If all arguments are ordinal numbers, the Max(a, b, ...) calling sequence returns the largest of the arguments with respect to the ordering of ordinals, and the Min(a, b, ...) calling sequence returns the smallest of the arguments.

Any of the arguments can be a (possibly nested) list, and the argument sequence is converted into a non-nested, flat sequence of ordinal numbers first.

Max() returns 0, and Min() returns $\mathrm{NULL}$.

Parametric ordinals are accepted. If the left difference of two ordinal numbers cannot be determined in the parametric case, an error will be raised.

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

$a≔\mathrm{Ordinal}\left(\left[\left[\mathrm{\omega }\,3\right]\,\left[3\,5\right]\,\left[1\,1\right]\,\left[0\,4\right]\right]\right)$

$a≔{\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 5\+\mathbf{\omega }\+4$

$b≔\mathrm{Ordinal}\left(\left[\left[\mathrm{\omega }\,3\right]\,\left[3\,3\right]\,\left[2\,2\right]\right]\right)$

$b≔{\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 3\+{\mathbf{\omega }}^2\cdot 2$

$\mathrm{Max}\left(3\,a\,\mathrm{\omega }\,b\right)$

${\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 5\+\mathbf{\omega }\+4$

$\mathrm{Min}\left(\left[3\,\left[a\,\mathrm{\omega }\right]\right]\,b\right)=\mathrm{Min}\left(3\,a\,\mathrm{\omega }\,b\right)$

$3=3$

$\mathrm{sort}\left(\left[3\,a\,\mathrm{\omega }\,b\right]\,\mathrm{LessThan}\right)$

$\left[3\,\mathbf{\omega }\,{\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 3\+{\mathbf{\omega }}^2\cdot 2\,{\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 5\+\mathbf{\omega }\+4\right]$

$\mathrm{Max}\left(\left[\right]\right)$

$0$

$c≔\mathrm{Ordinal}\left(\left[\left[1\,x\right]\,\left[0\,2\right]\right]\right)$

$c≔\mathbf{\omega }\cdot x\+2$

$\mathrm{Max}\left(b\,3\,c\right)$

${\mathbf{\omega }}^{\mathbf{\omega }}\cdot 3\+{\mathbf{\omega }}^3\cdot 3\+{\mathbf{\omega }}^2\cdot 2$

$\mathrm{Min}\left(b\,3\,c\right)$

Error, (in Ordinals:-degree) cannot determine if x is nonzero

$\mathrm{Min}\left(b\,3\,\mathrm{Eval}\left(c\,x=x+1\right)\right)$

$3$

$\mathrm{Max}\left(\mathrm{Eval}\left(c\,x=x+1\right)\,\mathrm{Eval}\left(c\,x=x^2+1\right)\right)$

Error, (in Ordinals:-Max) unable to determine maximal element

The Ordinals[Max] and Ordinals[Min] commands were introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.