Package edu.jas.ufd

Class SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>>

java.lang.Object
edu.jas.ufd.SquarefreeAbstract<C>
edu.jas.ufd.SquarefreeFieldCharP<C>
edu.jas.ufd.SquarefreeFiniteFieldCharP<C>
All Implemented Interfaces:
Squarefree<C>, Serializable
public class SquarefreeFiniteFieldCharP<C extends GcdRingElem<C>> extends SquarefreeFieldCharP<C>
Squarefree decomposition for finite coefficient fields of characteristic p.
See Also:

  • Field Details

    • logger

      private static final org.apache.logging.log4j.Logger logger

  • Constructor Details

    • SquarefreeFiniteFieldCharP

      public SquarefreeFiniteFieldCharP(RingFactory<C> fac)
      Constructor.

  • Method Details

    • rootCharacteristic

      public SortedMap<C,Long> rootCharacteristic(C p)
      Characteristics root of a coefficient. Note: not needed at the moment.
      Parameters:
      p - coefficient.
      Returns:
      [p -> k] if exists k with e=k*characteristic(c) and c = p**e, else null.

    • coeffRootCharacteristic

      public C coeffRootCharacteristic(C c)
      Characteristics root of a coefficient.
      Parameters:
      c - coefficient.
      Returns:
      r with r**p == c, if such an r exists, else null.

    • rootCharacteristic

      public SortedMap<GenPolynomial<C>,Long> rootCharacteristic(GenPolynomial<C> P)
      Characteristics root of a polynomial. Note: call only in recursion.
      Parameters:
      P - polynomial.
      Returns:
      [p -> k] if exists k with e=k*characteristic(P) and P = p**e, else null.

    • baseRootCharacteristic

      public GenPolynomial<C> baseRootCharacteristic(GenPolynomial<C> P)
      GenPolynomial char-th root univariate polynomial. Base coefficient type must be finite field, that is ModInteger or AlgebraicNumber<ModInteger> etc.
      Specified by:
      baseRootCharacteristic in class SquarefreeFieldCharP<C extends GcdRingElem<C>>
      Parameters:
      P - GenPolynomial.
      Returns:
      char-th_rootOf(P), or null if no char-th root.

    • recursiveUnivariateRootCharacteristic

      public GenPolynomial<GenPolynomial<C>> recursiveUnivariateRootCharacteristic(GenPolynomial<GenPolynomial<C>> P)
      GenPolynomial char-th root univariate polynomial with polynomial coefficients.
      Specified by:
      recursiveUnivariateRootCharacteristic in class SquarefreeFieldCharP<C extends GcdRingElem<C>>
      Parameters:
      P - recursive univariate GenPolynomial.
      Returns:
      char-th_rootOf(P), or null if P is no char-th root.