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RegularChains[MatrixTools]

  

MatrixOverChain

  

normal form of a matrix with respect to a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MatrixOverChain(A, rc, R)

Parameters

A

-

Matrix with coefficients in the field of fractions of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command MatrixOverChain(A, rc, R) returns the normal form of A with respect to rc. In broad terms, this is obtained by mapping RegularChains[NormalForm] on the coefficients of A.

• 

The result is viewed as a matrix with coefficients in the total ring of fractions of R/I where I is 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 MatrixOverChain(..) 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][MatrixOverChain](..).

Examples

withRegularChains:withChainTools:withMatrixTools:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

TEmptyR:

TChainz+1z+2,y2+z,xzxy,T,R

T:=regular_chain

(2)

EquationsT,R

x2+yzx+zy,y2+z,z2+3z+2

(3)

mMatrixx,y,z,x2,y2,z2,x3,y5,z6

m:=xyzx2y2z2x3y5z6

(4)

MatrixOverChainm,T,R

xyzxy+xzyzz23zxyz4xz+3yz2x+2y3z23yz2y63z62,regular_chain

(5)

See Also

Chain

Empty

Equations

IsStronglyNormalized

IsZeroMatrix

JacobianMatrix

LowerEchelonForm

Matrix

MatrixInverse

MatrixMultiply

MatrixTools

NormalForm

PolynomialRing

RegularChains

 


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