. There is a new class
GreatestCommonDivisorFake in which gcd
methods always return 1.
Bugfix in two-sided Gröbner bases right coefficient multipliers.
Fixed the polynomial parser to accept some more
ASCIIMath expressions. Small improvements and
refactoring of the HTML documentation.
SolvableIdeal. New right module Gröbner bases and
right module syzygies. Syzygy methods added to scripting interfaces.
Performance improvements for solvable polynomial multiplication and
polynomial reduction. Small bug fixes and improvements.
Moved one JAS repository from Google code to
GitHub
since Google code will be discontinued.
SGBProxy and
SGBFactory.
Refactor term order optimization methods to naturally / better suited
classes. Make use of ModLong classes and the improved
RingFactory parser in the scripting interfaces. Remove
the dependency on Junit from the src-tree. Some more small fixes and
improvements. Ivy resolve task for log4j and junit libraries.
WordResidue and
WordResidueRing for residue classes modulo twosided
ideals WordIdeal in word polynomial rings (free
non-commutative algebas). Fix missing critical pairs to consider in
word Gröbner bases. Code cleanup and small fixes and
improvements.
RingElem class in the jython and Ruby script interface.
Small improvements for recursive pseudo division Gröbner bases
and corrections, new Junit test cases.
PolyRing(QQ(),"x,y") are directly available as script
variables x, y with out calling r.gens().
Improved jas script to run also under Debian with
MathLibre. Small updates, new diagrams and pictures.
BigDecimalComplex for complex floating point
arithmetic. Some fixes and other small improvements for floating
point calculations.
The Java bytecode of JAS is now dual licenced under the
Apache 2.0 licence to allow its usage in Android projects.
edu.jas.fd is now in a usable condition. The definition
of greatest common divisor has changed slightly and left and right
gcds are now distinguished. Various improvements, refactorings and
bug fixes. Detection of wrong method dispatching by JRE in
GenSolvablePolynomial and GenPolynomial.
Cleanup of Gröbner base packages. Completion of GB class
constructors with PairList parameters. New parallel
recursive polynomial Gröbner base computation. Refactoring of
Quotient coefficient cases. Handle more cases in
GBAlgorithmBuilder and GBFactory. jython
scripting GB with selectable sig-based GB algorithm. Unit tests for
the new algorithms.
PrimeList. Restore and keep
MPJ Express compatibility and test cases.
edu.jas.fd for solvable polynomial common
divisor computation. It will contain algorithms for (non-unique)
factorization domains. There are methods for polynomial pseudo
remainder computation over Ore domains in class FDUtil.
Further, methods for common divisors are included, but not yet
finished. Converge and cleanup MPJ and MPI implementations. Added
Javadocs for JLinAlg adapter.
SolvableLocalResidue as
solvable quotient field modulo an ideal. New generic solvable
polynomials QLRSolvablePolynomial with abstracted generic
coefficients from solvable quotient, local or local-residue rings.
Implemented corresponding interfaces QuotPair and
QuotPairFactory in respective classes.
Adjust and extend scripting examples for the new classes.
Removed differences and clean-up different versions of
Run*GB stand alone Gröbner base programs.
leftSimplifier().
Some code refactoring to break package dependency cycles. Fixed, cleaned
and worked-around some more Findbugs and
Eclipse issues. Dropped Java-5 compatibility in most
places.
ibvdev InfiniBand device), MPJ is thread-safe for
niodev Java NewIO device. As work-around the transport
layer of both versions is split to allow selection of TCP/IP sockets
or MPI/MPJ channels for transport. The channels and distributed hash
tables have been simplified for both MPJ and MPI. Socket based
distributed hash table now implements the clear()
method. This caused unspecific errors in iterated distributed
Gröbner base computations. Simplified solvable
multiplication. Fixes and improvements to Jython and JRuby scripts.
LocalSolvablePolynomialRing and
LocalSolvablePolynomial. New scripting examples for
solvable polynomials with solvable local coefficients. Refactoring
for non-commutative relation handling of solvable polynomials with
interface RelationGenerator. Fixed and cleanup some
more Findbugs and Eclipse issues. Several fixes
and improvements for jruby of Android.
