compute the image of a variety or a constructible set under a rational map
RationalMapImage(F, RM, R, S)
RationalMapImage(F, H, RM, R, S)
RationalMapImage(CS, RM, R, S)
list of polynomials
a list of rational functions in R
a polynomial ring (source)
a polynomial ring (target)
The command RationalMapImage(F, RM, R, S) returns a constructible set cs which is the image of the variety V⁡F under the rational map RM.
If H is specified, let W be the variety defined by the product of polynomials in H. The command RationalMapImage(F, H, RM, R, S) returns the image of the constructible set V-W under the rational map RM.
The command RationalMapImage(CS, RM, R, S) returns the image of the constructible set CS under the rational map RM.
Both rings R and S should be over the same ground field.
The variable sets of R and S should be disjoint.
The number of polynomials in RM is equal to the number of variables of ring S.
The following example is related to the tacnode curve.
S ≔ PolynomialRing⁡t
T ≔ PolynomialRing⁡x,y
RM ≔ t3−6⁢t2+9⁢t−22⁢t4−16⁢t3+40⁢t2−32⁢t+9,t2−4⁢t+42⁢t4−16⁢t3+40⁢t2−32⁢t+9
cs ≔ RationalMapImage⁡F,RM,S,T
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