newton

Project developed to assist with simplification and search for approximate solution of power equation systems.

Currently does the following:

• Computes a fundamental solution of a linear inequations system
  • Uses Motzkin-Burger algorithm
• Computes minimal convex hull (referred as Newton polyhedron, but can work with fractions) for the given polynomial
  • Computes all N-faces and normal cones for highest-dimension faces
  • Generates the lookup table between polynomial terms (polyhedron vertices) and normal vectors
  • Can visualize 2D and 3D polys
• Has utility calculation methods
  • These includes matrces operations like inversion, determinant and minors computation

Also contains unfinished work for the said simplification itself. Note that theory becomes somewhat vague at this point.

Building

Java binary can be assembled via SBT by running sbt buildDistr command (will create a jar-file in _build subfolder and copy Java3D libs there if possible). GUI can then be launched via java -jar newton-<VER>.jar. Main class is org.newtonpolyhedron.NewtonEntry.

Usage

See instructions in English or Russian.

Authors

• Alexander Abdugafarov (https://github.com/frozenspider/) - programming
• Elvira Settarova - math
• Alexander Orkin - math
• Ahmadjon Soleev - supervision, math

Developed primarily for Samarkand State University