Package edu.jas.application

Class ExtensionFieldBuilder

java.lang.Object

edu.jas.application.ExtensionFieldBuilder

All Implemented Interfaces:

java.io.Serializable

public class ExtensionFieldBuilder
extends java.lang.Object
implements java.io.Serializable

Builder for extension field towers.

Author:

Heinz Kredel

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
RingFactory	factory	The current factory.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	ExtensionFieldBuilder()	Constructor not for use.
	ExtensionFieldBuilder(RingFactory base)	Constructor.

Method Summary

Modifier and Type	Method	Description
ExtensionFieldBuilder	algebraicExtension(java.lang.String var, java.lang.String expr)	Algebraic field extension.
static ExtensionFieldBuilder	baseField(RingFactory base)	Set base field.
RingFactory	build()	Build the field tower.
ExtensionFieldBuilder	complexAlgebraicExtension(java.lang.String var, java.lang.String expr, java.lang.String root)	Complex algebraic field extension.
ExtensionFieldBuilder	finiteFieldExtension(int n)	Finite field extension.
ExtensionFieldBuilder	matrixExtension(int n)	Matrix ring extension.
ExtensionFieldBuilder	polynomialExtension(java.lang.String vars)	Polynomial ring extension.
ExtensionFieldBuilder	realAlgebraicExtension(java.lang.String var, java.lang.String expr, java.lang.String root)	Real algebraic field extension.
java.lang.String	toScript()	Get a scripting compatible string representation.
java.lang.String	toString()	String representation of the ideal.
ExtensionFieldBuilder	transcendentExtension(java.lang.String vars)	Transcendent field extension.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

factory

public final RingFactory factory

The current factory.

Constructor Detail

ExtensionFieldBuilder

protected ExtensionFieldBuilder()

Constructor not for use.

ExtensionFieldBuilder

public ExtensionFieldBuilder(RingFactory base)

Constructor.

Parameters:

base - the base field.

Method Detail

build

public RingFactory build()

Build the field tower. TODO: optimize field tower for faster computation.

baseField

public static ExtensionFieldBuilder baseField(RingFactory base)

Set base field.

Parameters:

base - the base field for the extensions.

transcendentExtension

public ExtensionFieldBuilder transcendentExtension(java.lang.String vars)

Transcendent field extension.

Parameters:

vars - names for the transcendent generators.

polynomialExtension

public ExtensionFieldBuilder polynomialExtension(java.lang.String vars)

Polynomial ring extension.

Parameters:

vars - names for the polynomial ring generators.

matrixExtension

public ExtensionFieldBuilder matrixExtension(int n)

Matrix ring extension.

Parameters:

n - dimension of n x n matrix.

finiteFieldExtension

public ExtensionFieldBuilder finiteFieldExtension(int n)

Finite field extension. Construct a finite field with q = p**n elements, where p is the characteristic of the base field.

Parameters:

n - exponent.

algebraicExtension

public ExtensionFieldBuilder algebraicExtension(java.lang.String var,
                                                java.lang.String expr)

Algebraic field extension.

Parameters:

var - name(s) for the algebraic generator(s).

expr - generating expresion, a univariate or multivariate polynomial in vars.

realAlgebraicExtension

public ExtensionFieldBuilder realAlgebraicExtension(java.lang.String var,
                                                    java.lang.String expr,
                                                    java.lang.String root)

Real algebraic field extension.

Parameters:

var - name for the algebraic generator.

expr - generating expresion, a univariate polynomial in var.

root - isolating interval for a real root.

complexAlgebraicExtension

public ExtensionFieldBuilder complexAlgebraicExtension(java.lang.String var,
                                                       java.lang.String expr,
                                                       java.lang.String root)

Complex algebraic field extension.

Parameters:

var - name for the algebraic generator.

expr - generating expresion, a univariate polynomial in var.

root - isolating rectangle for a complex root.

toString

public java.lang.String toString()

String representation of the ideal.

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()