Class ExtensionFieldBuilder

java.lang.Object
edu.jas.application.ExtensionFieldBuilder
All Implemented Interfaces:
Serializable

public class ExtensionFieldBuilder extends Object implements Serializable
Builder for extension field towers.
See Also:
  • Field Details

    • factory

      public final RingFactory factory
      The current factory.
  • Constructor Details

    • ExtensionFieldBuilder

      protected ExtensionFieldBuilder()
      Constructor not for use.
    • ExtensionFieldBuilder

      public ExtensionFieldBuilder(RingFactory base)
      Constructor.
      Parameters:
      base - the base field.
  • Method Details

    • 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(String vars)
      Transcendent field extension.
      Parameters:
      vars - names for the transcendent generators.
    • polynomialExtension

      public ExtensionFieldBuilder polynomialExtension(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(String var, String expr)
      Algebraic field extension.
      Parameters:
      var - name(s) for the algebraic generator(s).
      expr - generating expression, a univariate or multivariate polynomial in vars.
    • realAlgebraicExtension

      public ExtensionFieldBuilder realAlgebraicExtension(String var, String expr, String root)
      Real algebraic field extension.
      Parameters:
      var - name for the algebraic generator.
      expr - generating expression, a univariate polynomial in var.
      root - isolating interval for a real root.
    • complexAlgebraicExtension

      public ExtensionFieldBuilder complexAlgebraicExtension(String var, String expr, String root)
      Complex algebraic field extension.
      Parameters:
      var - name for the algebraic generator.
      expr - generating expression, a univariate polynomial in var.
      root - isolating rectangle for a complex root.
    • toString

      public String toString()
      String representation of the ideal.
      Overrides:
      toString in class Object
      See Also:
    • toScript

      public String toScript()
      Get a scripting compatible string representation.
      Returns:
      script compatible representation for this Element.
      See Also: