test membership to the radical of a saturated ideal - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : ChainTools Subpackage : RegularChains/ChainTools/IsInRadical

RegularChains[ChainTools][IsInRadical] - test membership to the radical of a saturated ideal

Calling Sequence

IsInRadical(p, rc, R)

Parameters

p

-

polynomial of R

rc

-

regular chain of R

R

-

polynomial ring

Description

• 

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

• 

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

Examples

withRegularChains:

withChainTools:

R:=PolynomialRingy,x

R:=polynomial_ring

(1)

sys:=x2+1,y+2x2

sys:=y+2x2,x2+1

(2)

Note that this input system is already a regular chain.

out:=Triangularizesys,R;rc:=out1

out:=regular_chain

rc:=regular_chain

(3)

Equationsrc,R

y2+4xy4,x2+1

(4)

NumberOfSolutionsrc,R

4

(5)

Is y+2x in the saturated ideal of rc?

IsInSaturatey+2x,rc,R

false

(6)

Is y+2x is the radical of the saturated ideal of rc?

IsInRadicaly+2x,rc,R

true

(7)

The function Triangularize can remove the squares as follows.

out:=Triangularizesys,R,radical=yes;sfrc:=out1

out:=regular_chain

sfrc:=regular_chain

(8)

Equationssfrc,R;NumberOfSolutionssfrc,R

y+2x,x2+1

2

(9)

Is y+2x in the saturated ideal of sfrc?

IsInSaturatey+2x,sfrc,R

true

(10)

See Also

ChainTools, EqualSaturatedIdeals, Equations, IsIncluded, IsInSaturate, NumberOfSolutions, PolynomialRing, RegularChains, Triangularize


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam