aisejohan / grobner Goto Github PK

Description
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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
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You will need a compiler and the gmp library installed.

Usage
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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
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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.