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RegularChains[ConstructibleSetTools]

  

PolynomialMapImage

  

compute the image of a variety under a polynomial map

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

PolynomialMapImage(F, PM, R, S)

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

PolynomialMapImage(CS, PM, R, S)

Parameters

F

-

list of polynomials in R

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 PolynomialMapImage(F, PM, R, S) returns a constructible set cs which is the image of the variety VF under the polynomial map PM.

• 

The command PolynomialMapImage(F, H, PM, R, S) returns a constructible set cs which is the image of the difference of the variety VF by the variety VH under the polynomial map PM.

• 

The command PolynomialMapImage(CS, PM, R, S) returns a constructible set cs which is the image of the constructible set CS under the polynomial map PM.

• 

Both rings R and S should be over the same base field.

• 

The variable sets of R and S should be disjoint.

• 

The number of polynomials in PM is equal to the number of variables of ring S.

• 

This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form PolynomialMapImage(..) 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][PolynomialMapImage](..).

Examples

withRegularChains:

withConstructibleSetTools:

The following example is related to the Whitney umbrella.

RPolynomialRingu,v

R:=polynomial_ring

(1)

SPolynomialRingx,y,z

S:=polynomial_ring

(2)

PMuv,u,v2

PM:=uv,u,v2

(3)

csPolynomialMapImage,PM,R,S

cs:=constructible_set

(4)

csMakePairwiseDisjointcs,S

cs:=constructible_set

(5)

Infocs,S

x,y,1,x2y2z,y

(6)

See Also

ConstructibleSet

ConstructibleSetTools

Difference

MakePairwiseDisjoint

Projection

RegularChains

 


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