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

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Summary

Description	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)))
Date	7 May 2017
Source	Own work
Author	BrightR
SVG development InfoField	The SVG code is valid. This vector image was created with Inkscape. The file size of this SVG image may be irrationally large because its text has been converted to paths inhibiting translations. Default font is Computer Modern Serif, with functions in bold

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File history

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	Date/Time	Dimensions	User	Comment
current	12:50, 14 November 2018	1,000 × 2,000 (120 KB)	BrightR	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 2018	1,550 × 1,500 (79 KB)	Zar2gar1	Redraw diagram to use monad functions discussed in the section; condense the SVG file some
	07:25, 25 April 2018	1,000 × 2,000 (120 KB)	BrightR	same width for all arrow tails
	07:22, 25 April 2018	1,000 × 2,000 (119 KB)	BrightR	changed red to black to remove the differentiation between the bind operator and the other parts of the monad.
	22:24, 12 May 2017	1,000 × 2,000 (119 KB)	BrightR	replaced asterisks with degree symbols to prevent confusion