Package edu.jas.vector

Class BasicLinAlg<C extends RingElem<C>>

  • Type Parameters:
    C - coefficient type
    All Implemented Interfaces:
    java.io.Serializable
    public class BasicLinAlg<C extends RingElem<C>>
extends java.lang.Object
implements java.io.Serializable
    Basic linear algebra methods. Implements Basic linear algebra computations and tests. Note: will eventually use wrong method dispatch in JRE when used with GenSolvablePolynomial.
    Author:
    Heinz Kredel
    See Also:
    Serialized Form

    • Constructor Summary

      Constructors 
      Constructor Description
      BasicLinAlg()
      Constructor.

    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      java.util.List<C> genVector​(int n, C a)
      Generation of a vector of ring elements.
      java.util.List<C> genVector​(int n, C a, java.util.List<C> A)
      Generation of a vector of ring elements.
      boolean isZero​(java.util.List<C> a)
      Test vector of zero ring elements.
      GenVector<C> leftProduct​(GenVector<C> G, GenMatrix<C> F)
      Product of a vector and a matrix of ring elements.
      java.util.List<C> leftScalarProduct​(java.util.List<C> G, java.util.List<java.util.List<C>> F)
      Scalar product of vectors and a matrix of ring elements.
      GenVector<C> rightProduct​(GenVector<C> G, GenMatrix<C> F)
      Product of a vector and a matrix of ring elements.
      java.util.List<C> rightScalarProduct​(java.util.List<C> G, java.util.List<java.util.List<C>> F)
      Scalar product of vectors and a matrix of ring elements.
      java.util.List<C> scalarProduct​(C p, java.util.List<C> F)
      Scalar product of ring element with vector of ring elements.
      java.util.List<C> scalarProduct​(java.util.List<C> F, C p)
      Scalar product of vector of ring element with ring element.
      C scalarProduct​(java.util.List<C> G, java.util.List<C> F)
      Scalar product of vectors of ring elements.
      java.util.List<C> vectorAdd​(java.util.List<C> a, java.util.List<C> b)
      Addition of vectors of ring elements.
      java.util.List<C> vectorCombineOld​(java.util.List<C> a, java.util.List<C> b)
      Combination of vectors for old representation.
      java.util.List<C> vectorCombineRep​(java.util.List<C> a, java.util.List<C> b)
      Combination of vectors for reduction representation.
      java.util.List<C> vectorCombineSyz​(java.util.List<C> a, java.util.List<C> b)
      Combination of vectors for syzygy representation.
      java.util.List<C> vectorNegate​(java.util.List<C> a)
      Negative of vectors of ring elements.

      • Methods inherited from class java.lang.Object

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

    • Constructor Detail

    • Method Detail

      • scalarProduct

        public C scalarProduct​(java.util.List<C> G,
                       java.util.List<C> F)
        Scalar product of vectors of ring elements.
        Parameters:
        G - a ring element list.
        F - a ring element list.
        Returns:
        the scalar product of G and F.

      • leftScalarProduct

        public java.util.List<C> leftScalarProduct​(java.util.List<C> G,
                                           java.util.List<java.util.List<C>> F)
        Scalar product of vectors and a matrix of ring elements.
        Parameters:
        G - a ring element list.
        F - a list of ring element lists.
        Returns:
        the scalar product of G and F.

      • rightScalarProduct

        public java.util.List<C> rightScalarProduct​(java.util.List<C> G,
                                            java.util.List<java.util.List<C>> F)
        Scalar product of vectors and a matrix of ring elements.
        Parameters:
        G - a ring element list.
        F - a list of ring element lists.
        Returns:
        the right scalar product of G and F.

      • vectorAdd

        public java.util.List<C> vectorAdd​(java.util.List<C> a,
                                   java.util.List<C> b)
        Addition of vectors of ring elements.
        Parameters:
        a - a ring element list.
        b - a ring element list.
        Returns:
        a+b, the vector sum of a and b.

      • vectorNegate

        public java.util.List<C> vectorNegate​(java.util.List<C> a)
        Negative of vectors of ring elements.
        Parameters:
        a - a ring element list.
        Returns:
        -a, the vector of -a.

      • vectorCombineRep

        public java.util.List<C> vectorCombineRep​(java.util.List<C> a,
                                          java.util.List<C> b)
        Combination of vectors for reduction representation.
        Parameters:
        a - a ring element list.
        b - a ring element list.
        Returns:
        a-b, the vector difference of a and b, with one entry more.

      • vectorCombineSyz

        public java.util.List<C> vectorCombineSyz​(java.util.List<C> a,
                                          java.util.List<C> b)
        Combination of vectors for syzygy representation.
        Parameters:
        a - a ring element list.
        b - a ring element list.
        Returns:
        (-a)+b, the vector sum of -a and b, with one entry more.

      • vectorCombineOld

        public java.util.List<C> vectorCombineOld​(java.util.List<C> a,
                                          java.util.List<C> b)
        Combination of vectors for old representation.
        Parameters:
        a - a ring element list.
        b - a ring element list.
        Returns:
        -a-b, the vector difference of -a and b, with one entry more.

      • genVector

        public java.util.List<C> genVector​(int n,
                                   C a)
        Generation of a vector of ring elements.
        Parameters:
        n - length of vector.
        a - a ring element to fill vector entries.
        Returns:
        V, a vector of length n and entries a.

      • genVector

        public java.util.List<C> genVector​(int n,
                                   C a,
                                   java.util.List<C> A)
        Generation of a vector of ring elements.
        Parameters:
        n - length of vector.
        a - a ring element to fill vector entries.
        A - vector of starting first entries.
        Returns:
        V, a vector of length n and entries a, respectively A.

      • isZero

        public boolean isZero​(java.util.List<C> a)
        Test vector of zero ring elements.
        Parameters:
        a - a ring element list.
        Returns:
        true, if all polynomial in a are zero, else false.

      • scalarProduct

        public java.util.List<C> scalarProduct​(C p,
                                       java.util.List<C> F)
        Scalar product of ring element with vector of ring elements.
        Parameters:
        p - a ring element.
        F - a ring element list.
        Returns:
        the scalar product of p and F.

      • scalarProduct

        public java.util.List<C> scalarProduct​(java.util.List<C> F,
                                       C p)
        Scalar product of vector of ring element with ring element.
        Parameters:
        F - a ring element list.
        p - a ring element.
        Returns:
        the scalar product of F and p.

      • leftProduct

        public GenVector<C> leftProduct​(GenVector<C> G,
                                GenMatrix<C> F)
        Product of a vector and a matrix of ring elements.
        Parameters:
        G - a vectors of ring elements.
        F - a matrix of ring element lists.
        Returns:
        the left product of G and F.

      • rightProduct

        public GenVector<C> rightProduct​(GenVector<C> G,
                                 GenMatrix<C> F)
        Product of a vector and a matrix of ring elements.
        Parameters:
        G - a vector of element list.
        F - a matrix of ring element lists.
        Returns:
        the right product of G and F.