  The Rogers-Ramanujan identities and various analogous identities (Gordon,
Andrews-Bressoud, Capparelli, etc.) form a family of very deep identities
concerned with integer partitions. These identities (written in generating
function form) are typically of the form "product side" equals "sum side," with
the product side enumerating partitions obeying certain congruence conditions
and the sum side obeying certain initial conditions and difference conditions
(along with possibly other restrictions). We use symbolic computation to
generate various such sum sides and then use Euler's algorithm to see which of
them actually do produce elegant conjectured product sides. We not only
rediscover many of the known identities but also discover some apparently new
ones, as conjectures supported by strong mathematical evidence.
