The command Equations(rc,R) returns the list of the polynomials of rc by decreasing order of main variable.

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

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

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

$R≔\mathrm{polynomial\_ring}$

$\mathrm{rc}≔\mathrm{Empty}\left(R\right)$

$\mathrm{rc}≔\mathrm{regular\_chain}$

$\mathrm{rc}≔\mathrm{Chain}\left(\left[z^2+1\,y^2-z\,x+y+z\right]\,\mathrm{rc}\,R\right)$

$\mathrm{rc}≔\mathrm{regular\_chain}$

$\mathrm{Equations}\left(\mathrm{rc}\,R\right)$

$\left[x+y+z\,y^2-z\,z^2+1\right]$