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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_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</ | * In all dialects, it is used as [[wikipedia:decimal separator|decimal separator]], for example <source lang=apl inline>3.14</syntaxhighlight> 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</ | * In all dialects, it is a [[dyadic operator]] with function [[operand]]s, deriving a [[dyadic function]] (<source lang=apl inline>X f.g Y</syntaxhighlight>) which is the generalised [[Inner Product]]. Specifically, <source lang=apl inline>X +.× Y</syntaxhighlight> 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</ | * 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</syntaxhighlight>) which is a generalisation of [[wikipedia:determinant|determinant]]s and [[wikipedia:permanent|permanent]]s. Specifically, <source lang=apl inline>-.× Y</syntaxhighlight> 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</ | * 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</syntaxhighlight> 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>..</ | * In [[NARS2000]], two immediately adjacent dots, <source lang=apl inline>..</syntaxhighlight>, form a [[bi-glyph]], and represents the [[Sequence]] function (represented by the ellipsis, <source lang=apl inline>…</syntaxhighlight> in [[dzaima/APL]] and [[Extended Dyalog APL]]). | ||
Due to its use in numeric constants, letting <source lang=apl inline>.</ | Due to its use in numeric constants, letting <source lang=apl inline>.</syntaxhighlight> be a dyadic operator that takes numeric operands or a function that takes numeric arguments, is potentially problematic or at least confusing: | ||
<source lang=apl> | <source lang=apl> | ||
4.6 | 4.6 | ||
Line 22: | Line 22: | ||
4 . . 10 | 4 . . 10 | ||
∧ | ∧ | ||
</ | </syntaxhighlight>{{Works in|[[NARS2000]]}} | ||
{{APL glyphs}}[[Category:Glyphs]] | {{APL glyphs}}[[Category:Glyphs]] |
Revision as of 21:11, 10 September 2022
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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 <source lang=apl inline>3.14</syntaxhighlight> representing .
- In all dialects, it is a dyadic operator with function operands, deriving a dyadic function (<source lang=apl inline>X f.g Y</syntaxhighlight>) which is the generalised Inner Product. Specifically, <source lang=apl inline>X +.× Y</syntaxhighlight> 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 (<source lang=apl inline>+.× Y</syntaxhighlight>) which is a generalisation of determinants and permanents. Specifically, <source lang=apl inline>-.× Y</syntaxhighlight> is the 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</syntaxhighlight> 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, <source lang=apl inline>..</syntaxhighlight>, form a bi-glyph, and represents the Sequence function (represented by the ellipsis, <source lang=apl inline>…</syntaxhighlight> in dzaima/APL and Extended Dyalog APL).
Due to its use in numeric constants, letting <source lang=apl inline>.</syntaxhighlight> be a dyadic operator that takes numeric operands or a function that takes numeric arguments, is potentially problematic or at least confusing: <source lang=apl>
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 ∧
</syntaxhighlight>
Works in: NARS2000
APL glyphs [edit] | |
---|---|
Information | Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics ∙ Overstrikes ∙ Migration level |
Individual glyphs | Jot (∘ ) ∙ Right Shoe (⊃ ) ∙ Up Arrow (↑ ) ∙ Zilde (⍬ ) ∙ High minus (¯ ) ∙ Dot (. ) ∙ Del (∇ )
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