elementary-divisor.rd

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# Algebra::ElementaryDivisor

(Elementary Divisor Module)

Module to get the elementary divisors of the matrix of polynomial. This is included by the class Algebra::MatrixAlgebra.

## File Name:

- elementary-divisor.rb

## Included Modules:

none.

## Associated Functions:

`Algebra::MatrixAlgebra#i2o`

  Converts the matrix of polynomials into the polynomial of matrices.

`Algebra::MatrixAlgebra#e_deg`

  Returns the max degree of the matrix of polynomials.

## Class Methods:

`::factorize(ary)`

  Returns the array of the factors (instances of Algebra::Factors), factorizing the each entries of the array ary of the elementary divisors of a matrix.

## Methods:

`e_diagonalize!`

  Deforms to the diagonal matrix of the elementary divisors. If can't, raise an error.

`e_diagonalize`

  Same as `dup.e_diagonalize!`.

`elementary_divisor`

  Returns the array of the elementary divisors.

`e_inverse`

  Returns the inverse matrix of the matrix over Euclidian ring. If can't, raise an error.