LowerEchelonForm - Maple Help
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RegularChains[MatrixTools]

  

LowerEchelonForm

  

lower echelon form of a matrix modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

LowerEchelonForm(A, rc, R)

Parameters

A

-

square Matrix with coefficients in the ring of fractions of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command LowerEchelonForm(A, rc, R) returns a list of pairs  where  is a regular chain, and  is the lower echelon form of A modulo the saturated ideal of rc_i.

• 

All the returned regular chains  form a triangular decomposition of rc (in the sense of Kalkbrener).

• 

It is assumed that rc is strongly normalized.

• 

The algorithm is an adaptation of the algorithm of Bareiss.

• 

This command is part of the RegularChains[MatrixTools] package, so it can be used in the form LowerEchelonForm(..) only after executing the command with(RegularChains[MatrixTools]).  However, it can always be accessed through the long form of the command by using RegularChains[MatrixTools][LowerEchelonForm](..).

Examples

(1)

(2)

(3)

(4)

(5)

See Also

Chain

Empty

Equations

IsStronglyNormalized

IsZeroMatrix

JacobianMatrix

MatrixInverse

MatrixMultiply

MatrixOverChain

MatrixTools

NormalForm

PolynomialRing

RegularChains

 


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