Center Focus over finite fields Files

Centerfocus
===========

Overview
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Centerfocus provides a fast C++ implementation of Frommer's Algorithm to compute
focal values of plane autonomous systems over finite fields, together with the
experimental data used in:

H.-Chr. Graf v. Bothmer, J. Kroeker
"A Survey of the Poincare Center Problem in Degree 3 using Finite Field Heuristics"
arXiv:1012.3402 -- https://arxiv.org/abs/1012.3402

An interactive database (query interface and exports) is hosted at:
https://centerfocus.de

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Folder layout (on SourceForge)
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- source/ : Regular C++ source packages (centerfocus-$version).
- survey/ : Survey edition (the version used for computations in the survey paper).
            Includes:
              * C++ source (LinuxSrc)
              * Macaulay2 packages (macaulay-packages)
              * Macaulay2 scripts (macaulay-scripts/survey2.m2)
              * examples and external libraries
- data/   : SQL dumps of the experimental database (e.g. characteristic 29 points).

Project files:
https://sourceforge.net/projects/centerfocus/files/centerfocus/

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Online database (quick start)
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At https://centerfocus.de -> "Database access":

- Query statistics
  Toggle "rank statistics" and click "query rank statistic".
  Reproduces global counts such as Figure 1 in the paper.

- Query points
  Filter by characteristic, degree, number of focal values, vanished focal values,
  (sub-)Jacobian/quadrics ranks, smoothness/lift settings, limits/offsets.
  Export results as Macaulay2-readable point lists for further processing.

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Using the data dumps
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Download a dump from data/ and import into MySQL/MariaDB:

    mysql -u <user> -p <dbname> < centerfocus_experiments.sql

Notes:
- Original dumps were created with MySQL 5.0; they also work with recent MySQL/MariaDB.
- The online interface is often the fastest way to explore without local import.

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Macaulay2 workflow
------------------

- Macaulay2 packages Frommer and CenterFocus are included in the survey edition
  under macaulay-packages/.
- The script macaulay-scripts/survey2.m2 contains computations related to the paper.
- Export point sets from the online DB ("Query points") in Macaulay2-readable format.
- Additional code and updates are available at:
  https://github.com/bothmer/centerfocus

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Documentation & links
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- Online docs: https://centerfocus.de/docs
- Interactive DB: https://centerfocus.de
- Source code (regular releases): source/
- Survey edition (paper computations): survey/
- Data dumps: data/
- Paper (arXiv): https://arxiv.org/abs/1012.3402

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Citation
--------

If you use Centerfocus or the data in your work, please cite:

H.-Chr. Graf v. Bothmer, J. Kroeker,
"A Survey of the Poincare Center Problem in Degree 3 using Finite Field Heuristics",
arXiv:1012.3402.