3. Parma Polyhedron Library

4. Challenges in detail

5. Benchmarking results

8. n-dimensions

9. 2- polytope: polygon

11. Convex polytopes

12. Star polytopes

13. Abstract polytopes

14. Self-dual polytopes

16. (V-representation)

17. Half space representation

20. Fast numerical algorithms

21. Easy building of prototypes

23. Used to create convex polytopes

24. Very user friendly (you write x + 2*y + 5*z <= 7 when you mean it)

25. Efficient

26. Very precise by using GMP data types (precision is limited by the available memory)

28. External interface function which allow to interface with C/C++ or Fortran subroutines.

30. Speed

32. void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]){ if ((nrhs == 2)&&(nlhs == 1)){ double *Input0 = mxGetPr(prhs[1]); double *Input1 = mxGetPr(prhs[2]); double *Return_arg = mxGetPr(plhs[0]); Return_arg[0] = Input0[0] + Input1[0]; } }

36. Compile to .mexglx files with Eclipse

37. Find a structure to be easily maintained Double mpz_class Linear expression inequations Constraint System Polytope Double mpz_class Linear expression inequations Constraint System mxArray mxArray Polytope computation

40. http://en.wikipedia.org/wiki/File:3dpoly.svg

41. http://t1.gstatic.com/images?q=tbn:luK1qGow7LqkwM:http://megashareslink.com/wp-content/uploads/2009/04/matlab_logo.gif&t=1