README

Proof-of-concept implementation using sagemath.

Requirements:

1. Ensure you have the following files:

2. algorithms.py;

3. TestTheorem1.py;

4. TestTheorem2.py;

5. TestLemma2.py;

6. TestLemma3.py; and

7. TestRemark7.py.

8. Sagemath installed

9. MSolve library installed

Description

The scripts require as argument inputs:

• the matrix dimension n,
• Groebner basis flag (optional),
• number of samples flag (optional),
• a verbose flag (optional). A single example is excutated in verbose mode.

More precisely,

Parses command.

options:
  -h, --help            show this help message and exit
  -n DIMENSION, --dimension DIMENSION
                        Matrix dimension: n-by-n matrices
  -gb, --groebner_basis
                        Groebner basis approach
  -v, --verbose         verbose help
  -r NUMBER_OF_SAMPLES, --number_of_samples NUMBER_OF_SAMPLES
                        Number of samples to be used in the Groebner basis approach

Testing ONE random instance

Just run (for example):

# Linearization approach
% sage -python TestTheorem1.py -n 16 --verbose
% sage -python TestLemma2.py -n 16 --verbose
% sage -python TestLemma3.py -n 16 --verbose
% sage -python TestRemark7.py -n 16 --verbose
# Groebner basis approach
% sage -python TestTheorem1.py -n 16 -gb --verbose
% sage -python TestTheorem2.py -n 16 --verbose
% sage -python TestLemma2.py -n 16 -gb --verbose
% sage -python TestLemma3.py -n 16 -gb --verbose
% sage -python TestRemark7.py -n 16 -gb --verbose

Testing 25 random instances

Just run (for example):

# Linearization approach
% sage -python TestTheorem1.py -n 8
% sage -python TestLemma2.py -n 8
% sage -python TestLemma3.py -n 8
% sage -python TestRemark7.py -n 8
# Groebner basis approach
% sage -python TestTheorem2.py -n 8
% sage -python TestLemma2.py -n 8 -gb
% sage -python TestLemma3.py -n 8 -gb
% sage -python TestRemark7.py -n 8 -gb

License

Apache License Version 2.0, January 2004