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.
R ≔ PolynomialRing⁡u,v
R ≔ polynomial_ring
S ≔ PolynomialRing⁡x,y,z
S ≔ polynomial_ring
PM ≔ u⁢v,u,v2
cs ≔ PolynomialMapImage⁡,PM,R,S
cs ≔ constructible_set
cs ≔ MakePairwiseDisjoint⁡cs,S
Download Help Document
What kind of issue would you like to report? (Optional)
Thank you for submitting feedback on this help document. Your feedback will be used
to improve Maple's help in the future.