ResidueSolvablePolynomialRing and
ResidueSolvablePolynomial. Methods to compute
annihilators with respect to ideals and solvable ideals. New
scripting examples for solvable polynomials with solvable residue
coefficients. Fixed associativity of solvable multiplication by
considering all Ore conditions.
RecSolvablePolynomialRing and
RecSolvablePolynomial. New solvable polynomial rings
with solvable quotient coefficients are avaliable in classes
QuotSolvablePolynomialRing and
QuotSolvablePolynomial. This rings feature
non-commutative multiplication of variables with coefficients.
New scripting examples for recursive solvable polynomial rings and
solvable polynomials with solvable quotient coefficients.
SolvableIdeal, and new structures for solvable
polynomial rings in classes SolvableQuotient,
SolvableResidue and the corresponding factories
SolvableQuotientRing,
SolvableResidueRing. There is a new theme for Ruby rdoc
documentation and the scripts have been adapted to a newer version of
jruby (1.7.3). Further small fixes and improvements.
GBFactory and added new option to select Gebauer &
Möller critical pair handling in
GBAlgorithmBuilder. Switch to DECIMAL128 as default in
BigDecimal. Improved
GreatestCommonDivisorHensel by using integer evaluation
points and other optimizations.
scaleSubtractMultiple(b, g, a, e, S) to compute the expression b
xg this - a xe S in one rush. There is now first
version of an Android App. The JAS App uses its JRuby
scripting interface and runs within the Ruby IRB Android App
Ruboto.
GroebnerBaseDistributedMPJ for the pure distributed
version and GroebnerBaseDistributedHybridMPJ for the
distributed and multi-threaded version.
WordGroebnerBase
and new classes WordGroebnerBaseAbstract and
WordGroebnerBaseSeq. jython and jruby access to
non-commutative polynomials in WordPolyRing and
WordIdeal. Improved selection of (commutative)
Gröbner base algorithm implementations in class
GBAlgorithmBuilder. For example in case of rational
number coefficients a fraction free algorithm with optimization of
the variable order can be requested by gbab.fractionFree()
.optimize() .build().
Clonable from Element and renamed
clone() to copy(). New classes for free
non-commutative associative rings in GenWordPolynomial
and GenWordPolynomialRing.
CharacteristicSetWu. Unit tests are in
CharSetTest. jython and jruby script access to
characteristic set algorithms in methods CS(),
isCS(), csReduction(). Small fixes and
improvements.
PolyRing are now
injecting the polynomial ring variables into the top level
interpreter environment by default. New class
GroebnerBaseFGLM to compute a Gröbner base
according to the "FGLM" algorithm. It computes a Gröbner base
with respect to a graded term order and then constructs the
Gröbner base with respect to the requested term order via linear
algebra in the residue class ring. Changes from '{}' to
'()' in GenPolynomial to string conversion.
New launcher shell script jas. Small fixes, improvements
and a missing method implemented and in PolyUtilApp.
edu.jas.ufdroot to remove cyclic
package dependencies again. Improved selection of factorization
implementations in FactorFactory classes and better
suited constructors of the factorization implementations. Small
fixes and improvements.
PolyGBUtil. Small fixes and improvements.
GreatestCommonDivisor* classes in the
edu.jas.ufd package. Fixed ModLong to
ModInteger conversion. Small fixes, improvements and
refactorings of methods to right classes.
jas.py in JAS for the
required methods. More JRuby examples. Small improvements and
fixes.
factorsSquarefreeHensel() in class
FactorInteger. Improved multivariate Hensel lifting in
class HenselMultUtil. Small improvements and fixes.
complexAlgebraicRoots() in class
PolyUtilApp. Simple isolating interval refinement for
real and complex roots. Alternative factoring of univariate
polynomials over algebraic number fields via prime ideal
decomposition in class FactorAlgebraicPrim. Improved
parsing of complex numbers. Forced term orders in some situations
and further small improvements and fixes.
RealAlgebraicNumber and RealAlgebraicRing
in package edu.jas.application. New experimental
RootFactory with methods to compute complex roots for
polynomials with coefficients in some complex algebraic extension
field of the rational numbers. Uses the respective classes form
package edu.jas.root in a recursive setting.
New generic factorization classes FactorRealAlgebraic
and FactorRealReal. Small improvement for reduced / minimal
Gröbner base computation.
