RegularChains[ConstructibleSetTools]
PolynomialMapPreimage
compute the preimage of a variety under a polynomial map
Calling Sequence
Parameters
Description
Examples
PolynomialMapPreimage(F, PM, R, S)
PolynomialMapPreimage(F, H, PM, R, S)
PolynomialMapPreimage(CS, PM, R, S)
F
-
list of polynomials of S
PM
list of polynomials in R
R
polynomial ring (source)
S
polynomial ring (target)
H
CS
constructible set
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.
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 VH under the polynomial map PM.
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.
Both rings R and S should be over the same ground field.
The variable sets of R and S should be disjoint.
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](..).
withRegularChains:
withConstructibleSetTools:
R≔PolynomialRingx,y,z
R≔polynomial_ring
S≔PolynomialRings,t
S≔polynomial_ring
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.
MP≔x2,y2
F≔s−1,t−1
cs≔PolynomialMapPreimageF,MP,R,S
cs≔constructible_set
Infocs,R
x+1,y−1,1,x−1,y−1,1,x+1,y+1,1,x−1,y+1,1
See Also
ConstructibleSet
ConstructibleSetTools
Difference
MakePairwiseDisjoint
PolynomialMapImage
Projection
RegularChains
Download Help Document