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License: GNU General Public License v2.0
Frobenius computation project
License: GNU General Public License v2.0
Description ----------- Partial implementation of the algorithm by Timothy G. Abbott, Kiran S. Kedlaya, and David Roe described in the preprint math.NT/0601508, with the additional twist that you can do surfaces in weigthed projected spaces. Requirements ------------ You will need a compiler and the gmp library installed. Usage ----- Step 1: Edit the files data.h and the Makefile. data.h: Choose degrees d1,d2,d3,d4 of the coordinates in weighted projective space and the degree of the surface d. Choose the prime p and the prime power r (the precision). As well choose q which determines the number of terms in the expansion to compute. It is best to choose d1 <= d2 <= d3 <= d4 Makefile: change --march=nocona to --march=<your-cpu-type> or just remove the --march= option entirely. Step 2: Compile with the command ``make''. Step 3: Run with ./tester Enjoy! TODO ---- 1. Make one_step_down faster by implementing Kiran's idea of precomputing the expressions for suitable powers of the coordinates. Tried this but it is not faster in our setup. Done. 2. Use/find/implement a better library for scalars. Done: now the program uses the GMP, the GNU Multiple Precision Arithmetic Library. 3. Output to file for input in pari. Started doing this: now there is a pari script that tries to find a Weil polynomial p-adically close to a given integer polynomial, it is called post.gp 4. Implement the algorithm for estimating precision from math.NT/0601508 5. Make the program work in cases where the function check_flatness returns -1. Done: It now works for any quasi-smooth hypersurface.
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