construct the empty constructible set - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : SemiAlgebraicSetTools Subpackage : RegularChains/ConstructibleSetTools/EmptyConstructibleSet

RegularChains[ConstructibleSetTools][EmptyConstructibleSet] - construct the empty constructible set

RegularChains[SemiAlgebraicSetTools][EmptySemiAlgebraicSet] - construct the empty semi-algebraic set

Calling Sequence

EmptyConstructibleSet(R)

EmptySemiAlgebraicSet(R)

Parameters

R

-

polynomial ring

Description

• 

The command EmptyConstructibleSet(R) returns the empty set of the affine space over the algebraic closure of the base field of R and whose dimension is equal to the total number of variables of R.

• 

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

• 

The command EmptySemiAlgebraicSet(R) returns the empty set of the euclidean space over the real numbers and whose dimension is equal to the total number of variables of R.

• 

This command is part of the RegularChains[SemiAlgebraicSetTools] submodule, so it can be used in the form EmptySemiAlgebraicSet(..) only after executing the command with(RegularChains[SemiAlgebraicSetTools].  However, it can always be accessed through the long form of the command by using RegularChains[SemiAlgebraicSetTools][EmptySemiAlgebraicSet](..).

Examples

withRegularChains:

withConstructibleSetTools:

Define a polynomial ring R first.

R:=PolynomialRingx,y

R:=polynomial_ring

(1)

Then construct an empty constructible set cs as follows.

cs:=EmptyConstructibleSetR

cs:=constructible_set

(2)

IsEmptycs,R

true

(3)

See Also

ConstructibleSet, ConstructibleSetTools, IsContained, IsEmpty, RegularChains, SemiAlgebraicSetTools


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam