Difference between revisions of "Dot"
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The [[glyph]] '''dot''' or '''period''' refers to the <code>.</code> character. It represents several unrelated concepts, some derived from traditional mathematical notation. The dot is one of the most [[wikipedia:Operator_overloadingoverloaded]] APL symbols:  The [[glyph]] '''dot''' or '''period''' refers to the <code>.</code> character. It represents several unrelated concepts, some derived from traditional mathematical notation. The dot is one of the most [[wikipedia:Operator_overloadingoverloaded]] APL symbols:  
−  * In all dialects, it is used as [[wikipedia:decimal_separatordecimal_separator]], for example <source lang=apl inline>3.14</source> representing <math>3+\  +  * In all dialects, it is used as [[wikipedia:decimal_separatordecimal_separator]], for example <source lang=apl inline>3.14</source> representing <math>3+\tfrac{14}{100}</math>. 
* In all dialects, it is a [[dyadic operator]] with function [[operand]]s, deriving a [[dyadic function]] (<source lang=apl inline>X f.g Y</source>) which is the generalised [[Inner Product]]. Specifically, (<source lang=apl inline>X +.× Y</source>) is the [[wikipedia:dot productdot product]].  * In all dialects, it is a [[dyadic operator]] with function [[operand]]s, deriving a [[dyadic function]] (<source lang=apl inline>X f.g Y</source>) which is the generalised [[Inner Product]]. Specifically, (<source lang=apl inline>X +.× Y</source>) is the [[wikipedia:dot productdot product]].  
* In all dialects (although deprecated in [[SAX]]), dot with a [[Jot]] on on its left, forms the [[Outer Product]] operator.  * 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 [[monadic functionmonadically]] and then represents the [[Alternant]] (<source lang=apl inline>+.× Y</source>) which is a generalisation of [[wikipedia:determinantdeterminant]]s and [[wikipedia:permanentpermanent]]s. Specifically, (<source lang=apl inline>.× Y</source>) is the [[wikipedia:determinantdeterminant]].  * In [[SHARP APL]] and [[NARS2000]], the function derived from two functions operands, can also be called [[monadic functionmonadically]] and then represents the [[Alternant]] (<source lang=apl inline>+.× Y</source>) which is a generalisation of [[wikipedia:determinantdeterminant]]s and [[wikipedia:permanentpermanent]]s. Specifically, (<source lang=apl inline>.× Y</source>) is the [[wikipedia:determinantdeterminant]].  
* In [[SHARP APL]], with a function left operand and an array right operand, called ''ply'', is used for the [[Power Operator]] (<source lang=apl inline>f⍣k</source> in several other dialects).  * In [[SHARP APL]], with a function left operand and an array right operand, called ''ply'', is used for the [[Power Operator]] (<source lang=apl inline>f⍣k</source> 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 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, <source lang=apl inline>..</source>, form a biglyph, and represents the [[Sequence]] function (represented by the ellipsis, <source lang=apl inline>…<⍳0</source> in [[dzaima/APL]] and [[Extended Dyalog APL]]).  * In [[NARS2000]], two immediately adjacent dots, <source lang=apl inline>..</source>, form a biglyph, and represents the [[Sequence]] function (represented by the ellipsis, <source lang=apl inline>…<⍳0</source> in [[dzaima/APL]] and [[Extended Dyalog APL]]). 
Latest revision as of 10:28, 13 May 2020
.

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 .  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 biglyph, 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
APL glyphs [edit]  

Information  Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics ∙ Overstrikes 
Individual glyphs  Jot (∘ ) ∙ Right Shoe (⊃ ) ∙ Up Arrow (↑ ) ∙ Zilde (⍬ ) ∙ High minus (¯ ) ∙ Dot (. ) ∙ Del (∇ )
