compute the preimage of a variety under a polynomial map - Maple Help

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RegularChains[ConstructibleSetTools][PolynomialMapPreimage] - compute the preimage of a variety under a polynomial map

Calling Sequence

PolynomialMapPreimage(F, PM, R, S)

PolynomialMapPreimage(F, H, PM, R, S)

PolynomialMapPreimage(CS, PM, R, S)

Parameters

F

-

list of polynomials of S

PM

-

list of polynomials in R

R

-

polynomial ring (source)

S

-

polynomial ring (target)

H

-

list of polynomials in R

CS

-

constructible set

Description

• 

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](..).

Examples

withRegularChains:

withConstructibleSetTools:

R:=PolynomialRingx,y,z

R:=polynomial_ring

(1)

S:=PolynomialRings,t

S:=polynomial_ring

(2)

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

MP:=x2,y2

(3)

F:=s1,t1

F:=s1,t1

(4)

cs:=PolynomialMapPreimageF,MP,R,S

cs:=constructible_set

(5)

Infocs,R

x+1,y1,1,x1,y1,1,x+1,y+1,1,x1,y+1,1

(6)

See Also

ConstructibleSet, ConstructibleSetTools, Difference, MakePairwiseDisjoint, PolynomialMapImage, Projection, RegularChains


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