test membership to the radical of a saturated ideal
IsInRadical(p, rc, R)
polynomial of R
regular chain of R
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](..).
R ≔ PolynomialRing⁡y,x
sys ≔ x2+1,y+2⁢x2
Note that this input system is already a regular chain.
out ≔ Triangularize⁡sys,R;rc ≔ out1
Is y+2⁢x in the saturated ideal of rc?
Is y+2⁢x is the radical of the saturated ideal of rc?
The function Triangularize can remove the squares as follows.
out ≔ Triangularize⁡sys,R,radical=yes;sfrc ≔ out1
Is y+2⁢x in the saturated ideal of sfrc?
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