2,951
edits
Complex floor: Difference between revisions
Jump to navigation
Jump to search
m
no edit summary
m (→References: Scalar monadic functions category) |
mNo edit summary |
||
| Line 19: | Line 19: | ||
:# ''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> | ||