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RegularChains[ConstructibleSetTools]

  

RationalMapPreimage

  

compute the preimage of a variety under a polynomial map

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RationalMapPreimage(F, RM, R, S)

RationalMapPreimage(F, H, RM, R, S)

RationalMapPreimage(CS, RM, R, S)

Parameters

F

-

list of polynomials of S

RM

-

a list of rational functions in R

R

-

a polynomial ring (source)

S

-

a polynomial ring (target)

H

-

list of polynomials

CS

-

constructible set

Description

• 

The command RationalMapPreimage(F, RM, R, S) returns a constructible set cs over R. cs is the preimage of the variety VF 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.

Examples

withRegularChains:

withConstructibleSetTools:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

SPolynomialRings,t

S:=polynomial_ring

(2)

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.

RMx2x+y,y2x+y

RM:=x2x+y,y2x+y

(3)

Fs1,t1

F:=s1,t1

(4)

csRationalMapPreimageF,RM,R,S

cs:=constructible_set

(5)

Infocs,R

x2,y2,1

(6)

See Also

ConstructibleSet

Difference

MakePairwiseDisjoint

Projection

RationalMapImage

RegularChains

 


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