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

RegularChains

  

ConstructibleSetTools[EmptyConstructibleSet]

  

construct the empty constructible set

  

SemiAlgebraicSetTools[EmptySemiAlgebraicSet]

  

construct the empty semi-algebraic set

 

Calling Sequence

Parameters

Description

Examples

Compatibility

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.

RPolynomialRingx,y

Rpolynomial_ring

(1)

Then construct an empty constructible set cs as follows.

csEmptyConstructibleSetR

csconstructible_set

(2)

IsEmptycs,R

true

(3)

Compatibility

• 

The RegularChains[SemiAlgebraicSetTools][EmptySemiAlgebraicSet] command was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

ConstructibleSet

ConstructibleSetTools

IsContained

IsEmpty

RegularChains

SemiAlgebraicSetTools