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RegularChains[MatrixTools]

  

IsZeroMatrix

  

check whether a matrix is null modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsZeroMatrix(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 IsZeroMatrix(A, rc, R) returns true if and only if A is null modulo the saturated ideal of rc.

• 

It is assumed that rc is strongly normalized.

• 

This command is part of the RegularChains[MatrixTools] package, so it can be used in the form IsZeroMatrix(..) 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][IsZeroMatrix](..).

Examples

withRegularChains:withChainTools:withMatrixTools:

RPolynomialRingy,z

R:=polynomial_ring

(1)

rcEmptyR

rc:=regular_chain

(2)

rcChainz4+1,y2z2,rc,R:

Equationsrc,R

y2z2,z4+1

(3)

mMatrix1,y+z,0,yz

m:=1y+z0yz

(4)

IsZeroMatrixm,rc,R

false

(5)

See Also

Chain

Empty

Equations

IsStronglyNormalized

JacobianMatrix

LowerEchelonForm

MatrixInverse

MatrixMultiply

MatrixOverChain

MatrixTools

NormalForm

PolynomialRing

RegularChains

 


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