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Comparison with traditional mathematics: Difference between revisions
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Comparison with traditional mathematics (view source)
Revision as of 12:02, 21 November 2019
, 12:02, 21 November 2019Convert LaTeX symbols to commands
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<source lang=apl inline>((x + y) × (x - y)) = (f ∘ g)(x, y)</source> | <source lang=apl inline>((x + y) × (x - y)) = (f ∘ g)(x, y)</source> | ||
<math>((x + y) | <math>((x + y) \times (x - y)) = (f \circ g)(x, y)</math> | ||
</div> | </div> | ||
Now note that they are identical, letter for letter | Now note that they are identical, letter for letter. Computer Scientists tend to have great difficulty in approaching APL until they let go of the notion that APL is just another programming language (despite its name!) and instead look at it as an executable mathematical notation. | ||
It is notable that APL traditionally was written with a font wherein letters were always italicised, while everything else wasn't. Here is how it looks in the default font for [[SAX]]: | It is notable that APL traditionally was written with a font wherein letters were always italicised, while everything else wasn't. Here is how it looks in the default font for [[SAX]]: | ||
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! style="width:33%" | Traditional notation !! style="width:33%" | APL !! Article | ! style="width:33%" | Traditional notation !! style="width:33%" | APL !! Article | ||
|- | |- | ||
| <math>\sim q</math> | | <math>\sim q</math> || <source lang="apl" inline>~ q</source> || [[Not]] | ||
|- | |- | ||
| <math> | | <math>p \wedge q</math> || <source lang="apl" inline>p ∨ q</source> || [[Or]] | ||
|- | |- | ||
| <math> | | <math>p \vee q</math> || <source lang="apl" inline>p ∧ q</source> || [[And]] | ||
|- | |- | ||
| <math> | | <math>a \times b</math> || <source lang="apl" inline>a × b</source> || [[Multiply]] | ||
|- | |- | ||
| <math> | | <math>a \div b</math> || <source lang="apl" inline>a ÷ b</source> || [[Divide]] | ||
|- | |- | ||
| <math>a \in S</math> || <source lang="apl" inline>a ∊ S</source> || [[Membership]] | | <math>a \in S</math> || <source lang="apl" inline>a ∊ S</source> || [[Membership]] | ||
|- | |- | ||
| <math>A | | <math>A \cup B</math> || <source lang="apl" inline>A ∪ B</source> || [[Union]] | ||
|- | |- | ||
| <math>A | | <math>A \cap B</math> || <source lang="apl" inline>A ∩ B</source> || [[Intersection]] | ||
|} | |} | ||
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! style="width:25%" | Traditional notation !! style="width:25%" | <small>Parenthesised<br></small>APL !! style="width:25%" | <small>Normal<br></small>APL !! Article | ! style="width:25%" | Traditional notation !! style="width:25%" | <small>Parenthesised<br></small>APL !! style="width:25%" | <small>Normal<br></small>APL !! Article | ||
|- | |- | ||
| <math>[ | | <math>[a \equiv b]</math> || <source lang="apl" inline>(a ≡ b)</source> || <source lang="apl" inline>a ≡ b</source> || [[Match]] | ||
|- | |- | ||
| <math>[a=b]</math> | | <math>[a=b]</math> || <source lang="apl" inline>(a = b)</source> || <source lang="apl" inline>a = b</source> || [[Equal]] | ||
|- | |- | ||
| <math>[ | | <math>[a \ne b]</math> || <source lang="apl" inline>(a ≠ b)</source> || <source lang="apl" inline>a ≠ b</source> || [[Not Equal]] | ||
|- | |- | ||
| <math>[ | | <math>[a \le b]</math> || <source lang="apl" inline>(a ≤ b)</source> || <source lang="apl" inline>a ≤ b</source> || [[Less Than or Equal]] | ||
|- | |- | ||
| <math>( | | <math>(f \circ g)(x)</math> || <source lang="apl" inline>(f ∘ g)(x)</source> || <source lang="apl" inline>f ∘ g x</source> || [[Bind]] | ||
|- | |- | ||
| <math>f(g(x))</math> | | <math>f(g(x))</math> || <source lang="apl" inline>f(g(x))</source> || <source lang="apl" inline>f g x</source> || | ||
|- | |- | ||
| <math>(f+g)(x)</math> || <source lang="apl" inline>(f+g)(x)</source> || <source lang="apl" inline>(f+g) x</source> || [[Train]]s | | <math>(f+g)(x)</math> || <source lang="apl" inline>(f+g)(x)</source> || <source lang="apl" inline>(f+g) x</source> || [[Train]]s | ||
|} | |} | ||
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! style="width:33%" | Traditional notation !! style="width:33%" | APL !! Article | ! style="width:33%" | Traditional notation !! style="width:33%" | APL !! Article | ||
|- | |- | ||
| <math>n \pi</math> || <source lang="apl" inline>○n</source> || [[Pi Times]] | | <math>n \pi</math> || <source lang="apl" inline>○n</source> || [[Pi Times]] | ||
|- | |- | ||
| <math>x!</math> | | <math>x!</math> || <source lang="apl" inline>!x</source> || [[Factorial]] | ||
|- | |- | ||
| <math>|x|</math> | | <math>|x|</math> || <source lang="apl" inline>|x</source> || [[Magnitude]] | ||
|- | |- | ||
| <math> | | <math>\lceil x \rceil</math> || <source lang="apl" inline>⌈x</source> || [[Ceiling]] | ||
|- | |- | ||
| <math> | | <math>\lfloor x \rfloor</math> || <source lang="apl" inline>⌊x</source> || [[Floor]] | ||
|} | |} | ||
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| <math>\prod_{n=1}^{N} n</math> || <source lang="apl" inline>×/ ⍳N </source> | | <math>\prod_{n=1}^{N} n</math> || <source lang="apl" inline>×/ ⍳N </source> | ||
|- | |- | ||
| <math> | | <math>\forall x, P(x)</math> || <source lang="apl" inline>∧/P(x)</source> | ||
|- | |- | ||
| <math> | | <math>\exists x, P(x)</math> || <source lang="apl" inline>∨/P(x)</source> | ||
|} | |} | ||
{{APL syntax}} | {{APL syntax}} | ||