Multiple precision package.

[B. Narasimhan]

I recently saw a post about some multiple precsion package that a user 
found on his unix machine. The user then solicited input regarding other 
multiple precision packages.                    

There is a truly outstanding multiple precision package for PC's and it is
available absolutely free! It is UBASIC, a modified BASIC language interpreter
written by a Japanese number theorist, Yuji Kida. A review of this software
appears in "Computers and Mathematics", May/June 1989, by Prof. Walter Neumann.
Features include some C-like syntax, exact arithmetic, real, integer, complex,
on large numbers, etc. But nothing is more impressive than the bunch of 
number-theoretic routines. These include factorisation algorithms using some 
of the latest techniques, Quadratic sieve, Elliptic curve methods, and    
Adleman's primality testing routines. There is a specific version for 386 
machines that takes advantage of 32-bit arithmetic. 

I was a heavy user of MAPLE on our sun until I discovered this. We needed a 
60-digit number factored. MAPLE chugged along for a week and did not come
up with the answer even after a week (our machine is not so heavily used),
but UBASIC cracked it in 1 Hr and 44 minutes!!! Another useful feature is that
UBASIC gives you the factors as it discovers them, so that you can stop and
continue the rest of the factorisation when you want. Yesterday, UBASIC amazed
me even more by cracking b^14+b^7+1, where b=2^32-5, a 134-digit number in
about 2hrs.

I have a copy of UBASIC, but I wonder if I would mess up Prof. Neumann's plans
for distribution by volunteering to make it available to everyone. In any case,
his e-mail address is TS2534 at OHSTVMA.BITNET . I believe AMS is discussing setting up a bulletin board for this purpose.

B. Narasimhan
e-mail naras at stat.fsu.edu