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

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

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

Basic linear algebra for solvable polynomials. Implements basic linear algebra computations and tests.

Author:

Heinz Kredel

Constructor Summary

SolvableBasicLinAlg()
Constructor.

Method Summary

boolean	isZero(java.util.List<GenSolvablePolynomial<C>> a) test vector of zero polynomials.
java.util.List<GenSolvablePolynomial<C>>	leftScalarProduct(GenSolvablePolynomial<C> p, java.util.List<GenSolvablePolynomial<C>> F) Scalar product of polynomial with vector of polynomials.
java.util.List<GenSolvablePolynomial<C>>	leftScalarProduct(java.util.List<GenSolvablePolynomial<C>> F, GenSolvablePolynomial<C> p) Scalar product of vector of polynomials with polynomial.
GenSolvablePolynomial<C>	leftScalarProduct(java.util.List<GenSolvablePolynomial<C>> r, java.util.List<GenSolvablePolynomial<C>> F) Scalar product of vectors of polynomials.
java.util.List<GenSolvablePolynomial<C>>	leftScalarProduct(java.util.List<GenSolvablePolynomial<C>> r, ModuleList<C> F) Product of vector and matrix of polynomials.
java.util.List<GenSolvablePolynomial<C>>	rightScalarProduct(java.util.List<GenSolvablePolynomial<C>> r, ModuleList<C> F) Product of vector and matrix of polynomials.
java.util.List<GenSolvablePolynomial<C>>	vectorAdd(java.util.List<GenSolvablePolynomial<C>> a, java.util.List<GenSolvablePolynomial<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

SolvableBasicLinAlg

public SolvableBasicLinAlg()

Constructor.

Method Detail

leftScalarProduct

public GenSolvablePolynomial<C> leftScalarProduct(java.util.List<GenSolvablePolynomial<C>> r,
                                                  java.util.List<GenSolvablePolynomial<C>> F)

Scalar product of vectors of polynomials.

Type parameter:

C coefficient type.

Parameters:

r - a polynomial list.

F - a polynomial list.

Returns:

the left scalar product of r and F.

leftScalarProduct

public java.util.List<GenSolvablePolynomial<C>> leftScalarProduct(java.util.List<GenSolvablePolynomial<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 list.

Returns:

the left scalar product of r and F.

rightScalarProduct

public java.util.List<GenSolvablePolynomial<C>> rightScalarProduct(java.util.List<GenSolvablePolynomial<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 list.

Returns:

the right scalar product of r and F.

vectorAdd

public java.util.List<GenSolvablePolynomial<C>> vectorAdd(java.util.List<GenSolvablePolynomial<C>> a,
                                                          java.util.List<GenSolvablePolynomial<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<GenSolvablePolynomial<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.

leftScalarProduct

public java.util.List<GenSolvablePolynomial<C>> leftScalarProduct(GenSolvablePolynomial<C> p,
                                                                  java.util.List<GenSolvablePolynomial<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 left scalar product of p and F.

leftScalarProduct

public java.util.List<GenSolvablePolynomial<C>> leftScalarProduct(java.util.List<GenSolvablePolynomial<C>> F,
                                                                  GenSolvablePolynomial<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 left scalar product of F and p.