ResidueRing. Jruby and Jython versions and examples of
the extension field builder. Small improvements and bug fixes for
latest Eclipse and Java 1.7 version.
ExtensionFieldBuilder with methods for algebraic and
transcendental field extensions. Improvements in real and complex
algebraic numbers. Improved polynomial parser for recursive
representations. Small bug fixes.
HenselMultUtil for multivariate Hensel lifting.
Will be used in polyomial factorization in the future.
Some parts of greatest common divisor using multivariate Hensel lifting.
The JAS source (r3408) compiles on Apache Harmony 6.0 (r991881). The
unit tests pass with the exception of test cases involving object
serialization.
toScript() methods rewritten to reflect the Ruby
language requirements and to differentiate between Ruby and Python.
More precise exceptions for modular computations to return also the
discovered factors.
GenPolynomialTokenizer
to RingFactoryTokenizer. Some artificial code was
required to use solvable polynomials as ring elements since solvable
polynomials cannot implement
RingElem<GenSolvablePolynomial<C>>. This
resulted in some cases in wrong method dispatch for the
multiply() method due to compiler optimizations. A work
around to detect and repair this is now implemented in class
GenPolynomial.
OrderedSyzPairlist. Refactoring of Gröbner base
classes to optionally use the new pair selection. Back port of some
JDK 1.6 constructs to be again compatible with JDK 1.5. Small
improvements in Kronecker factor combination in class
FactorAbstract. Fixed race condition in
ThreadPool and improved termination detection in
Terminator. Fixes in parallel reduced Gröbner base
computations. Fixed univariate polynomial construction in
Ideal.
Quotient* to package edu.jas.ufd.
Fixed small bugs and cosmetic.
MultiVarPowerSeries
and MultiVarPowerSeriesRing. Mora's tangent cone reduction
algorithm and standard base computation for power series in package
edu.jas.ps. Iterator over exponent vectors.
BigDecimal
coefficients. Removed the use of the underscore for algebraic number
coefficients in the polynomial parser. Now every recursive call of
parse() from a ring factory is triggered by braces which
can be nested to any depth. Fixed synchronization bug in solvable
polynomial relation tables and a parallelization bug in parallel
solvable polynomial Gröbner base computation. Use of unbounded
thread pools to avoid dead-locks. Added remaining parts for the
square-free decomposition in polynomial rings of characteristic p
> 0. Changed the script representation of AN
(AlgebraicNumbers).
edu.jas.kern.TimeStatus to provide user feedback for
long running tasks via method checkTime().
Implemented some missing extGB() methods. GBFactory for
the selection of appropriate Gröbner base implementations.
New method isFinite() for all ElemFactorys and usage
in SquarefreeFactory. Added some missing parts for the factorization
in polynomial rings of characteristic p > 0 and ideal decomposition.
GBFactory.
New GBProxy like GCDProxy to run a sequential and a parallel
Gröbner base computation concurrently.
Primitive element computation via normalPositionFor() in
methods primitiveElement() together with several
conversion methods convertToPrimitiveElem(). A new
index of all algorithms from the book
Gröbner bases to their JAS equivalents.
Ideal with methods
radicalDecomposition(),
decomposition(),
primeDecomposition() and
primaryDecomposition().
Computation of extension and contraction ideals.
Unit tests for the decomposition methods.
Fixed a bug in multivariate polynomial factorization in Kronecker's method.
Fixed a bug in squarefree decomposition in inseparable case.
Added NO_THREADS flag to edu.jas.kern.ComputerThreads
to avoid (some) thread creation for usage in Google app engine.
Ideal with methods
zeroDimRadicalDecomposition(),
zeroDimDecomposition(),
zeroDimPrimeDecomposition(),
zeroDimPrimaryDecomposition() and
zeroDimRootDecomposition(). Exact 0-dim ideal real root
computation and approximation in methods
PolyUtilApp.realAlgebraicRoots() and
decimalApproximation(). Small enhancements to Javadoc
comments.
edu.jas.ufd,
simplified and improved the factory classes. Refactorings of
parallel Gröbner bases computations for solvable polynomial
rings. Improved logging for distributed Gröbner bases and
distributed middle-ware.
PrimeList.
Construction of minimal univariate polynomials in zero dimensional ideals.
