Re: math alphabets, WAS: Proprietary Card Decks

From: Hans Aberg (haberg-1@telia.com)
Date: Fri Apr 15 2011 - 14:13:59 CDT

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On 15 Apr 2011, at 20:06, Asmus Freytag wrote:

>> It has been discussed before.
>
> This doesn't answer my question.

What might that be?

>> One can make in effect a computer language on top of Unicode which tells writing directions. If moved into Unicode, there would need to be special characters for that.
>>
>> For example, a/b might be written like that, but it might be written (still inline) with 'a' over 'b' and a horizontal stroke between. In addition, there is "a over b" which does not have such a stroke (but normally parenthesizes). So one might have a character telling that two parts should be grouped over each other.
>
> Just FYI, that distinction is presentational, not semantic, where fractions are concerned.
>
> The choice often depends on rendering (layout) context, and if that context is known, it can be made by the layout software to good effect. For example, when writing 51 1/2 inline, the vertical build is more readable.

Unicode contains both semantic and graphic descriptions. In math, for example, ELEMENT OF 2208 was originally an epsilon, which some use. And RIGHTWARDS ARROW FROM BAR 21A6 is normally used as a function variable binder (as in lambda calculus), called mapsto in TeX, so here Unicode has a graphic description of a semantic object. In math, there is no semantic difference of the length of the arrows, but Unicode has RIGHTWARDS ARROW 2192 and LONG RIGHTWARDS ARROW 27F6, perhaps as a legacy from TeX.

So a clean semantic approach in math will run into problems.

> UTN#28 describes how to indicate the semantic "fraction".

The paper suggests using '/' for writing fractions on top each other and "\/" for inline. As you point out there is no, semantic difference. I think about it as writing the same thing in different ways, so I would find it natural to use '/' and add a character to indicate which writing direction.

Hans

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