This repo contains a series of guided tutorials to perform various tasks in Computer Algebra with Macaulay2.
keywords: Ideals and Rings, Groebner Basis, polynomial systems of equations, computational algebraic geometry
This material is aimed at people with a basic understanding of algebraic geometry (rings, ideals, algebraic varieties). In each tutorial, a problem is stated at the top and a worked out solutions follows. The learner/reader is strongly advised to attempt to solve the problem alone, before reading the presented solutions.
- Generalize Gaussian Elimination
- Computing a Groebner basis
- Solving the first polynomial system of equations
- A system with no solutions
- Computing the generators of the ring of invariants
- Ideal membership and division
- A surface and a Curve in space
- A polynomial system over the complex numbers
- Optimization via Lagrange multipliers
- Implicit equations of a parametric curve
- Implicit equations of a ruled surface
- Sums of Powers
- Many thanks to @MBender who helped me designing some of the above tutorials.
Created by @marcoramponi - feel free to contact me!