Position vs Part

Question

What's the difference between Part and Position?

How can I "move" from the form used by Part to that of Position (and vicerversa?)

Thanks!

Answer 1

The part specification used by Position is shared by Extract:

g = Plot[Sin[x], {x, 1, 5}];

pos = Position[g, _Directive]

Extract[g, pos]

{{1, 1, 3, 1}, {2, 11, 2}}

{Directive[ (* omitted *) ], Directive[GrayLevel[0.5, 0.4]]}

Note that Extract supports extracting multiple disjoint subexpressions at once. Part can only extract one of these at a time.* Each part specification such as {1, 1, 3, 1} needs to be converted from a list into a bare sequence. Available methods include pattern replacement and Function/SlotSequence along with Apply at level one (short form @@@):

Replace[pos, {x__} :> g[[x]], 1]

g[[##]] & @@@ pos

---

* These meaning the two elements in pos in my example. Part specifications at each level may be disjoint but apply to all parts in the extraction. Positions must have all but the last index in common.

m = Partition[Range@9, 3]

$\left( \begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \\ \end{array} \right)$

m[[2, {1, 3}]]

{4, 6}

Index 2 applies to all elements extracted; one cannot extract (only) elements 4 and 9 with a single evaluation of Part for example, whereas you can with Extract:

Extract[m, {{2, 1}, {3, 3}}]