LBL"BCa/b1" and LBL"BCa/b2" are two versions of the same
program, written by Sherman Lowell. The first requires the Paname
ROM, available from PPCİParis, and the second requires the HP
Extended I/O ROM; both ROMs contain the function ANUMDEL, used
extensively in the program. The program's purpose is to compute
Rational Binomial Coefficients, C(m,n), n = 0,1,2,3,... for m =
a/b, where a and b are positive or negative integers. (RBC's are
the coefficients in the expansion of (1+x)^(a/b).) At start a and
b are put in Yİ and Xİregisters. The results are returned in the
ALPHA register, where they are AVIEWed, and are also printed
automatically, if a printer is attached. If a/b is a positive
integer, the nonİzero coefficients are finite in number,
followed by a string of 0/1, else the nonİzero sequence continues
forever. (At some stage the numbers overflow the capacity of the
ALPHA register.) Remarkably, because of the exceptional power of
the ANUMDEL function, an algorithm can be written that does all
of the extensive arithmetic, including reduction of fractions to
lowest terms, without using any numbered storage registers or
any synthetic instructions. A description of the program
algorithm, which began with a clever program for the HPİ25C,
written by the late Swiss mathematician Peter Henrici, will be
submitted in the near future to PPCİParis. X<>Y