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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

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