compute the preimage of a variety under a polynomial map
RationalMapPreimage(F, RM, R, S)
RationalMapPreimage(F, H, RM, R, S)
RationalMapPreimage(CS, RM, R, S)
list of polynomials of S
a list of rational functions in R
a polynomial ring (source)
a polynomial ring (target)
list of polynomials
The command RationalMapPreimage(F, RM, R, S) returns a constructible set cs over R. cs is the preimage 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 RationalMapPreimage(F, H, RM, R, S) returns the preimage of the constructible set V-W under the rational map RM.
The command RationalMapPreimage(CS, RM, R, S) returns the preimage 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 rational functions in RM is equal to the number of variables of ring S.
R ≔ PolynomialRing⁡x,y,z
R ≔ polynomial_ring
S ≔ PolynomialRing⁡s,t
S ≔ polynomial_ring
Note that the rational map should be a list of rational functions of R. Also, the number of polynomials in RM equals the number of variables of S.
RM ≔ x2x+y,y2x+y
F ≔ s−1,t−1
cs ≔ RationalMapPreimage⁡F,RM,R,S
cs ≔ constructible_set
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