Right-to-left mathematics

From: Marco.Cimarosti@icl.com
Date: Tue Jan 11 2000 - 05:40:04 EST


Some Unicode character have the "mirrored" property. This means that, when
they occur in a right-to-left context, they should be displayed with an
alternative reversed glyph. For example, an open parenthesis looks like "("
in LTR, but like ")" in RTL.

a) This applies to all opening/closing punctuation, e.g.:
        U+0028 / U+0029 (LEFT ... / RIGHT PARENTHESIS)

b) The same applies with some pairs of mathematical operators, that are the
opposite of each other, both in shape as in meaning; e.g.:
        U+003C / U+003E (LESS-... / GREATER-THAN SIGN)
        U+2208 / U+220B (ELEMENT OF / CONTAINS AS MEMBER)

c) But also some unpaired mathematical operators have the "mirrored"
property, e.g.:
        U+221A (SQUARE ROOT)
        U+222B (INTEGRAL)

I guess that, in cases (a) and (b), fonts actually just contain one pair of
glyphs, and "swap" their encoding as needed by the bidi context. But, for
case (c), ad-hoc reversed glyphs must be designed separately.

Are the mirrored glyphs for case (c) operators actually used in
right-to-left languages?

What do mathematical formulas look like in Hebrew, Arabic, Urdu, Pashto,
Thaana, etc.? Are they always RTL or is sometimes LTR used (as is the case
for Hebrew music)?

What is the attitude of font designers? Are you providing "reversed" maths
glyphs for RTL scripts?

Anyone knows examples of mathematical applications that implement bidi? How
do they work?


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