Supersets of complex and real roots of zero dimensional ideals. More unit tests for
real and complex roots of univariate polynomials and zero dimensional ideal roots.
Minor enhancements and fixes.
GroebnerBasePartial.
Small enhancements: polynomial recursive coefficient parser and a
matrix parser. Book-keeping of all used polynomial variable names.
New and improved unit tests.
Complex coefficients via algebraic
coefficients in Q(i).
New classes ModLong and ModLongRing for faster modular arithmetic.
New interfaces Modular and ModularRingFactory implemented also by
ModInteger to make both interchangable.
Improved factorization and serveral refactorings. Factorization mod p = 2 is now implemented.
ComplexRoots, ComplexRootsAbstract,
ComplexRootsSturm.
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.
MultiplicativeSet, in sub-classes
polynomials made co-prime in MultiplicativeSetCoPrime,
polynomials made co-prime and squarefree in MultiplicativeSetSquarefree
and polynomials made irreducible in MultiplicativeSetFactors.
New distributed hybrid Gröbner base computation with new class
TaggedMesageChannel to handle multiple message types and partners over
one socket connection. Improved object serialization in distributed hash table.
Adapter updated for JLinAlg version 0.6.
ToRational used for BigRational
and RealAlgebraicNumber to remove type case distinctions
in Interval.
clone() removed from Element interface because
of compiler changes.
Squarefree, abstract class is
SquarefreeAbstract. Other main classes are
SquarefreeFieldChar0, SquarefreeFiniteFieldCharP
and SquarefreeInfiniteFieldCharP.
FactorAlgebraic can now also handle factorizations over
multiple algebraic extensions like for example Q(i)(sqrt(2)).
Class FactorAbsolute is now also extended
by FactorAlgebraic, so that absolute factorizations can
be computed over algebraic extensions of Q. Added new containers for
absolute factorization results and tests for correct absolute
factorizations. More toScript() methods and
improvements in Jython script interface. Minor additions and fixes.
ZZ, ZM, QQ, DD, CC, Quat, Oct,
PolyRing, AN, RealN, RF, RC, LC, SolvPolyRing
and RR, PS, Vec, Mat for the construction of rings and elements.
Added generic Complex class and ComplexRing factory.
Fixed a programming bug in factorization code.
factory() method to Element interface to have an uniform way to
obtain a corresponing ring object.
Improved RealAlgebraicNumber so that it can be used as polynomial coefficients,
for example GenPolynomial<RealAlgebricNumber<BigRational>>.
Real root isolation can now also be used for polynomials with real algebraic coefficients,
for example RealRootsSturm<RealAlgebraicNumber<BigRational>>.
edu.jas.root during CISIS/ECDS 2009.
Reached 100.000 lines of Java code.
edu.jas.ring to edu.jas.gb
and edu.jas.module to edu.jas.gbmod.
Factorization interface with FactorAbstract class for common codes.
Factorization of univariate polynomials with several coefficient rings:
modulo primes in class FactorModular,
over integers in class FactorInteger,
over rational numbers in class FactorRational and
over algebraic numbers in class FactorAlgebraic<C>
(where C can be ModInteger or BigRational).
Multivatiate polynomials are reduced to the univariate polynomials via Kronecker substitution
and are therefore not very efficient.
Refactorings and fixes.
compareTo to be transitive as required by
Javas SortedMap implementations.
Implemented an adaptor package for Apache Log4j to delegate logging calls to native Java logging.
RingElem and RingFactory types
in package edu.jas.ps
in classes UnivPowerSeries and UnivPowerSeriesRing.
The implementation follows the "Infinite Streams in Java" paper of D. Gruntz
in PPPJ2006.
Condition
and ColoredSystem classes.
Conditions consist of an ideal
(with lazy Groebner base computation) for the conditions equal to zero
and a multiplicative set for the conditions not equal to zero.
Non-zero condition polynomials are reduced modulo the ideal of
condition zero polynomials.
The squarefree part from both condition polynomials is used.
It differs from the MAS implementation by Schoenfeld, Pesch and others
by the ideal used to store the zero conditions and some more details.
long,
int (now the default, as seems to be the fastest),
short and byte.
The respective classes are ExpVectorLong,
ExpVectorInteger,
ExpVectorShort and ExpVectorByte.
RGroebnerBaseSeq and RGroebnerBasePseudoSeq.
