**From:** Philippe Verdy (*verdy_p@wanadoo.fr*)

**Date:** Mon Jun 16 2003 - 19:33:50 EDT

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From: "Kenneth Whistler" <kenw@sybase.com>

To: <Patrick.Andries@xcential.com>

Cc: <unicode@unicode.org>; <kenw@sybase.com>

Sent: Monday, June 16, 2003 11:53 PM

Subject: Re: Looking for two mathematical characters

*> Patrick Andries asked:
*

*>
*

*> > I'm looking for two mathematical characters.
*

*> > 2) An angle operator (combining mark ?) looking like this _| , where
*

*> >
*

*> > a )
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*> > n| a ) n occurrences of a
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*> > a ¯ means a )
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*> >
*

*> > n|
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*> > obviously a¯ should all be written on a single line.
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*>
*

*> And Philippe Verdy responded (after a long mathematical analysis):
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*>
*

*> > If there such character "_|" in Unicode ? Yes.
*

*> > With mathematical properties? Yes.
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*> > With the correct semantic? No.
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*> >
*

*> > The existing semantic of this mathematical character means "not",
*

*> To answer Patrick's follow-up question:
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*> > Which character are you thinking of ? Which code point ?
*

*> One would have to surmise that Philippe had U+00AC NOT SIGN in
*

*> mind, because of what he claimed it meant.
*

Sorry, effectively the not operator has effectively the wrong orientation.

(though there's many variation on the glyph actually used to mean not,

and such confusion is common).

Other mathematical operators can also be selected from the technical

APL operators.

*> U+2A3C INTERIOR PRODUCT
*

*>
*

*> which has the "_|" orientation. A usage of the symbol (with a
*

*> graphic approximation of the intended glyph, parallel to the
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*> "_|" ASCII art version) can be seen at:
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*>
*

*> http://www.hindawi.dk/books/775945046/B9775945046000361.pdf
*

Other notations found in ASCII sources is the use of the digraph "^^"

In fact for plain text notations, any writer would need to define a notation

explained by full language, and then would use it. If there is really a need

to specify anexact glyph, MathML or other rich-text or layout language

will probably offer a better solution.

Also, because Maths can use any glyph or character as a notation, it is

not restricted to those characters defined in Mathemetics blocks.

So the box-drawing characters could produce the desired effect, as

some examples come with the notation of horizontal division bars:

n

─┘

a

(look at this email with a monospaced font preference, on a system supporting

a font with box drawing characters (as they are used in DOS/OEM charsets)

Due to this, a plain text mapping (without formatting) could use the

"┘" character (U+2518) and "─" (U+2500), as in:

a ┘n

or:

a ┘(n+1)

which could be rendered by a 2D layout engine knowing the maths semantics of

parentheses, and allowing to define custom layout rules in a maths style-sheet:

n+1

──┘

a

Note that box-drawing characters are often much easier to locate in fonts

than many maths operators.

However the main problem of these box drowing characters is that they are

difficult to align on multiple lines as they work best only with coherent

monospaced fonts, but poorly when multiple monospaced fonts are

needed (because each font has its own width for the same point size).

This is not a problem with Unicode, because Unicode plain text normally

has no layout and end of lines normally mean nothing else than the end of

a paragraph.

In the APL subblock of the Misc.Technical block, the character "⌟" (U+231F)

is also a small bottom-right corner operator, and "⌋" (U+230B) is the second

(right) character of a floor operator, which can combine with "⌊" (U+230A)

the first (left) one in the pair. Its representative metrics seems quite good to

align it with the "n" exponent-order. On Windows, with MS fonts, they are

supported only with "Arial Unicode MS" (part of Office, not of core Windows

fonts). May be the Code2000 font has them. The floor characters exist however

in "Lucida Sans Unicode".

Floor pairs of characters also exist in non-Unicode fonts like "Symbol", which

maps the floor pair at 0xEB and 0xFB (with the Symbol encoding, originally

defined in PostScript). But it seem that they were initially intended to create

tall square brackets, by joining 2 or more characters vertically.

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