GBAlgorithmBuilder

java.lang.Object
- edu.jas.application.GBAlgorithmBuilder<C>

All Implemented Interfaces:

java.io.Serializable
```
public class GBAlgorithmBuilder<C extends GcdRingElem<C>>
extends java.lang.Object
implements java.io.Serializable
```
Builder for commutative Gröbner bases algorithm implementations.
Usage: To create objects that implement the GroebnerBase interface one can use the GBFactory or this GBAlgorithmBuilder. This class will select and compose an appropriate implementation based on the types of polynomial coefficients C and the desired properties. To build an implementation start with the static method polynomialRing() to define the polynomial ring. Then continue to construct the algorithm with the methods
- optimize() or optimize(boolean) for term order (variable order) optimization (true for return of permuted polynomials),
- normalPairlist() (default), syzygyPairlist() or simplePairlist() for pair-list selection strategies,
- fractionFree() for clearing denominators and computing with pseudo reduction,
- graded() for using the FGLM algorithm to first compute a Gröbner base with respect to a graded term order and then constructing a Gröbner base wrt. a lexicographical term order,
- walk() for using the Gröbner walk algorithm to first compute a Gröbner base with respect to a graded term order and then constructing a Gröbner base wrt. a lexicographical term order,
- iterated() for using the iterative GB algorithm to compute a Gröbner base adding one polynomial after another,
- F5(), GGV() and Arri() for using the respective iterative signature based GB algorithm (over field coefficients) to compute a Gröbner base adding one polynomial after another,
- parallel() additionaly compute a Gröbner base over a field or integral domain in parallel,
- euclideanDomain() for computing a e-Gröbner base,
- domainAlgorithm(Algo) for computing a d- or e-Gröbner base,
Finally call the method build() to obtain an implementaton of class GroebnerBaseAbstract. For example
```
 GenPolynomialRing<C> pf = new GenPolynomialRing<C>(cofac, vars);
 GroebnerBaseAbstract<C> engine;
 engine = GBAlgorithmBuilder.<C> polynomialRing(pf).fractionFree().parallel().optimize().build();
 c = engine.GB(A);
 
```
For example, if the coefficient type is BigRational, the usage looks like
```
 GenPolynomialRing<BigRational> pf = new GenPolynomialRing<BigRational>(cofac, vars);
 GroebnerBaseAbstract<BigRational> engine;
 engine = GBAlgorithmBuilder.<BigRational> polynomialRing(pf).fractionFree().parallel().optimize().build();
 c = engine.GB(A);
 
```
Note: Not all combinations are meanigful
Author:

Heinz Kredel

See Also:

GroebnerBase, GBFactory, Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

GenPolynomialRing<C> ring
The current polynomial ring.

PairList<C> strategy
Requested pairlist strategy.

Fields
Modifier and Type	Field and Description
`GenPolynomialRing<C>`	`ring` The current polynomial ring.
`PairList<C>`	`strategy` Requested pairlist strategy.

Constructor Summary

Constructors
Modifier	Constructor and Description
`protected`	`GBAlgorithmBuilder()` Constructor not for use.
	`GBAlgorithmBuilder(GenPolynomialRing<C> ring)` Constructor.
	`GBAlgorithmBuilder(GenPolynomialRing<C> ring, GroebnerBaseAbstract<C> algo)` Constructor.
	`GBAlgorithmBuilder(GenPolynomialRing<C> ring, GroebnerBaseAbstract<C> algo, PairList<C> strategy)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`GBAlgorithmBuilder<C>`	`Arri()` Request iterated Arri signature based GB algorithm.
`GroebnerBaseAbstract<C>`	`build()` Build the GB algorithm implementaton.
`GBAlgorithmBuilder<C>`	`domainAlgorithm(GBFactory.Algo a)` Request d-, e- or i-GB algorithm.
`GBAlgorithmBuilder<C>`	`euclideanDomain()` Request e-GB algorithm.
`GBAlgorithmBuilder<C>`	`F5()` Request iterated F5 signature based GB algorithm.
`GBAlgorithmBuilder<C>`	`fractionFree()` Request fraction free algorithm.
`GBAlgorithmBuilder<C>`	`GGV()` Request iterated GGV signature based GB algorithm.
`GBAlgorithmBuilder<C>`	`graded()` Request FGLM algorithm.
`GBAlgorithmBuilder<C>`	`iterated()` Request iterated GB algorithm.
`GBAlgorithmBuilder<C>`	`normalPairlist()` Select normal critical pair-list strategy.
`GBAlgorithmBuilder<C>`	`optimize()` Request term order optimization.
`GBAlgorithmBuilder<C>`	`optimize(boolean rP)` Request term order optimization.
`GBAlgorithmBuilder<C>`	`parallel()` Request parallel algorithm.
`GBAlgorithmBuilder<C>`	`parallel(int threads)` Request parallel algorithm.
`static <C extends GcdRingElem<C>> GBAlgorithmBuilder<C>`	`polynomialRing(GenPolynomialRing<C> fac)` Define polynomial ring.
`GBAlgorithmBuilder<C>`	`simplePairlist()` Select simple critical pair-list strategy.
`GBAlgorithmBuilder<C>`	`syzygyPairlist()` Select syzygy critical pair-list strategy.
`java.lang.String`	`toScript()` Get a scripting compatible string representation.
`java.lang.String`	`toString()` String representation of the GB algorithm implementation.
`GBAlgorithmBuilder<C>`	`walk()` Request Groebner walk algorithm.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - ring
```
public final GenPolynomialRing<C extends GcdRingElem<C>> ring
```
    The current polynomial ring.
  - strategy
```
public final PairList<C extends GcdRingElem<C>> strategy
```
    Requested pairlist strategy.
- Constructor Detail
  - GBAlgorithmBuilder
```
protected GBAlgorithmBuilder()
```
    Constructor not for use.
  - GBAlgorithmBuilder
```
public GBAlgorithmBuilder(GenPolynomialRing<C> ring)
```
    Constructor.
    
