A version of Flagmatic with added functionality such as assumptions and stability checks. It is known to work with Sage-9.5.

flagmatic

To install, navigate to the directory with setup.py file:

cd path/to/flagmatic/pkg

Then run the following code to install CSDP solver:

sage -i csdp

or alternatively, download the CSDP package from https://projects.coin-or.org/Csdp/ and copy csdp to your PATH.

Finally, install Flagmatic with the command below.

sage -python setup.py install

POSSIBLE ISSUES:

• Check whether the installation finished without errors. If you're missing permissions, re-run the last command with sudo privileges.
• Make sure you refresh/restart your Terminal after the install for changes to take effect.
• If you are on a MacOS and are getting an error about a missing gcc, install Command Line Tools.

Running example scripts

Make sure that the script begins with from flagmatic.all import * or that you have imported everything yourself. Assuming the script is called test.sage, navigate to the directory with the script and type

sage test.sage

Alternatively, you can type the script into the Sage interpreter one line at a time.

Verifying stability

Sage is needed. Tested with Sage7.4 on Mac OSX Sierra and Ubuntu 16.04.

Assuming your certificates and inspect_certificate.py are in the same directory and that you have writing permissions there, from that directory type:

sage -python inspect_certificate.py <cert1> --stability <bound> <tau> <B> [<cert2> [<cert3>]]

(otherwise use full paths for filenames). The arguments are:

• <cert1>: filename of the flag algebras certificate for the problem you want to verify stability for, e.g. c5.js
• <bound>: lower bound for this problem (should match the FA upper bound), e.g. 24/625
• <tau> : type you chose, e.g. "3:12"
• <B> : B-graph you chose, e.g. "5:1223344551"
• <cert2>: filename of the FA certificate with, additionally, tau forbidden as induced subgraph, e.g. cert_robust_stab.js; not needed, if tau = 1:.
• <cert3>: filename of the FA certificate with, additionally, B forbidden as induced subgraph, e.g. cert_perfect_stab.js; not needed if Q_tau has corank 1.

EXAMPLE: Prove that if triangles are forbidden, C₅ density is at most 24/625. Prove that this problem is perfectly-C₅-stable. Given are certificates c5.js and c5_stab.js.

sage -python inspect_certificate.py c5.js --stability 24/625 "3:12" "5:1223344551" c5_stab.js

Check the output, it indicates if conditions of the Theorem 7.1 in Strong forms of stability from flag algebra calculations are met.

WARNING: When verifying stability for Clebsch Graph, make sure you use the following string: "g:12131415162728292a373b3c3d484b4e4f595c5e5g6a6d6f6g7e7f7g8c8d8g9b9d9fabacaebgcfde". It's hardcoded for speed.