Refactorings and fixes.
Product and RegularRingElem.
Added fraction free pseudo reduction and Groebner bases
GroebnerBasePseudoSeq.
Minor refactorings and fixes.
DGroebnerBaseSeq and EGroebnerBaseSeq.
Added test methods for reducibility and refactored sequential
Groebner base implementations.
Implemented noncommutative product for solvable polynomials, together with relation tables. SolvableOrderedMapPolynomial extends OrderedMapPolynomial. RatSolvableOrderedMapPolynomial extends SolvableOrderedMapPolynomial. Interface SolvablePolynomial extends Ordered Polynomial. Some more left multiplication methods, left reduction and left Groebner Bases, twosided Groebner Base test and computation. Pairlist class changed to avoid usage of criterion 4 if running for SolvablePolynomials, also criterion4() method itself checks for SolvablePolynomials.
| run / n | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| first | 3 | 13 | 32 | 92 | 128 | 188 | 274 | 420 | 683 | 1126 | 1795 | 2793 | 4380 | 6741 |
| second | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 10 | 13 | 16 | 21 | 27 | 35 |
Timings in ms on AMD XP 2800+. Computation of (Y^n) * (X^n) with respect to the relation Y * X = X Y - H. In the first run the relation table is populated with the products Y^i * X^i, i = 2,...,n. In the second run the relations are reused, showing almost no computing time anymore for the products.
| run / n | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|
| first | 28 | 94 | 303 | 1234 | 5185 | 24647 |
| second | 1 | 12 | 107 | 782 | 4569 | 23897 |
Second example shows the computation of ( Xa + Xb + Xc + Ya + Yb + Yc + Ha + Hb )^n in U(sl_3). Since in the relation table only products of two variables are stored, the improvement is minimal (for low n).
| # Threads CPUs |
# JVMs | time (sec) | #put | #remove | % total |
|---|---|---|---|---|---|
| 1, seq | 1 | 160.2 | 70 | 327 | 13.5 |
| 1, par | 1 | 157.0 | 70 | 327 | 13.5 |
| 2, par | 1 | 82.2 | 72 | 329 | 12.7 |
| 1, dist | 1 | 177.2 | 77 | 334 | 11.4 |
| 2, dist | 2 | 92.2 | 90 | 347 | 8.6 |
| 4, dist | 2 | 56.2 | 112 | 369 | 5.9 |
| 8, dist | 2 | 58.9 | 255 | 516 | 1.5 |
| 4, dist | 4 | 51.2 | 117 | 374 | 5.5 |
| 6, dist | 4 | 43.7 | 129 | 386 | 4.6 |
| 8, dist | 4 | 62.9 | 259 | 519 | 1.5 |
Timings taken on a 16 CPU Intel Xeon SMP computer running
at 2.7 GHz and with 32 GB RAM.
JVM 1.4.2 started with AggressiveHeap and UseParallelGC.
#JVMs = number of distinct Java virtual machines.
#put = number of polynomials put to pair list.
#remove = number of pairs removed from pair list,
i.e. after application of criterions,
but including nulls up to now.
% total = per cent of removed pairs from total pairs generated,
#remove / ( #put * (#put-1) / 2 ) * 100.
| # Threads CPUs |
# JVMs | time (sec) | #put | #remove | % total |
|---|---|---|---|---|---|
| 1, dist | 1 | 24726.2 | 140 | 781 | 8.0 |
| 2, dist | 2 | 12356.1 | 165 | 806 | 5.9 |
| 4, dist | 4 | 6859.3 | 218 | 859 | 3.6 |
| 8, dist | 4 | 7465.1 | 411 | 1054 | 1.2 |
| 8, dist | 8 | 6412.9 | 344 | 986 | 1.6 |
| 8, dist | 8 | 7173.3 | 399 | 1041 | 1.3 |
Overhead for distributed variant is about 10% in Katsura 6 (G). Distributed 1 means one distributed process is running for the reduction of S-polynomials. There is always a master process handling polynomial input / output, setup and management of distributed workers and handling of the pair list. Communication between master and workers is always via TCP/IP with object serialization, even if running on one computer.
