Re: Solidus variations

2011/10/7 Hans Aberg <haberg-1_at_telia.com>:
> On 7 Oct 2011, at 22:22, Murray Sargent wrote:
>
>> In the linear format of UTN #28, 1/2/3/4 builds up as ((1/2)/3)/4 as in computer languages like C.
>
> OK. I looked through the paper again, and could not find a description of that.
>
>> The notation actually started with C semantics and then added a larger set of operators, and finally adopted the full Unicode set of mathematical operators.
>
> In view of the problems of C semantics, as C++ shows, I am actually reviewing it.
>
>> You can try it out in Microsoft Office applications.
>
> I do not have access to that.
>
>> Different groupings can be obtained by using parentheses, which may be discarded after build up as explained in UTN #28. As Asmus points out, I started working on this notation back in the late 1970's and the latest version is built into a number of popular products. So it's pretty thoroughly tested.
>
> I am worrying also about the underlying mathematical semantics, where one can have different models. One is having the set if integers ℤ different from the set of rational ℚ numbers (as in C/C++), or viewing it as embedded (as in Scheme). In math, one shifts between the two according to context. The ideal would be to avoid implicit type conversions, but that would not work if one would want to be able to be able to enter numbers in common form.

Within the diverse variations of the solidus to be added to
mathematical notations, note the pending addition of

27CB ⟋ MATHEMATICAL RISING DIAGONAL
= \diagup
→ 2215 ∕  division slash

which is listed for inclusion in the next release of Unicode and ISO
10646... This is a small variant, more or less the same size and
position as the multiplication sign (but only a single stroke), and
with 45° angle. I don't think it is intended to be used with digits in
numerator superscript or denominator subscript styles, but this more
or less ressembles a lot to many existing representation of fractions
; but not all of them use a 45° stroke, given that digits are taller
than they are large, and a 60° angle is often easier to position
readable digits with a not too small size to fit the standard
line-height between the standard baseline and the cap-height
(45°angles are more convenient when placing more than one digit on the
numerator or denominator to avoid extending the width of the
fraction)...

It comes as well with the mathemetical falling diagonal, another new
variant of the backslash. And once again comes the discussion about
the mirrorability in RTL contexts...

Well, in maths, every operator has a strong glyph design that should
not be confused. It is frequent to make visual distinctions between
operators that look superficially similar but operate very
differently, so each encoded operator should be considered distinct
(even if there are general purpose fonts, not really defined for maths
notation purpose, that will attempt to unify their glyphs).

This is exactly the same "problem" as with letters used to designate
various entities (and note that there's a very fuzzy line between
variable names, constant symbols, function names, operators, because
all these entities are also members of sets that may be joined in a
larger set, or group, where they can be combined with a specifically
defined arithmetic or logic to create other special objects). Math
formula editors or renderers (including the various TeX dialects)
frequently need fonts specifically built to exhibit the necessary
distinctions, and that will avoid some features such as ligatures or
kerning.
Received on Mon Oct 10 2011 - 19:29:29 CDT