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RegularChains

  

RegularizeInitial

  

make the initial of a polynomial regular

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RegularizeInitial(f, rc, R, 'normalized'='yes')

Parameters

f

-

polynomial of R

rc

-

regular chain of R

R

-

polynomial ring

'normalized'='yes'

-

boolean flag (optional)

Description

• 

The command RegularizeInitial(f, rc, R) returns a list of pairs fi,rci where each rci is a regular chain of R and each fi is a polynomial of R.

• 

The set of all the regular chains rci form a decomposition of in_rc in the sense of Kalkbrener.

• 

Each polynomial fi is either constant or its initial is regular modulo rci.

• 

Each polynomial fi is equal to f modulo the saturated ideal of rci.

• 

The function is based on Regularize.

• 

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

Examples

withRegularChains:withChainTools:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

TEmptyR

T:=regular_chain

(2)

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

T:=regular_chain

(3)

rtlRegularizeInitialz+1x3+5,T,R

rtl:=x3z+x3+5z+5,regular_chain,5z+5,regular_chain

(4)

foritonopsrtldoEquationsrtli2,R;IsRegularrtli1,rtli2,Rend do

false

(5)

See Also

Chain

ChainTools

Empty

Equations

Initial

Inverse

IsRegular

PolynomialRing

RegularChains

RegularGcd

Regularize

 


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