New classes implementing a distributed hash table to hold the polynomials in distributed GB. Index of polynomials in Pairlist is used as hash key. Communication is now using message types GBTransportMess. Now polynomials are only transported once to each reducer since only polynomial hash indexes are transported. Distributed list is asynchronous and late updated, so some duplicate H-polynomials (head terms) could be (are) produced. Solution by local put to hash table with dummy index? Timings are not dramatically better.
Todo: check reduction algorithm to use later arriving polynomials.
-Xms200M -Xmx400M -XX:+AggressiveHeap -XX:+UseParallelGCMemory must be adjusted with respect to your situation.
Seperated versions with Pair Sequence Respecting Order (PS) and normal versions. PS versions try to keep the order of reduced polynomials added to the ideal base the same as in the sequential version. Normal versions now running OK on parallel computer with the right JVM options. Refactoring with Eclipse (organize imports, static methods).
| # Threads CPUs |
Katsura 6 TO(G) load* |
Katsura 6 TO(G) empty* |
Katsura 7 TO(G) load* |
Katsura 7 TO(G) empty* |
|---|---|---|---|---|
| seq | 184.5 | 153.3 | ||
| 1 | 181.5 | 4% / 159.7 | 28418.6 | |
| 2 | 118.6 | s2.02 / p2.11 / 75.6 | p2.06 / 13760.0 | |
| 4 | 76.8 | s3.79 / p3.95 / 40.4 | 6256.9 | p4.56 / 6225.1 |
| 8 | 43.2 | s7.19 / p7.49 / 21.3 | 3240.7 | p8.56/ 3318.8 |
| 10 | 42.5 | |||
| 12 | 40.5 | 2288.1 | p9.90 / 2868.4 | |
| 14 | 31.2 | |||
| 16 | 51.9 | s8.19 / p8.54 / 18.7 | 5376.4 | p12.59 / 2256.1 |
Timings taken on a 16 CPU Intel Xeon SMP computer running
at 2.7 GHz and with 32 GB RAM.
JVM 1.4.2 started with AggressiveHeap and UseParallelGC.
*) timing taken with other load on the CPUs.
+) timing taken with no other load on the CPUs.
Speedup: s = relative to sequential,
p = relative to parallel with one thread / CPU.
Scaling from 8 to 16 CPUs is bad, but also observed on
non CA / GB Examples (Java and C/FORTRAN).
| N vars = N+1 |
TermOrder | Seconds | TermOrder | Seconds |
|---|---|---|---|---|
| 7 | G | 32044.204 | L | |
| 6 | G | 112.641 | L | |
| 5 | G | 4.195 | L | |
| 4 | G | 0.431 | L | 11.650 |
| 3 | G | 0.153 | L | 0.310 |
| 2 | G | 0.031 | L | 0.032 |
putParallel(), removeParallel() and
helper methods. Sequence numbers are generated and reduced polynomials
are only put to the pair list if corresponding pair number is in
correct (sequential) sequence.
The ordered list / queue pairsequence (TreeMap/SortedMap)
keeps track of the polynomials not yet put to the pairlist.
ExecutableServer) for remote execution
of objects implementing the RemoteExecutable interface.
New setup for the distributed computation of GBs: the GB master now sends the client code to some ExecutableSevers based on a maschine file with host and port infos about the distributed environment.
Improved the PolynomialTokenizer so that it can read almost unedited
old MAS GB input files: ** exponents and parenthesis
around polynomials.
Lines starting with # are treated as comments.
Comments (* *) and parenthesis within polynomials are
still not supported.
Implemented a common driver for GB computations RunGB.
Sequential, thread parallel and distributed computation can be selected
by command line parameters. The input is taken from a file. The number
of threads respectively the number of distributed clients can be specified.
For distributed execution the host and port information is taken from
a maschines file.
Usage: RunGB [seq|par|dist|cli] <file> #procs [machinefile]
Added methods putCount() and remCount()
in OrderedPairlist to count the number of polynomials
put and get from the pair data structure.
| # Threads | 1 seq | 1 par | 2 par | 2 par | 3 par | 4 par | 5 par | 1 dist | 2 dist | 3 dist | 4 dist | 4 dist | 4 dist | 5 dist |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| # put | 22 | 22 | 43 | 26 | 28 | 28 | 28 | 22 | 25 | 28 | 37 | 40 | 33 | 27 |
| # remove | 25 | 25 | 61 | 30 | 32 | 32 | 41 | 26 | 33 | 42 | 47 | 61 | 54 | 69 |
Timings @ 500 MHz on one CPU and one maschine and log4j level INFO are:
ca. 2.5 - 3.5 seconds for sequential GB,
ca. 2.5 - 6 seconds for parallel GB,
ca. 5.5 - 9 seconds plus 5 seconds sync time for distributed GB.
