Difference between revisions of "Dot"

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{{Glyphbox|.}}
 
{{Glyphbox|.}}
 
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_overloading|overloaded]] 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_overloading|overloaded]] APL symbols:
* In all dialects, it is used as [[wikipedia:decimal_separator|decimal_separator]], for example <source lang=apl inline>3.14</source> representing <math>3+\frac{14}{100}</math>.
+
* In all dialects, it is used as [[wikipedia:decimal_separator|decimal_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 product|dot 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 product|dot 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 function|monadically]] and then represents the [[Alternant]] (<source lang=apl inline>+.× Y</source>) which is a generalisation of [[wikipedia:determinant|determinant]]s and [[wikipedia:permanent|permanent]]s. Specifically, (<source lang=apl inline>-.× Y</source>) is the [[wikipedia:determinant|determinant]].
 
* In [[SHARP APL]] and [[NARS2000]], the function derived from two functions operands, can also be called [[monadic function|monadically]] and then represents the [[Alternant]] (<source lang=apl inline>+.× Y</source>) which is a generalisation of [[wikipedia:determinant|determinant]]s and [[wikipedia:permanent|permanent]]s. Specifically, (<source lang=apl inline>-.× Y</source>) is the [[wikipedia:determinant|determinant]].
 
* 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 all dialects but [[SHARP APL]], <source lang=apl inline>∘</source>, named [[nil]], is the [[enclose]]d [[empty]] [[numeric]] [[vector]], which may also be written <source lang=apl inline><⍳0</source>.
 
 
* 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 bi-glyph, 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 bi-glyph, 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:

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 GlyphTyping glyphs (on Linux) ∙ UnicodeFontsMnemonicsOverstrikes
Individual glyphs Jot () ∙ Right Shoe () ∙ Up Arrow () ∙ Zilde () ∙ High minus (¯) ∙ Dot (.) ∙ Del ()