File:Sixth root as a composite function of cbrt and sqrt.svg

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English: Diagram showing how a list monad can be used to compose complex roots of a number. sqrt and cbrt are, respectively, the complex multivalued square and cube root functions. When composed with the "bind" operator "•" they produce the sixth root function. Here z is a complex number, and the square brackets denote an array.
unit(z) := [ z ]
‌
(f•g)(z) := append(map(f,g(z)))
‌
lift(f) = f° := unit•f = f•unit
‌
sqrt°(z) =
= append(map(unit,sqrt(z)))
= append(map(sqrt,unit(z)))
‌
sxrt(z) = (cbrt°•sqrt°)(z)
= append(map(cbrt°,sqrt°(z)))
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Author BrightR
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Date/TimeThumbnailDimensionsUserComment
current12:50, 14 November 2018Thumbnail for version as of 12:50, 14 November 20181,000 × 2,000 (120 KB)BrightR (talk | contribs)Reverted to version as of 07:25, 25 April 2018 (UTC) - the point of this diagram is to show monads WITHOUT Haskell syntax
00:10, 9 November 2018Thumbnail for version as of 00:10, 9 November 20181,550 × 1,500 (79 KB)Zar2gar1 (talk | contribs)Redraw diagram to use monad functions discussed in the section; condense the SVG file some
07:25, 25 April 2018Thumbnail for version as of 07:25, 25 April 20181,000 × 2,000 (120 KB)BrightR (talk | contribs)same width for all arrow tails
07:22, 25 April 2018Thumbnail for version as of 07:22, 25 April 20181,000 × 2,000 (119 KB)BrightR (talk | contribs)changed red to black to remove the differentiation between the bind operator and the other parts of the monad.
22:24, 12 May 2017Thumbnail for version as of 22:24, 12 May 20171,000 × 2,000 (119 KB)BrightR (talk | contribs)replaced asterisks with degree symbols to prevent confusion

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