Network shuffling of polynomials seems to account for 3 seconds in
this example.
Problem uncovered: the distributed version of GB needs an avarage of 5 seconds to sync with all clients (on one maschine). This is way to much for execution times in the range of 2 to 8 seconds.
Redesign of DistributedList, now using TreeMap to keep the list
entries in proper sequence. As key a natural number is used, which is
assigned by the server to successive add() requests.
The server now also holds a copy of the list by itself. So the
retransmission of list elements to late arriving clients is possible.
This doubles the space required to store polynomials, but removes
initial delays to sync all clients to receive all list elements.
By retransmission the DistributedList synchronization delay during
DistributedGB could be removed.
However the problem of about 5 seconds delay in startup
of DistributedGB still remains. It is not visible where and why this
delay occurs.
Further improvements would be the removal of list elements or the
clearing of the list.
Next steps could be distributed HashMap or TreeMap.
An important improvement would be to keep serialized copies of the
list elements (polynomials) at the server and to
avoid many time serialization during broadcast.
mpirun,
a daemon to run on a distributed system to work with the launcher,
solvable polynomials and non-commutative GBs.
With one thread the time is 30.6 h. Besides the better CPU speed, this makes a 5 % improvement on JDK 1.4 compared to the older timings from a JDK 1.3 and the new polynomial implementation.
Multiplication with ordered polynomials is about 8-10 times faster than the multiplication with unordered polynomials. Also the multiplication with semi-ordered polynomials (LinkedHashMap) with orderpreserving addition is about 7-8 times slower than multiplication with ordered polynomials.
All implementations are based on Map interface and classes. The Map maps exponent vectors (from some monoid) to coefficients (from some domain). This is in sync with the mathematical definition of multivariate polynomials as mappings from some monoid to some domain. Term orders are represented by a TermOrder class which provides the desired Comparator classes for the SortedMap implementation.
However the merging add/subtact implementation is a factor of
2 slower than the TreeMap implementation.
Complexity for a+b is
2*(length(a)+length(b))
for access and merging pre sorted polynomials and
2*length(a)+length(b)+length(b)*log2(length(a+b))
for TreeMap clone, access and insertion.
The merging multiplication implementation is by a factor of
10 slower than the TreeMap implementation.
Polynomial size was ~100 terms and the product contained ~8000 terms.
Complexity for a*b is
lab = length(a)*length(b) coefficient multiplications for both implementations
plus 2*length(a*b)*length(b) for merging summands, respectively
plus length(a)*length(b)*log2(length(a*b)) for TreeMap insertion.
Since for sparse polynomials length(a*b) = lab, the TreeMap complexity
is asymptotically better in this case:
2*length(a)*length(b)*length(b) =>= length(a)*length(b)*log2(length(a*b))
For dense polynomials with length(a*b) ~ length(a)[+length(b)], then
the LinkedHashMap complexity is asymptotically better:
2*length(a)*length(b) =<= length(a)*length(b)*log2(length(a*b))
Parallel computations with the Rose example are at 18 h with 4 threads on 2 Pentium 4 @ 2.4 GHz hyperthreading CPUs. With one thread the time is 40 h.
Does this influence the validity of criterion 3? Access to pairlist is synchronized. Pairs are marked as reduced as soon they are taken from the list. But the algorithm terminates only after all reductions of pairs have terminated. So criterion 3 holds.
New implementation of parallel version of GB. Removal of pairs is now also in parallel. But ordering of pair insertion is no more preserved
Timings are more stable and slightly better than that of sequential GB.
Todo: unit tests, comments, ...
Improved parallel version of GB.
