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RegularChains[ChainTools]

  

IsInSaturate

  

test membership to the saturated ideal of a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

IsInSaturate(p, rc, R)

Parameters

p

-

polynomial of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

The command IsInSaturate(p,rc,R) returns true if and only if p belongs to the saturated ideal of rc.

• 

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

Examples

withRegularChains:withChainTools:

RPolynomialRingz,y,x

Rpolynomial_ring

(1)

pzxz2+y2+1

pzxz2+y2+1

(2)

pxx2+1

pxx2+1

(3)

rcChainpx,pz,EmptyR,R

rcregular_chain

(4)

Lppz,px,pz+px,x2pzpx,px2,3px+xypz

Lpz2x+y2+1,x2+1,xz2+x2+y2+2,z2x+y2+1x2x21,x2+12,z2x+y2+1xy+3x2+3

(5)

foritonopsLpdoIsInSaturateLpi,rc,Rend do

true

true

true

true

true

true

(6)

See Also

Chain

ChainTools

Empty

EqualSaturatedIdeals

IsIncluded

IsInRadical

PolynomialRing

RegularChains

Triangularize