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RegularChains[ChainTools][IsInRadical] - test membership to the radical of a saturated ideal
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Calling Sequence
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IsInRadical(p, rc, R)
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Parameters
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p
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polynomial of R
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rc
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regular chain of R
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R
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polynomial ring
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Description
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The command IsInRadical(p, rc, R) returns true if and only if p belongs to the radical of the saturated ideal of rc.
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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](..).
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Examples
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![R := PolynomialRing([y, x])](/support/helpjp/helpview.aspx?si=5376/file06447/math96.png)
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Note that this input system is already a regular chain.
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 ![rc := out[1]](/support/helpjp/helpview.aspx?si=5376/file06447/math113.png)
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![[y^2+4*x*y-4, x^2+1]](/support/helpjp/helpview.aspx?si=5376/file06447/math126.png)
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Is  in the saturated ideal of rc?
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Is  is the radical of the saturated ideal of rc?
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The function Triangularize can remove the squares as follows.
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 ![sfrc := out[1]](/support/helpjp/helpview.aspx?si=5376/file06447/math169.png)
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Is  in the saturated ideal of sfrc?
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