Todo: CVS, comments, polynomial implementation using LinkedList, parallel GB simplify
With the improved algorithm the running time of the parallel GB becomes more stable and not slower than the sequential GB. However there is still no significant speedup.
| # Threads | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 16 |
|---|---|---|---|---|---|---|---|---|---|
| # Reductions | 25 | 25 | 27 | 25 | 25 | 25 | 25 | 25 | 25 |
| # Threads | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 16 |
|---|---|---|---|---|---|---|---|---|---|
| # Reductions | 22 | 24 | 30, 28, 24, 29 | 28 | 29 | 42 | 32 | 32 | 37 |
parallel results:
Trinks 7: mas 0.598 sec, jas 0.918 sec, jas par 0.955 sec
Trinks 6: mas 26.935 sec, jas 3.211 sec, jas par 3.656 sec
mas: including startup and gc time,
jas: excluding startup of jvm and including gc time,
jas par on single processor
timing on P-3@450
implemented edu.jas.arith.BigInteger which implements Coefficient, tested with IntPolynomial which extends Polynomial
todo: alternative Implementations, cleanup RatPolynomial, parallel GB, conversion RatPolynomial <--> IntPolynomial
second results (with new criterion 3 in jas):
Trinks 7: mas 0.598 sec, jas 1.159 sec
Trinks 6: mas 26.935 sec, jas 6.468 sec
mas: including startup and gc time,
jas: excluding startup of jvm and including gc time
third results (with new criterion 3 in jas and GBminimal):
Trinks 7: mas 0.598 sec, jas 0.918 sec
Trinks 6: mas 26.935 sec, jas 3.211 sec
mas: including startup and gc time,
jas: excluding startup of jvm and including gc time
timing on P-3@450
this makes for a factor of 8-9 better, all tests with output to files, startup of JVM is approx. 1.0-1.2 sec, most time is spent in BigInteger:
java -Xrunhprof:cpu=times,format=a CPU TIME (ms) BEGIN (total = 136) Thu Jan 2 18:33:53 2003 rank self accum count trace method 1 15,44% 15,44% 596610 21 java.math.MutableBigInteger.rightShift 2 13,24% 28,68% 582132 15 java.math.MutableBigInteger.difference 3 12,50% 41,18% 612760 19 java.math.MutableBigInteger.getLowestSetBit 4 9,56% 50,74% 2 9 java.lang.Object.wait 5 9,56% 60,29% 5271 22 java.math.MutableBigInteger.binaryGCD 6 6,62% 66,91% 612760 23 java.math.BigInteger.trailingZeroCnt 7 5,88% 72,79% 592152 18 java.math.BigInteger.bitLen 8 5,88% 78,68% 6018 20 java.math.MutableBigInteger.binaryGCD 9 5,15% 83,82% 578887 25 java.math.MutableBigInteger.normalize 10 4,41% 88,24% 550992 24 java.math.MutableBigInteger.primitiveRightShift 11 4,41% 92,65% 1 10 java.lang.Object.wait 12 3,68% 96,32% 582132 12 java.math.MutableBigInteger.compare 13 0,74% 97,06% 35965 13 edu.jas.poly.ExpVector.EVILCP 14 0,74% 97,79% 11612 14 java.math.BigInteger.divide 15 0,74% 98,53% 5866 11 java.math.MutableBigInteger.divide 16 0,74% 99,26% 9032 16 java.math.MutableBigInteger.divide 17 0,74% 100,00% 9032 17 java.math.BigInteger.divide CPU TIME (ms) END
first results (without criterion 3 in jas):
Trinks 7: mas 0.598 sec, jas 1.373 sec
Trinks 6: mas 26.935 sec, jas 30.935 sec
mas: including startup and gc time,
jas: excluding startup of jvm and including gc time.
timing on P-3@450
Implemented and testet ExpVector based on Javas int arrays.
Implemented and testet RatPolynomial based on Javas TreeMap.
static methods: DIRPDF, DIRPWR via toString, DIRPON, DIRPMC,
DIRPPR, DIRPSM, DIRRAS.
Consider replacing keySet/get by entrySet/getval where appropriate.
Can there be an generic Polynomial class?
This will be the end of list processing for Jas.
DIPRNGB needs DIRPDF, DIRPWR, DIRPON, DIRPMC, DIRPPR, DIRPSM.
These need RNDIF, RNDWR, RNINT, RNSIGN, ISRNONE, RNONE, RNZERO,
RNINV (and DIRPRP), RNPROD, RNSUM.
Last modified: Tue Jul 4 09:58:27 CEST 2023