The Support command returns the list of the monomials present in a polynomial f. It automatically maps onto lists and sets, and can be used to quickly reveal the structure of a large Groebner basis.

An optional second argument T may be a list or set of variables or a MonomialOrder or ShortMonomialOrder.  If a monomial order is supplied then the resulting list of monomials is sorted in the monomial order.  If T is a list then the monomials are sorted in lexicographical order, or if T is a set then the monomials are not sorted.

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

$f≔87xy-56xy{z}^2-62x^2{z}^3+97x{y}^{3}z-73y{z}^4$

$f≔-62x^2{z}^3+97x{y}^{3}z-73y{z}^4-56xy{z}^2+87xy$

$\mathrm{Support}\left(f\right)$

$\left[x^2{z}^3\,x{y}^{3}z\,y{z}^4\,xy{z}^2\,xy\right]$

$\mathrm{Support}\left(f\,\left[x\,y\,z\right]\right)$

$\left[x^2{z}^3\,x{y}^{3}z\,xy{z}^2\,xy\,y{z}^4\right]$

$\mathrm{Support}\left(f\,\mathrm{grlex}\left(x\,y\,z\right)\right)$

$\left[x^2{z}^3\,x{y}^{3}z\,y{z}^4\,xy{z}^2\,xy\right]$

$F≔\left[x^2+5y^4\,x^8-8y^4\,z^8+64y^2-x^8+100\right]$

$F≔\left[5y^4+x^2\,x^8-8y^4\,-x^8+z^8+64y^2+100\right]$

$G≔\mathrm{Groebner}\left[\mathrm{Basis}\right]\left(F\,\mathrm{plex}\left(x\,y\,z\right)\right)$

$G≔\left[390625z^{64}+312500000z^{56}+109375000000z^{48}+21874994880000z^{40}+2734360643520000z^{32}+218740742876160000z^{24}+10935189454281097216z^{16}+312260738651419443200z^8+3897556646490972160000\,264000003515625z^{56}+141792004560937500z^{48}+36975233639881250000z^{40}+5116635466117234680000z^{32}+535841466606972146400000z^{24}-4111661799133622084480000z^{16}+27769709934963826285883486208z^8+2305845823963169687985887117312y^2+3096625863672405027833148620800\,-1320000017578125z^{56}-708960022804687500z^{48}-184876168199406250000z^{40}-25583177330586173400000z^{32}-2679207333034860732000000z^{24}+20558308995668110422400000z^{16}+41295655322303500444480000000z^8+288230727995396210998235889664x^2+2531291181350238048224000000000\right]$

$\mathrm{Support}\left(G\,\mathrm{plex}\left(x\,y\,z\right)\right)$

$\left[\left[z^{64}\,z^{56}\,z^{48}\,z^{40}\,z^{32}\,z^{24}\,z^{16}\,z^8\,1\right]\,\left[y^2\,z^{56}\,z^{48}\,z^{40}\,z^{32}\,z^{24}\,z^{16}\,z^8\,1\right]\,\left[x^2\,z^{56}\,z^{48}\,z^{40}\,z^{32}\,z^{24}\,z^{16}\,z^8\,1\right]\right]$