    Parameters:
    
    ring - the polynomial ring.
  - GBAlgorithmBuilder
```
public GBAlgorithmBuilder(GenPolynomialRing<C> ring,
                          GroebnerBaseAbstract<C> algo)
```
    Constructor.
    
    Parameters:
    
    ring - the polynomial ring.
    
    algo - already determined algorithm.
  - GBAlgorithmBuilder
```
public GBAlgorithmBuilder(GenPolynomialRing<C> ring,
                          GroebnerBaseAbstract<C> algo,
                          PairList<C> strategy)
```
    Constructor.
    
    Parameters:
    
    ring - the polynomial ring.
    
    algo - already determined algorithm.
    
    strategy - pairlist strategy.
- Method Detail
  - build
```
public GroebnerBaseAbstract<C> build()
```
    Build the GB algorithm implementaton.
    
    Returns:
    
    GB algorithm implementaton as GroebnerBaseAbstract object.
  - polynomialRing
```
public static <C extends GcdRingElem<C>> GBAlgorithmBuilder<C> polynomialRing(GenPolynomialRing<C> fac)
```
    Define polynomial ring.
    
    Parameters:
    
    fac - the commutative polynomial ring.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - syzygyPairlist
```
public GBAlgorithmBuilder<C> syzygyPairlist()
```
    Select syzygy critical pair-list strategy. Gebauer and Möller algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - normalPairlist
```
public GBAlgorithmBuilder<C> normalPairlist()
```
    Select normal critical pair-list strategy. Buchberger, Winkler and Kredel algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - simplePairlist
```
public GBAlgorithmBuilder<C> simplePairlist()
```
    Select simple critical pair-list strategy. Original Buchberger algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - optimize
```
public GBAlgorithmBuilder<C> optimize()
```
    Request term order optimization. Call optimize(true) for return of permuted polynomials.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - optimize
```
public GBAlgorithmBuilder<C> optimize(boolean rP)
```
    Request term order optimization.
    
    Parameters:
    
    rP - true for return of permuted polynomials, false for inverse permuted polynomials and new GB computation.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - fractionFree
```
public GBAlgorithmBuilder<C> fractionFree()
```
    Request fraction free algorithm. For BigRational and Quotient coefficients denominators are cleared and pseudo reduction is used.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - euclideanDomain
```
public GBAlgorithmBuilder<C> euclideanDomain()
```
    Request e-GB algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - domainAlgorithm
```
public GBAlgorithmBuilder<C> domainAlgorithm(GBFactory.Algo a)
```
    Request d-, e- or i-GB algorithm.
    
    Parameters:
    
    a - algorithm from GBFactory.Algo.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - parallel
```
public GBAlgorithmBuilder<C> parallel()
```
    Request parallel algorithm. Additionaly run a parallel algorithm via GBProxy.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - parallel
```
public GBAlgorithmBuilder<C> parallel(int threads)
```
    Request parallel algorithm. Additionaly run a parallel algorithm via GBProxy.
    
    Parameters:
    
    threads - number of threads requested.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - graded
```
public GBAlgorithmBuilder<C> graded()
```
    Request FGLM algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - walk
```
public GBAlgorithmBuilder<C> walk()
```
    Request Groebner walk algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - iterated
```
public GBAlgorithmBuilder<C> iterated()
```
    Request iterated GB algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - F5
```
public GBAlgorithmBuilder<C> F5()
```
    Request iterated F5 signature based GB algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - GGV
```
public GBAlgorithmBuilder<C> GGV()
```
    Request iterated GGV signature based GB algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - Arri
```
public GBAlgorithmBuilder<C> Arri()
```
    Request iterated Arri signature based GB algorithm.
    
    Returns:
    
    GBAlgorithmBuilder object.
  - toString
```
public java.lang.String toString()
```
    String representation of the GB algorithm implementation.
    
    Overrides:
    
    toString in class java.lang.Object
    
    See Also:
    
    Object.toString()
  - toScript
```
public java.lang.String toScript()
```
    Get a scripting compatible string representation.
    
    Returns:
    
    script compatible representation for this Element.
    
    See Also:
    
    Element.toScript()

Class GBAlgorithmBuilder<C extends GcdRingElem<C>>

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

ring

strategy

Constructor Detail

GBAlgorithmBuilder

GBAlgorithmBuilder

GBAlgorithmBuilder

GBAlgorithmBuilder

Method Detail

build

polynomialRing

syzygyPairlist

normalPairlist

simplePairlist

optimize

optimize

fractionFree

euclideanDomain

domainAlgorithm

parallel

parallel

graded

walk

iterated

F5

GGV

Arri

toString

toScript