Automatic generator for a sparse resultant based polynomial solver

Required software

• Software: MATLAB and Maple.
• Currently supported MATLAB version: R2018a+
• Currently supported Maple version: 2018+

Setup

• MATLAB installation should include the symbolic maple toolbox
• The Maple installation has to be setup as the symbolic engine in MATLAB insallation
  • Older MATLAB versions connect to Maple through their symbolic math toolboz.
  • But MATLAB 2018+ have a separate Maple toolbox to be setup.
• One quick way to check is by executing one of the following in the command MATLAB window

  maple

  • If Maple is connected, the command should open a GUI Maple interface.
• For more help on installing Maple toolbox for MATLAB, one can refer to https://www.maplesoft.com/support/install/mtm11Install.html.

Generating a solver (OFFLINE stage)

Input

• A problem_name.m file which returns a structure of solver configuration parameters and a function that returns a set of input polynomial equations
• The problem_name.m file is to be stored in problems/ folder.
• The configuration parameters are housed in a matlab struct cfg.
• The function that returns the input polynomials has the signature

function eqs = retrieve_eqs(a1,a2,..,c1,c2,...)

• The configuration struct has the following fields
  • numOfCoeff
  • numOfVars
  • hiddenVarNum
  • sizeOfCombs or polyComb
  • noOfRowsToReduce
  • heurisiticTemplatesize

Output

• A solver.m file in 'solvers/problem_name'
• Two other files are generated in solvers/problem_name which are to be used for debugging purposes:
  • eqs.txt
  • A MAPLE script which was executed for generating the solver for problem problem_name

Usage

• Navigate to the main folder of the generator
• Execute

  build_test_solver(p1, p2, p3)

  • p1 is 1 if we want to generate a solver , 0 if we do not want to generate a solver
  • p2 is 1 if we want to test a solver , 0 if we do not want to test a solver
  • p3 is the number of random datapoints to be used for testing a solver
• When prompted for the problem name, enter the value of problem_name

Executing the solver (ONLINE stage)

• The solver for a problem problem_name is housed in solvers/problem_name.
• Execute

  build_test_solver(0, 1, p)

  • p is th number of random instances to be used for testing the solver
• When prompted for the problem name, enter the value of problem_name

Further questions or comments

• Please write to snehal.bhayani@oulu.fi or snehalbhayani04@gmail.com

Reference

• If you are using this generator software please cite the following:

[1] Bhayani, S., Kukelova, Z., & Heikkilä, J. (2019). A sparse resultant based method for efficient minimal solvers. ArXiv, abs/1912.10268. PDF