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RegularChains[ConstructibleSetTools]

  

RationalMapImage

  

compute the image of a variety or a constructible set under a rational map

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RationalMapImage(F, RM, R, S)

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

RationalMapImage(CS, RM, R, S)

Parameters

F

-

list of polynomials

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 RationalMapImage(F, RM, R, S) returns a constructible set cs which is the image 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 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.

Examples

withRegularChains:

withConstructibleSetTools:

The following example is related to the tacnode curve.

SPolynomialRingt

S:=polynomial_ring

(1)

TPolynomialRingx,y

T:=polynomial_ring

(2)

F

F:=

(3)

RMt36t2+9t22t416t3+40t232t+9,t24t+42t416t3+40t232t+9

RM:=t36t2+9t22t416t3+40t232t+9,t24t+42t416t3+40t232t+9

(4)

csRationalMapImageF,RM,S,T

cs:=constructible_set

(5)

Infocs,T

2x43yx2+y42y3+y2,y,10y+2x2+2y3y2y,964y6480y56858y44328y3888y272y2x288y8+2104y72316y6943y5+892y4+318y3+32y2+y,x,y1,1,x,y,1

2x43yx2+y42y3+y2,y,10y+2x2+2y3y2y,964y6480y56858y44328y3888y272y2x288y8+2104y72316y6943y5+892y4+318y3+32y2+y,x,y,1,x,y1,1

(6)

See Also

ConstructibleSet

Difference

MakePairwiseDisjoint

Projection

RegularChains

 


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