[UEB Maths] Formatting and special functions

[Janet Reynolds]

Many thanks Joe and Stephen for giving us all plenty to think about! I
will try to get some of my thoughts into words over the weekend.
Janet=20

-----Original Message-----
From: uebmaths-admin@nbp.org [mailto:uebmaths-admin@nbp.org] On Behalf
Of Phippen, Stephen
Sent: Wednesday, 1 June 2005 4:13 a.m.
To: uebmaths@nbp.org
Subject: RE: [UEB Maths] Formatting and special functions


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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