Skip to content
master
Switch branches/tags
Code

Latest commit

 

Git stats

Files

Permalink
Failed to load latest commit information.
Type
Name
Latest commit message
Commit time
 
 
 
 
 
 
 
 

algebraic-matroids

Collection of algorithms for Macaulay2, as well as code facilitating a Bertini computation. Algorithms are described in the pre-print "Computing Algebraic Matroids" by Zvi Rosen.

Symbolic Algebra:

The symbolic algorithm described in the paper is implemented in Macaulay2. The code is in the file matroids.m2.

Linear Algebra & Numerical Algebraic Geometry:

The Numerical Algebraic Geometry algorithm breaks up into a few steps:

  1. Generate a numerical Jacobian matrix, in one of the following ways:
    1. Compute a Jacobian symbolically, and then specialize to a generic point of the variety. A generic point can be obtained for a parametrization by choosing random values for the parameters, and for a variety defined by its ideal using Bertini Tracktype:1.
    2. Compute the Jacobian numerically using Bertini: Run Tracktype:1, save a witness point from main_data in start, and run Tracktype:-3.
  2. Use numerical linear algebra, in Sage, Maple, or MATLAB, to compute a list of bases and circuits from the Jacobian matrix.
  3. Run Bertini, Tracktype:5 on a list of projection vectors and extract the degree of the projection for the circuit degree, and the degree of the fiber for the base degree. Sample Bash scripts for this are included: decBases.sh and decCircs.sh.

About

Code accompanying the pre-print "Computing Algebraic Matroids" by Zvi Rosen.

Topics

Resources

Releases

No releases published

Packages

No packages published

Languages