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RegularChains[ConstructibleSetTools][PolynomialMapImage] - compute the image of a variety under a polynomial map
PolynomialMapImage(F, PM, R, S)
PolynomialMapImage(F, H, PM, R, S)
PolynomialMapImage(CS, PM, R, S)
list of polynomials in R
polynomial ring (source)
polynomial ring (target)
The command PolynomialMapImage(F, PM, R, S) returns a constructible set cs which is the image of the variety V⁡F under the polynomial map PM.
The command PolynomialMapImage(F, H, PM, R, S) returns a constructible set cs which is the image of the difference of the variety V⁡F by the variety V⁡H under the polynomial map PM.
The command PolynomialMapImage(CS, PM, R, S) returns a constructible set cs which is the image of the constructible set CS under the polynomial map PM.
Both rings R and S should be over the same base field.
The variable sets of R and S should be disjoint.
The number of polynomials in PM is equal to the number of variables of ring S.
This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form PolynomialMapImage(..) 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][PolynomialMapImage](..).
The following example is related to the Whitney umbrella.
ConstructibleSet, ConstructibleSetTools, Difference, MakePairwiseDisjoint, Projection, RegularChains
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