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](..).

$\mathrm{with}\left(\mathrm{RegularChains}\right)\:$

$\mathrm{with}\left(\mathrm{ConstructibleSetTools}\right)\:$

$R≔\mathrm{PolynomialRing}\left(\left[x\,y\right]\right)$

$R≔\mathrm{polynomial\_ring}$

$\mathrm{cs}≔\mathrm{EmptyConstructibleSet}\left(R\right)$

$\mathrm{cs}≔\mathrm{constructible\_set}$

$\mathrm{IsEmpty}\left(\mathrm{cs}\,R\right)$

$\mathrm{true}$

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

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