Re: Subscript & Superscript

From: William Overington (
Date: Wed Jul 31 2002 - 04:48:07 EDT

Some time ago in this list, Mr Bernard Miller posted a note about his Bytext

If one goes to and then goes through to the
documentation page at one may
download a copy of the latest edition of The Bytext Standard. I chose to
download the pdf file which is 606 kilobytes.

On pages 34 and 35 of that document are details of arrow parentheses
invented by Mr Miller.

On page 72 is a statement concerning intellectual property rights.

I feel that it would be very useful if these eight arrow parenthesis
characters are used in a Unicode compatible environment.

As some readers may know I have been researching on my courtyard codes

Courtyard codes are placed within the Private Use Area of Unicode. The
above document being indexed from an index page about some of my other uses
of the Private Use Area.

It occurs to me that if the eight arrow parenthesis characters were encoded
into my courtyard codes system, then that would be potentially of great

I am thinking in terms of U+F388 through to U+F38F being used for this
purpose, with the codes being assigned to the arrow parentheses in the order
in which Mr Miller lists them in The Bytext Standard.

If this happens then the way to express a subscript uppercase A character
would be as follows.

U+F38A U+0041 U+F38B

The U+0041 is the code for A in regular Unicode, so immediately there is a
general method for subscripting any Unicode character. Indeed subscripts of
subscripts could be used by nesting the arrow parentheses.

For example, a subscript A subscript B could be expressed as follows.

U+0061 U+F38A U+0041 U+F38A U+0042 U+F38B U+F38B

The U+0061 is the code for a in regular Unicode and the U+0042 is the code
for B in regular Unicode.

Arrow parentheses allow a mathematical expression involving superscripts,
subscripts, integral limits, summation limits and various other items to be
expressed in a linear manner, which makes those expressions able to be
stored in a Unicode file in what is essentially a plain text storage format,
though I mention that this will not be plain text as such as it involves the
use of code points for what might be considered markup.

I know little about XML so I do not know whether this suggestion will be a
suitable solution for the requirement of the person who wrote to the Unicode

However, perhaps it will be a helpful suggestion.

Certainly using the codings which I suggest would involve use of code points
from the Private Use Area. However, as the need is now, then even if the
arrow parenthesis characters are one day promoted to regular Unicode, the
use of Private Use Area characters now may be what is needed to achieve the
desired result.

By placing these code point ideas into this posting to the Unicode mail
list, they will be archived in the archives of the Unicode mail list and
also sent to many people interested in Unicode around the world. So,
although they are only Private Use Area encodings, it is possible that these
encodings will be noted in many places by many people. It is simply
speculation as to whether few or many people will choose to recognize such
code point allocations for their own uses.

The use of these code points would raise the question as to how a string
containing them should be displayed. The idea is that in a plain text
editor mode, the arrow parenthesis characters would be displayed with the
glyphs shown by Mr Miller in The Bytext Standard. In a graphical display,
the arrow parenthesis characters would not be displayed, yet would influence
how characters included between matching pairs of arrow parenthesis
characters are displayed. This is no more complicated in principle than
viewing an HTML page in Internet Explorer then viewing the source code of
the HTML page in Notepad then going back to the Internet Explorer display.

Whether any font makers would add glyphs for the eight arrow parenthesis
characters into the code positions U+F388 though to U+F38F remains to be
seen, though I am cautiously optimistic in the matter. Also the possibility
exists for the person who originally wrote to the Unicode Consortium to have
his or her own font produced in addition to any font maker making such a
font available.

William Overington

31 July 2002

-----Original Message-----
From: Magda Danish (Unicode) <>
To: unicode <>
Date: Tuesday, July 30, 2002 8:46 PM
Subject: Subscript & Superscript

>> -----Original Message-----
>> Date/Time: Tue Jul 30 12:26:40 EDT 2002
>> Contact:
>> Report Type: FAQ Suggestion
>> We need to know how to express a Subscript letter in Unicode.
>> On your site, we've found in 2070-208E how to express a
>> Superscript letter or number or a Subscript number, but there
>> is no information about how to write a Subscript letter.
>> We're using the XML Authoring Software Epic developed by
>> Arbortext. We need to be able to express mathmatical
>> formulas in XML and we're trying to use Unicode to do it.
>> -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
>> (End of Report)

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