The reports and codes for the project on algebraic geometry methods (Grobner and Graver Basis) to introduce algorithms and reduce the computational cost of Integer Programming and Stochastic Integer Programming under the supervision of Prof. Janosch Ortmann and Prof. Walter Rei at UQAM.
Some detail:
- Sympy Package for Algebra ( https://docs.sympy.org/latest/index.html ; https://mattpap.github.io/masters-thesis/html/index.html ).
- 'Compu_1.ipynb' and 'Compu_2.ipynb': some facts from Grobner Basis; application to commutative algebra theory and integer programming.
- 'Compu_3.ipynb' and 'Compu_4.ipynb': applications of Grobner Basis and Graver Basis to Stochastic Integer Programming.
- 'Compu_5.ipynb': lagrange relaxation.
- 'Algsto.pdf' and 'Algsto2.pdf': final reports containing theorems determing the relationships between Groebner and Graver Basis of IP and SIP and new algorithms in integer programming especially favorable to stochastic integer programming.
- 'Programmes' folder: realization of some algorithms including computation of Toric Ideal, Graver Basis and new algorithms in integer programming especially favorable to stochastic integer programming.
- 'Alg_1 Graver2Augmentation.ipynb': computation of Toric Ideal and Graver Basis of a matrix; augmentation algorithm.
- 'Alg_2 Ker2BunchBerg2Augmentation.ipynb': generating set of the Toric Ideal (i.e., kernel of a ring morphism)