fpLLL doctests

[Bill Hart]

Someone noted in ticket 1346 that the fpLLL doctests use random data,
and said that we should do tests with fixed data which return a known
result.

I don't agree with this. There is no reason why LLL should return the
same result from implementation to implementation. fpLLL may well
change the lattices returned and this would break any fixed doctests,
but would not necessarily constitute a bug in fpLLL.

Instead, the tests should generate random matrices of various kinds
using the programs provided with fpLLL for this purpose, then is
should reduce the lattices using the SAGE wrapping of fpLLL. Then it
should test that the lattices really have been reduced, using whatever
test you like. The one distributed with fpLLL for this purpose should
be sufficient, though one written in SAGE to directly test the Lovasz
condition or some such thing would be better.

I don't know how the doctests work at the moment, but I don't think
the defect as reported really is a defect.

Bill.