[UEB Maths] Formatting and special functions

[Phippen, Stephen]

To: UEB Maths Committee
From: Stephen Phippen
Date: 31 May 2005
Subject: Formatting and special functions.

As regards using format or some other means to imply grade one mode,
I agree with Joe that the method would not be watertight, e.g. for
braille to print translation. But I still regard it as practical,
and could well be used in transcription - independently of what is
specified in UEB. Indeed, regarded in this way, I would say that you
should not try to specify such things in UEB, because it is not
a coding matter as such, but a transcription technique.

In the same vein, I don't think we would necessarily expect
transcription agencies to use the formal UEB method of escaping from
UEB into another language code and back again for the entries in an
English-foreign language dictionary: surely a colon would do. I don't
regard this as contrary to UEB, but just being pragmatic. Of course
the formal mechanism is needed, but I wouldn't exclude these other
techniques.

On the other hand, I think the possibility raised by Joe of using
a single cell sign, dots 346, to indicate grade 1 passage mode is
intriguing, and this could sway me to thinking that, contrary to
what I have said above, I would want to use the indicator even for
set out maths. Would the presence of such an efficient indicator
affect what we have said in the draft about preference between using
the grade one symbol, word or passage modes? (I find the sign
specially attractive because it is similar to the sign aready used in
BAUK codes to introduce computer code, i.e. dot 6 dots 346, so would
be fairly familiar, and with an analogous meaning.) If we were to go
down this route I would prefer to retain the existing termination
sign (partly influenced by the following).

As for the question of special functions such as sin, cos, etc., I
am used to the perspective where these are treated as special objects
within maths; as they are typographically (i.e. being printed in
normal type as opposed to italic type for algebraic letters), in
typsetting languages like TEX, and of course in the BAUK braille
maths code. My instict is to be concerned about having the letters
of such functions loose amongst algebraic letters, especially with
rules as in the currect draft where spaces can be omitted (e.g. we
have example of tanx and argz with the algebraic letter unspaced,
and hence undistingushed, from the function). I don't think anything
is said in the draft about algebraic letters preceding a function,
but the issue is the same. In the BAUK maths code we have the fun
but realistic example w ord s (where w and s are algebraic letters,
and ord is a function) to highlight the issue.

In the BAUK code we use the dots 1246 sign to distingush such
functions (written in ordinary type) from algebraic letters. We
could do something similar in UEB using the free sign dots 16
(which Janet and Bruce have also suggested).
The rule could be something like:

"A function or other word fragment within a maths expression should
be preceded by the function indicator dots 16, which has force
over letters, stops, and the capital sign. The presence of any other
sign thus reverts to normal notation. The function termination sign
(say dot 3), may be used to terminate this mode in any case."

Thus [in the following I write dots 16 as a backslash (a la TEX!)]:

sin x would be coded \sin'x
sin(x) would be \sin(x)
w ord s would be w\ord's
log tan x would be \log\tan'x

etc., all in grade 1 mode.

Bruce and Janet more specificly were thinking about special forms
for common functions like sin and cos, etc. I think you could include
these within this scheme if we assume that you are not going to
get special functions with a single letter, i.e. in cases such as
f(x) the f is printed as an algebraic letter, not in a normal font
like sin or cos. So the above rule could be extended to include
a fixed set of common special functions:

"In addition to the general rule, \s represents sin, \c represents
cos, \l represents log, ..., (as opposed to single letter functions
s c and l, etc.)."

According to this you would still require a terminator as in the
general rule, so the examples would be changed to:

sin x would be coded \s'x
sin(x) would be \s(x)
w ord s would be w\ord's
log tan x would be \l\t'x

I agree with Joe that if we followed this route such coding would
formally have to be available in literary contexts, (i.e. you
could write "grade one indicator \s" for the word "sin") but I don't
this this would be very attractive and so could be discounted. After
all you could write "grade one indicator s i n" for "sin", but you
don't.

I'm sure Joe is (rightly) concerned with computability issues. I don't
see that braille to print would be a problem with such rules. Indeed,
to the contrary, it would enable better quality print to be produced
as you could then control the proper appearance of such functions
(e.g. if you were using a typesetting program like TEX, where sin needs
to be coded as \sin). I suppose the print to braille direction might
be a problem, but only where the functions are not properly identified
amongst the algebraic letters, which I would say they should be anyway.

To answer Janet's question: since this kind of method is already used
in the BAUK maths code it would certainly not be a problem for us.


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