edu.jas.vector
Class BasicLinAlg<C extends RingElem<C>>

java.lang.Object
  edu.jas.vector.BasicLinAlg<C>

public class BasicLinAlg<C extends RingElem<C>>
extends java.lang.Object

Basic linear algebra methods. Implements Basic linear algebra computations and tests.

Author:

Heinz Kredel

Constructor Summary

BasicLinAlg()
Constructor.

Method Summary

boolean	isZero(java.util.List<GenPolynomial<C>> a) test vector of zero polynomials.
java.util.List<GenPolynomial<C>>	scalarProduct(GenPolynomial<C> p, java.util.List<GenPolynomial<C>> F) Scalar product of polynomial with vector of polynomials.
java.util.List<GenPolynomial<C>>	scalarProduct(java.util.List<GenPolynomial<C>> F, GenPolynomial<C> p) Scalar product of vector of polynomials with polynomial.
GenPolynomial<C>	scalarProduct(java.util.List<GenPolynomial<C>> r, java.util.List<GenPolynomial<C>> F) Scalar product of vectors of polynomials.
java.util.List<GenPolynomial<C>>	scalarProduct(java.util.List<GenPolynomial<C>> r, ModuleList<C> F) product of vector and matrix of polynomials.
java.util.List<GenPolynomial<C>>	vectorAdd(java.util.List<GenPolynomial<C>> a, java.util.List<GenPolynomial<C>> b) Addition of vectors of polynomials.

Methods inherited from class java.lang.Object

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

Constructor Detail

BasicLinAlg

public BasicLinAlg()

Constructor.

Method Detail

scalarProduct

public GenPolynomial<C> scalarProduct(java.util.List<GenPolynomial<C>> r,
                                      java.util.List<GenPolynomial<C>> F)

Scalar product of vectors of polynomials.

Type parameter:

C coefficient type.

Parameters:

r - a polynomial list.

F - a polynomial list.

Returns:

the scalar product of r and F.

scalarProduct

public java.util.List<GenPolynomial<C>> scalarProduct(java.util.List<GenPolynomial<C>> r,
                                                      ModuleList<C> F)

product of vector and matrix of polynomials.

Type parameter:

C coefficient type.

Parameters:

r - a polynomial list.

F - a polynomial matrix.

Returns:

the scalar product of r and F.

vectorAdd

public java.util.List<GenPolynomial<C>> vectorAdd(java.util.List<GenPolynomial<C>> a,
                                                  java.util.List<GenPolynomial<C>> b)

Addition of vectors of polynomials.

Type parameter:

C coefficient type.

Parameters:

a - a polynomial list.

b - a polynomial list.

Returns:

a+b, the vector sum of a and b.

isZero

public boolean isZero(java.util.List<GenPolynomial<C>> a)

test vector of zero polynomials.

Type parameter:

C coefficient type.

Parameters:

a - a polynomial list.

Returns:

true, if all polynomial in a are zero, else false.

scalarProduct

public java.util.List<GenPolynomial<C>> scalarProduct(GenPolynomial<C> p,
                                                      java.util.List<GenPolynomial<C>> F)

Scalar product of polynomial with vector of polynomials.

Type parameter:

C coefficient type.

Parameters:

p - a polynomial.

F - a polynomial list.

Returns:

the scalar product of p and F.

scalarProduct

public java.util.List<GenPolynomial<C>> scalarProduct(java.util.List<GenPolynomial<C>> F,
                                                      GenPolynomial<C> p)

Scalar product of vector of polynomials with polynomial.

Type parameter:

C coefficient type.

Parameters:

F - a polynomial list.

p - a polynomial.

Returns:

the scalar product of F and p.