The command Empty(R) returns the empty regular chain of R, that is the regular chain of R with no polynomials.

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

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

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

$R≔\mathrm{polynomial\_ring}$

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

$T≔\mathrm{Empty}\left(R\right)$

$T≔\mathrm{regular\_chain}$