The command NumberOfElements(P) returns the number of elements of the partially ordered set P.

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

$\mathrm{divisibility}≔\left(x\,y\right)\mapsto \mathrm{irem}\left(y\,x\right)=0$

$\mathrm{divisibility}≔\left(x\,y\right)\mapsto \mathrm{irem}\left(y\,x\right)=0$

$V≔\varnothing \&colon;$$\mathrm{leq}≔\mathrm{`<=`}\&colon;$$\mathrm{empty\_poset}≔\mathrm{PartiallyOrderedSet}\left(V\&comma;\mathrm{leq}\right)$

$\mathrm{empty\_poset}≔\mathrm{<\; a\; poset\; with\; 0\; elements\; >}$

$\mathrm{NumberOfElements}\left(\mathrm{empty\_poset}\right)$

$0$

$S≔\left\{1\&comma;2\&comma;3\&comma;4\&comma;5\right\}\&colon;$$\mathrm{poset1}≔\mathrm{PartiallyOrderedSet}\left(S\&comma;\mathrm{leq}\right)$

$\mathrm{poset1}≔\mathrm{<\; a\; poset\; with\; 5\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset1}\right)$

$\mathrm{NumberOfElements}\left(\mathrm{poset1}\right)$

$5$

$Z≔\left\{1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;10\&comma;12\&comma;15\&comma;20\&comma;30\&comma;60\right\}$

$Z≔\left\{1\&comma;2\&comma;3\&comma;4\&comma;5\&comma;6\&comma;10\&comma;12\&comma;15\&comma;20\&comma;30\&comma;60\right\}$

$\mathrm{poset10}≔\mathrm{PartiallyOrderedSet}\left(Z\&comma;\mathrm{divisibility}\right)$

$\mathrm{poset10}≔\mathrm{<\; a\; poset\; with\; 12\; elements\; >}$

$\mathrm{DrawGraph}\left(\mathrm{poset10}\right)$

$\mathrm{NumberOfElements}\left(\mathrm{poset10}\right)$

$12$

Richard P. Stanley: Enumerative Combinatorics 1. 1997, Cambridge Studies in Advanced Mathematics. Vol. 49. Cambridge University Press.

The PartiallyOrderedSets[NumberOfElements] command was introduced in Maple 2025.

For more information on Maple 2025 changes, see Updates in Maple 2025.