The sparse indexing function is used to create a table or an array with a sparse representation, meaning that only nonzero elements are stored in the underlying data structure.

The sparse indexing function specifies that unassigned entries of a table or an array have the value 0. For example, array(sparse, 1..2, 1..2) is a zero matrix.

If T is a table and j is an unevaluated name, then T[j] returns unevaluated. However, if j evaluates to an integer, then T[j] returns either the value of T[j] or 0 if T[j] has no assigned value.

A default value other than zero can be used when constructing a sparse table.  The command, table(sparse=XXX), creates a table filled with XXXs at each entry.  This option is only available for tables.

Note: The command array has been superseded by Array.

$T≔\mathrm{table}\left(\mathrm{sparse}\,\left[A=a\right]\right)\:$

$T\left[A\right]$

$a$

$T\left[B\right]$

$0$

$a≔\mathrm{array}\left(\mathrm{sparse}\,1..2\right)\:$

$a\left[1\right]$

$0$

$a\left[j\right]$

$a_j$

$T≔\mathrm{table}\left(\mathrm{sparse}=\mathrm{undefined}\,\left\{1=1\,2=2\right\}\right)\:$

$T\left[1\right]$

$1$

$T\left[100\right]$

$\mathrm{undefined}$

The sparse indexing function was updated in Maple 2019.

The sparse=XXX option was updated in Maple 2019.