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Complex floor: Difference between revisions
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(Created page with "'''Complex Floor''' is a domain extension for the built-in function Floor to accept complex numbers. It was originally designed by Eugene McDonnell<...") |
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:# ''Compatability''. The complex floor function is compatible with the real floor function. Furthermore, its action on purely imaginary numbers is similar to the action of the real floor function on real numbers. In particular, <source lang=apl inline>(re⌊z)≤re⌈z</source> and <source lang=apl inline>(im⌊z)≤im⌈z</source>. | :# ''Compatability''. The complex floor function is compatible with the real floor function. Furthermore, its action on purely imaginary numbers is similar to the action of the real floor function on real numbers. In particular, <source lang=apl inline>(re⌊z)≤re⌈z</source> and <source lang=apl inline>(im⌊z)≤im⌈z</source>. | ||
Then he proposed a shape on the complex plane that satisfies all seven requirements: a rectangle of width <source lang=apl inline>√2</source> and height <source lang=apl inline>√÷2</source>, rotated 45 degrees clockwise so that the midpoint of the bottom side is placed on an integer <source lang=apl inline>b</source>, and the top two corners are placed on <source lang=apl inline>b+0j1</source> and <source lang=apl inline>b+1</source> respectively. The following is the APL model by McDonnell, rewritten using [[ | Then he proposed a shape on the complex plane that satisfies all seven requirements: a rectangle of width <source lang=apl inline>√2</source> and height <source lang=apl inline>√÷2</source>, rotated 45 degrees clockwise so that the midpoint of the bottom side is placed on an integer <source lang=apl inline>b</source>, and the top two corners are placed on <source lang=apl inline>b+0j1</source> and <source lang=apl inline>b+1</source> respectively. The following is the APL model by McDonnell, rewritten using [[dfn]]s: | ||
<source lang=apl> | <source lang=apl> | ||
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<references/> | <references/> | ||
{{APL features}}[[Category:Scalar monadic functions]] | |||