README

This package implements a search strategy for root-unitary polynomials 
(polynomials with all roots on the unit circle) described in:

K.S. Kedlaya, Search techniques for root-unitary polynomials, in 
    Computational Arithmetic Geometry, Contemporary Mathematics 463, 
    American Mathematical Society, 2008, 71-82;

plus some additional improvements described in:

K.S. Kedlaya and A.V. Sutherland, A census of zeta functions of
    quartic K3 surfaces over F_2, preprint (2015).

There are currently six source files:

-- prescribed_roots.sage: Sage code for user interaction
-- prescribed_roots_pyx.spyx: Cython intermediate layer wrapping C code
-- all_roots_in_interval.c: C code, using FLINT library, to test whether 
    a polynomial has its roots in a given interval (Sturm's theorem)
-- all_roots_in_interval.h: associated header file
-- power_sums.c: C code, using FLINT library, to enumerate the tree based on
    Sturm's theorem and additional bounds computed from power sums
-- power_sums.h: associated header file

From a Sage prompt, type
  sage: load("prescribed_roots.sage")
and everything should compile automatically.

There is one test script in this directory:

-- search-test.sage: Run computations from the 2008 paper

The scripts in the k3-scripts directory generate certain lists associated to
K3 surfaces. See the README file in that directory for more information.

The k3-quartic-f2 directory contains scripts and data files associated to
smooth quartic K3 surfaces over F_2. See the README file in that directory
and the paper "A census of zeta functions..." for more information.

POSSIBLE TODO LIST: 
-- Improve parallel computation in the current Cython model.
-- Port from Sage (based on Python) to Nemo (based on Julia).
-- Add some floating-point computations to isolate roots, thus reducing
    the dependence on Sturm's theorem.