Dot

.

The glyph dot or period refers to the . character. It represents several unrelated concepts, some derived from traditional mathematical notation. The dot is one of the most overloaded APL symbols:

• In all dialects, it is used as decimal separator, for example 3.14 representing $3+{\tfrac {14}{100}}$.
• In all dialects, it is a dyadic operator with function operands, deriving a dyadic function (X f.g Y) which is the generalised Inner Product. Specifically, X +.× Y is the dot product.
• In all dialects (although deprecated in SAX), dot with a Jot on on its left, forms the Outer Product operator.
• In SHARP APL and NARS2000, the function derived from two functions operands, can also be called monadically and then represents the Alternant (+.× Y) which is a generalisation of determinants and permanents. Specifically, -.× Y is the determinant.
• In SHARP APL, with a function left operand and an array right operand, called ply, is used for the Power Operator (f⍣k in several other dialects).
• In dialects that support object oriented programming, for example APLX and Dyalog APL, the dot is used to access members of objects.
• In NARS2000, two immediately adjacent dots, .., form a bi-glyph, and represents the Sequence function (represented by the ellipsis, …<⍳0 in dzaima/APL and Extended Dyalog APL).

Due to its use in numeric constants, letting . be a dyadic operator that takes numeric operands or a function that takes numeric arguments, is potentially problematic or at least confusing:

      4.6
4.6
      4..6
4 5 6 
      4...10 ⍝ this parses as 4 .. 0.10
4 3 2 1
      4. .10
4 0.1
      4 . . 10
SYNTAX ERROR
      4 . . 10
              ∧

Works in: NARS2000