Weeks 1 and 2. Note: If your web-browser does not start Maple when clicking on these Maple files, then it may be easier to download all files for weeks 1 and 2 in this zip file weeks_1_2.zip, then unpack it on your computer. This creates a folder weeks_1_2 with the files in it (the file "files.txt" indicates in which order we're using them).
In both cases, if the precision is too low, then the output could "irreducible" even if f is reducible. A p-adic precision that is provably high enough can be found in the LLL paper. With this bound one obtains a provably complete algorithm. Similarly, a floating point precision that is provably high enough was given by Schonhage.
Use LLL to find a non-zero integer solution of the following equation: 35178*x^2-4115*y^2+18107*z^2 = 0 (I will explain in class how to turn this into a lattice problem).