<html><head></head><body><div style="font-family: Verdana;font-size: 12.0px;"><div>In TeX and MathML, U+005E CIRCUMFLEX ACCENT ^ is used for superscript and U+005F LOW LINE _ for subscript. This also allows power towers like 2^(2^2), which are not possible with the existing Unicode characters. This notation is recognized by mathmaticians, physicists and chemists and widely accepted.</div>
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<div>In some programming languages, e. g. Java or C++, ^ is used for the XOR operation and _ for digit grouping, but that does not matter here, because the context is always the decisive factor.</div>
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<div>Many modern fonts have support for auto-alignment of digits in combination with U+2044 FRACTION SLASH ⁄ like in that example: 13⁄37. So it may be possible to design a font with special handling for ^ and _.</div>
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<div style="margin:0 0 10px 0;"><b>Gesendet:</b> Mittwoch, 22. März 2023 um 05:36 Uhr<br/>
<b>Von:</b> "Kent Karlsson via Unicode" <unicode@corp.unicode.org><br/>
<b>An:</b> "unicode@unicode.org" <unicode@corp.unicode.org><br/>
<b>Betreff:</b> Re: Missing Latin superscript lowercase letters</div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>Peter Constable wrote:</span></div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> Doug Ewell responded:</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> > an image of mathematical or engineering equations wouldn’t</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> > exactly be the best supporting evidence for encoding them in plain text.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> Not only would it not be the best supporting evidence, it wouldn’t be</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> considered supporting evidence _at all_ since math formula layout is not plain text.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>Says who? There is no law of nature (or of omputing) that says that math expressions</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>must be non-plain text. Just because all of neqn/eqn, (La)TeX, MathML, OMML, and indeed</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>UnicodeMath are representations of math expressions that are *not* plain text does not</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>mean that math expressions must be expressed by a higher level protocol. I.e. it could</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>very well be a text level protocol (where the ”math controls” are not expressed as</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>printable text, but as control codes).</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>Further, if some symbol/letter for some reason only ever occurred in superscript</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>position in math expressions, such examples would still be supporting evidence for</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>that symbol/letter. The closest practical example I can think of is the degree sign, which</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>in origin </span><span style="font-size: 11.0pt;">is a superscript 0.</span></div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>Asmus Freytag wrote:</span></div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> I[n] mathematical typesetting what is superscripted is not the individual</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> letter, but the expression. In principle, the superscripted expression</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> is arbitrarily complex and thus the superscript is fully recursive.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> This is precisely the kind of situation where hardcoding anything is not</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>> helpful.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>I would go even further than that, and say that with very few exceptions,</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>characters that have a compatibility decomposition have no business in a</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>math expression.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"> </div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>In my little project "math anywhere" (ok, I just thought of that name, and no,</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>of course I cannot implement it everywhere) I'm proposing a plain text format for</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>math expressions. Plus a version that is compatible with HTML and SVG. And also a</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>version that one can be best described as a "mark-down" version that is (relatively)</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>easy to input via a keyboard; all equivalent in what can be expressed. </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span> </span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>See </span><a href="https://github.com/kent-karlsson/control/blob/main/math-layout-controls-2023-A.pdf" style="color: rgb(5,99,193);" target="_blank"><span>https://github.com/kent-karlsson/control/blob/main/math-layout-controls-2023-A.pdf</span></a><span>.</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"> </div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span style="font-size: 11.0pt;">The plain text </span><span style="font-size: 11.0pt;">format for math expressions can well represent math expressions in an</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span style="font-size: 11.0pt;">otherwise </span><span style="font-size: 11.0pt;">plain </span><span style="font-size: 11.0pt;">text context. Whether you want to see the math expression themselves</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span style="font-size: 11.0pt;">as plain text is </span><span style="font-size: 11.0pt;">very much in the eye of the beholder. The HTML/SVG compatible version</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span style="font-size: 11.0pt;">does not </span><span style="font-size: 11.0pt;">have "clay feet”. The price for that is that additional parsing is needed. Unusual</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span style="font-size: 11.0pt;">in </span><span style="font-size: 11.0pt;">that that parsing must work on the DOM, but otherwise nothing strange and basically</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>the same parsing as for the ”plain text” version (where the parsing of course works</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>on the text). This (or these, considering the three variants) is also the only format for</span></div>
<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;"><span>math </span><span style="font-size: 11.0pt;">expression representation that can handle RTL math expressions reasonably.</span></div>
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<div style="margin: 0.0cm;font-size: 11.0pt;font-family: Calibri , sans-serif;">/Kent K</div>
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