The lowerbound and upperbound commands return the lower or upper bounds of the specified dimension, dim, of the array or rtable, a.

The lowerbound of a list is always 1.  The upperbound of a list is the same as numelems('a').  A list-of-lists or other recursive list structure is considered a one-dimensional object.

If a is an object that implements the lowerbound or upperbound methods, then lowerbound( a ) and upperbound( a ) (or lowerbound( a, dim ) and upperbound( a, dim )) depend on how the object a defines these numbers.

If dim is not specified, all lower or upper bounds are returned as a sequence.

To obtain a lower or upper bound on the data contained in the object a, use the min or max commands, respectively.

The following objects have an upperbound method:

The upperbound and lowerbound commands are thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

$M≔⟨⟨1\left|2\right|3⟩\,⟨4\left|5\right|6⟩⟩$

$M≔\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right]$

$m,n≔\mathrm{upperbound}\left(M\right)$

$m,n≔2,3$

$\mathrm{upperbound}\left(M\,1\right)$

$2$

$\mathrm{upperbound}\left(M\,2\right)$

$3$

$\mathrm{lowerbound}\left(M\,1\right)$

$1$

$\mathrm{upperbound}\left(\left[1\,2\,3\right]\right)$

$3$

$\mathrm{upperbound}\left(\left[\left[1\,2\,3\right]\,\left[4\,5\,6\right]\right]\right)$

$2$

The upperbound and lowerbound commands were introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.