00100	PRINTING MATHEMATICS ON THE XGP
00200	
00300		Printing typeset mathematics on the XGP offers
00400	considerable difficulties, but I am sure we will eventually
00500	solve them.  However, it is much easier to print the kind of
00600	mathematical notation used in reports and in some books.  For
00700	example, Benjamin publishes notes in this style.
00800	
00900		These reports are produced on a typewriter equipped
01000	with Typeit extra keys and using half spacing to get subscripts
01100	and superscripts.  Normally, only one type font is used, but
01200	some of the fancier systems have several available.
01300	Besides subscripts and superscripts, overscores are used.  The
01400	common overscores are bars, double bars, twiddles, carets, and
01500	single and double dots.  Underlining is also used sometimes.
01600	The alphabets used are latin, greek, german, and the hebrew letter
01700	aleph.  I believe this is all, but perhaps there is a bit more.
01800	
01900		Consider the problem of realizing this on the XGP.  I
02000	fear it cannot always be done on the fly, because the combination
02100	of characters, overscores, underlining and subscripts, etc.
02200	may require too much time to do on the fly.  This suggests that
02300	when PUB finds a line too hairy for the XGP service to do on the
02400	fly, it makes a picture out of this line which is buffered out
02500	as a collection of bits.  With a reasonable limit on the height
02600	of superscript towers, the actual number of bits required
02700	can be kept reasonable.
02800	
02900		Big sigmas and integral signs are another problem.  
03000	
03100		I can provide several samples of the kind of publication
03200	I have in mind.
03300	
03400		Solving this problem will bring the publications of our
03500	mathematical theory of computation group up to standard
03600	for mathematical reports.