The Classify(p, L, b1, ..., bn) function groups the elements of L into sets according to the characteristic property p. That is, it returns a table T with indices i such that T[i] is the set of elements e of L having value p(e, b1, ..., bn) = i.

If L is a table or rtable (such as an Array, Matrix, or Vector), the result is equivalent to applying this function to convert(L,list) with all other arguments the same.  (See convert/list.)

The call Classify(p, L, b1, ..., bn) is mostly equivalent to ListTools[Categorize]((x, y) -> p(x)=p(y), L, b1, ..., bn) but more efficient. The form of the output is also different: Categorize returns a sequence of lists, while Classify returns a table of sets. On the other hand, Categorize is more general in that it accepts two-argument relations which can not necessarily be written in the form (x, y) -> p(x)=p(y) for some property p.

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

$\mathrm{types}≔\mathrm{Classify}\left(\mathrm{whattype}\,\left[''Hello''\,1\,2.\,\mathrm{\pi }\,x\,x+y\,\exp \,''world!''\right]\right)\:$

$\mathrm{map}\left(\mathrm{print}\,\mathrm{op}\left(\mathrm{eval}\left(\mathrm{types}\right)\right)\right)\:$

$\mathrm{string}=\left\{''Hello''\,''world!''\right\}$

$\mathrm{symbol}=\left\{\mathrm{\pi }\,x\right\}$

$\mathrm{integer}=\left\{1\right\}$

$\mathrm{procedure}=\left\{\exp \right\}$

$\mathrm{float}=\left\{2.\right\}$

$\mathrm{`+`}=\left\{x+y\right\}$

$\mathrm{number\_of\_distinct\_prime\_factors}≔n\mapsto \mathrm{nops}\left(\mathrm{ifactors}\left(n\right)\left[2\right]\right)\:$

$\mathrm{npf30}≔\mathrm{Classify}\left(\mathrm{number\_of\_distinct\_prime\_factors}\,\left[\mathrm{`\$`}\left(1..30\right)\right]\right)\:$

$\mathrm{indices}\left(\mathrm{npf30}\,\mathrm{nolist}\right)$

$0,1,2,3$

$\mathrm{npf30}\left[0\right]$

$\left\{1\right\}$

$\mathrm{npf30}\left[1\right]$

$\left\{2\,3\,4\,5\,7\,8\,9\,11\,13\,16\,17\,19\,23\,25\,27\,29\right\}$

$\mathrm{npf30}\left[2\right]$

$\left\{6\,10\,12\,14\,15\,18\,20\,21\,22\,24\,26\,28\right\}$

$\mathrm{npf30}\left[3\right]$

$\left\{30\right\}$

The ListTools[Classify] command was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.