CIMAT Lectures

Minicourse on computation in agebraic geometry

References

• Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox, John Little, and Donal O'Shea
sagemath.org

Lecture Notes

• Programming in Python and Sage
• Lecture 1 Division algorithm, Groebner basis, monomial ideals , Hilbert functions and dimension
• Lecture 2 Hilbert functions and dimension
• Lecture 3 Elimination theory, lines on a cubic surface

Sage code

• Compute the roots of polynomial in GF(q)
• Division algorithm and Buchberger's algorithm
• Compute lines on cubic surface
• Elsenhans-Jahnel algorithm for determining whether the action of the Galois group on the lines is W(E6).