Minkowski question-mark function: Difference between revisions

Minkowski question-mark function (view source)

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used an over/under style for the two possible continued fraction representations.

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Revision as of 22:17, 13 November 2020 (view source) rosettacode>Gerard Schildberger m (→‎{{header\|REXX}}: added a TRANS.) ← Older edit		Revision as of 22:40, 13 November 2020 (view source) rosettacode>Gerard Schildberger m (used an over/under style for the two possible continued fraction representations.) Newer edit →
Line 9: The question-mark function is continuous and monotonically increasing, so it has an inverse. * Produce a function for {{math\|?(x)}}.   Be careful: rational numbers have two possible continued fraction representations — {{math\|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>]}} and {{math\|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>−1,1]}} — choose the one that will give a binary expansion ending with a 1.: :::*   {{math\|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>]}}     and :::*   {{math\|[a<sub>0</sub>;a<sub>1</sub>,... a<sub>n−1</sub>,a<sub>n</sub>−1,1]}} * Choose one of the above that will give a binary expansion ending with a   '''1'''. * Produce the inverse function {{math\|?<sup>-1</sup>(x)}} * Verify that {{math\|?(φ)}} = 5/3, where {{math\|φ}} is the Greek golden ratio.