LearningGBsize

This is code used for “Predicting the cardinality of a reduced Gröbner basis” by Shahrzad Jamshidi, Eric Kang, and Sonja Petrović.

Python files for NN

The Jupyter notebooks Vectors.ipynb and Features.ipynb contain the code for learning and prediction described in the paper.

Data files

The data files for 250,000 ideals are in the 4 text files zipped; the full data sets as described in the paper will be available on another platform, due to file size.

Code for generating data in M2 and small example output files

Here is an examle on how to run the Macaulay2 code to generate samples. This is the same code we used in the paper.

Load the file DataGeneratorScript.m2 and then run the following commands in M2:

-- preset parameters:
numVars = 5
maxDegree = 15
binomialsInEachSample = 5 

filename = "RandomBinomialDataSet."|toString numVars|"vars.deg"|toString maxDegree|"."|toString binomialsInEachSample|"binomialsEach.txt";
    
-- store the preset parameters for this data set on the first line of the data file: 
parameters = "numVars = "|toString numVars|", maxDegree = "|toString maxDegree|", binomialsInEachSample = "|toString binomialsInEachSample|", MonomialOrder = default";
	    f = openOut filename;
	    f << parameters << endl;
	    close f;
	    featurefile = openOut concatenate(filename,".features.txt");
	    featurefile << "min_deg_gen, max_deg_gen, mean_deg_gen, var_deg_gen, numgens, dim, deg, reg" << endl; --- Edit this code if you'd like to work with other features and write down what they are.
	    close featurefile;


generateGBdata(numVars,maxDegree,binomialsInEachSample,sampleSize=50, Homogeneous=>false,  
    SaveFeatures => {numcols@@mingens@@ideal,dim@@ideal,degree@@ideal,regularity@@ideal}  
--   ,  InfoLine=>false, InfoLineCompact=>true
    )
    -- ,    TimeLimit => 1) ---optional input for limiting the time we allow a GB computation to run for each sample point.

The code above will generate 4 text files for a sample of 50 binomial ideals in 5 variables, each generated by 5 binomials of degree 15:

• Exponent vectors of binomial ideal generators
• Features for each of the binomial ideals in the file above
• Maximum degrees of reduced grevlex Grobner basis
• Size of reduced grevlex Grobner basis

In every file, one ideal is represented by data on one line in the text file.