We are organizing a Macaulay2 workshop to take place at Max Planck Institute in Leipzig in 2018 from Monday June 4th to Friday June 8th. The purpose of the workshop is to bring the Macaulay 2 developers Dan Grayson and Mike Stillman together with those who would like to share or to develop their skills on Macaulay 2.
Performing Buchberger's algorithm, the standard algorithm for computing Groebner bases, involves making many important choices. In particular, the strategy for selecting the next s-pair to process can make dramatic differences in the time and space needed for the computation. While we have several heuristics for pair selection, reinforcement learning provides tools for exploring and developing new strategies for both Buchberger's algorithm and other algorithms in computer algebra.
MonodromySolver is a package for numerical solving of parametric polynomial systems. I will demonstrate how to set up and "solve" the classic enumerative problem, "how many lines on a general cubic surface in P^3?" Time permitting, I will also give examples of systems coming from applications.
Let $S=K[x_1,...,x_n]$ be a standard graded polynomial ring with arbitrary field $K$. Let $I_1,...,I_r$ be homogeneous ideals of $S$. The multi-Rees algebra $Rees(I_1,...,I_r)= S[I_1T_1,...,I_rT_1]$ encodes the information of any product like $I_1^{a_1}...I_r^{a_r}$ and is a standard tool in the study of regularity of $I_1^{a_1}...I_r^{a_r}$. In this short talk, we try to calculate the partial regularity of $Rees(I_1,...,I_r)$.
The Macaulay2 packages "SimplicialComplexes" and "SimplicialDecomposability" contain convenient tools for the study of the combinatorics of simplicial complexes. We give a brief overview of some of their functions by providing explicit examples.
