Every matroid is defined with respect to some set $E$ called its ground set. The GroundSet command returns this ground set as a list.

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

$A≔\mathrm{Matrix}\left(\left[\left[1\,1\,1\,0\,0\,0\right]\,\left[0\,0\,0\,1\,1\,1\right]\,\left[1\,0\,0\,1\,0\,0\right]\,\left[0\,1\,0\,0\,1\,0\right]\,\left[0\,0\,1\,0\,0\,2\right]\right]\right)$

$A≔\left[\begin{array}{cccccc}1& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1\\ 1& 0& 0& 1& 0& 0\\ 0& 1& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 2\end{array}\right]$

$M≔\mathrm{Matroid}\left(A\right)$

$M≔⟨\begin{array}{c}\mathrm{th\ⅇ\; lin\ⅇar\; matroi\ⅆ\; whos\ⅇ\; groun\ⅆ\; s\ⅇt\; is\; th\ⅇ\; s\ⅇt\; of\; column\; v\ⅇctors\; of\; th\ⅇ\; matrix:}\\ \left[\begin{array}{cccccc}1& 1& 1& 0& 0& 0\\ 0& 0& 0& 1& 1& 1\\ 1& 0& 0& 1& 0& 0\\ 0& 1& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 2\end{array}\right]\end{array}⟩$

$\mathrm{GroundSet}\left(M\right)$

$\left[1\,2\,3\,4\,5\,6\right]$

$M≔\mathrm{Matroid}\left(\left[''apples''\,''bananas''\,''coconuts''\right]\,\mathrm{bases}=\left[\left\{''apples''\,''bananas''\right\}\,\left\{''apples''\,''coconuts''\right\}\,\left\{''bananas''\,''coconuts''\right\}\right]\right)$

$M≔⟨\mathrm{th\ⅇ\; uniform\; matroi\ⅆ\; of\; rank\; 2\; on\; 3\; \ⅇl\ⅇm\ⅇnts}⟩$

$\mathrm{GroundSet}\left(M\right)$

$\left[''apples''\,''bananas''\,''coconuts''\right]$

James G. Oxley. Matroid Theory (Oxford Graduate Texts in Mathematics). New York: Oxford University Press. 2006.