RegularChains[ConstructibleSetTools][PolynomialMapPreimage] - compute the preimage of a variety under a polynomial map
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Calling Sequence
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PolynomialMapPreimage(F, PM, R, S)
PolynomialMapPreimage(F, H, PM, R, S)
PolynomialMapPreimage(CS, PM, R, S)
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Parameters
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F
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list of polynomials of S
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PM
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list of polynomials in R
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R
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polynomial ring (source)
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S
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polynomial ring (target)
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H
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list of polynomials in R
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CS
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constructible set
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Description
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The command PolynomialMapPreimage(F, PM, R, S) returns a constructible set cs over R, which is the preimage of the variety V(F) under the polynomial map PM.
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The command PolynomialMapPreimage(F, H, PM, R, S) returns a constructible set cs over R, which is the preimage of the difference of the variety V(F) by the variety under the polynomial map PM.
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The command PolynomialMapPreimage(CS, PM, R, S) returns a constructible set cs over R, which is the preimage of the constructible set CS under the polynomial map PM.
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Both rings R and S should be over the same ground field.
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The variable sets of R and S should be disjoint.
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This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form PolynomialMapPreimage(..) only after executing the command with(RegularChains[ConstructibleSetTools]). However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][PolynomialMapPreimage](..).
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Examples
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Note that the polynomial map should be a list of polynomials of R. Also the number of polynomials in PM equals the number of variables of S.
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