> Date: Sat, 3 Dec 2022 12:26:26 -0500
> From: Bradley Lucier <xxxxxx@math.purdue.edu>
> References: <xxxxxx@jupiter.mumble.net>
>
> On 11/28/22 9:59 PM, Taylor R Campbell wrote:
> > Attached is a collection of known-answer test that you could try -- I
> > generated it just now with MIT Scheme.  It tests the cartesian product
> > of:
> >
> > - the five operators {floor/, ceiling/, truncate/, euclidean/, round/}
> > - the nine numerators {0, 1, 2, 3, 4, 5, 6, 7, 8}
> > - both signs for numerators
> > - the eight denominators {1, 2, 3, 4, 5, 6, 7, 8}
> > - both signs for denominators
> >
> > These 1440 test cases cover zero, units, primes, a square, a composite
> > of distinct primes, and a cube.  (They don't, however, cover anything
> > that requires bignum arithmetic.)  I haven't vetted these answers in
> > any way other than verifying the tests pass in MIT Scheme -- I
> > recommend running them through the property tests, and eyeballing them
> > to spot-check for reasonableness.
>
> Just for curiosity's sake, I searched for arguments that would
> distinguish between every pair of the six (including balanced/) division
> procedures (i.e., for every pair of different division procedures, those
> two division procedures differ on at least one of these arguments).  The
> list is surprisingly short and simple, at least to me:
>
> ((-1 2) (2 3) (1 -2) (1 4) (1 2))

Neat.  Although The fact that none of these numerators is composite or
even greater than the denominator suggests maybe one should search a
larger space for such examples!