## Welcome

GBReLA 2 is a special session at the conference for Applications of Computer Algebra (ACA) 2015. Its theme lies in the intersection of Gröbner bases, resultants and linear algebra. The talks will range from comprehensible introductions to recent research results and ideas. Beginners in this area will have the chance to dive into the linear algebra approach to Gröbner bases and resultants, while advanced students and researchers will have the chance to learn about new insights into the connections of Gröbner bases, resultants and related matrix methods.

## Topics of interest

Everything in the intersection of Gröbner bases, linear algebra and resultants, including but not restricted to:

- (Sylvester, Macaulay, Dixon, ...)-resultant.
- Sparse resultant.
- Construction and structure of resultant matrices.
- Gröbner bases and resultants.
- Elimination ideals.
- Theory of Gröbner bases and variations (e.g. standard bases).

## Participants

Gregory BardA Brief Introduction to the Extended Linearization Method (or XL Algorithm) for Solving Polynomial Systems of Equations. pdf

Jean-Charles FaugèreGröbner Bases and Structured Systems: an overview. pdf

Anna KarasoulouResultant of an Equivariant Polynomial System With Respect to the Symmetric Group. pdf

Manuel Kauers:Integral Bases for D-Finite Functions. pdf

Robert Lewis:Symbolic Solution of Parametric Polynomial Systems with the Dixon Resultant. pdf

Suzy Maddah:LINDALG: Mathemagix Package for Symbolic Resolution of Linear Differential Systems with Singularities. pdf

Manfred Minimair:Design of a Maple Package for Dixon Resultant Computation. pdf

Dimitrios Poulakis:Bezout Matrices and Roots of Quaternion Polynomials. pdf

Elias Tsigaridas:Nearly Optimal Bit Complexity Bounds for Computations with Structured Matrices. pdf

Joris van der Hoeven:On the Complexity of Polynomial Reduction. pdf

Erol Yilmaz:Linear Algebraic Approach to H-Basis Computation. pdf

Dingkang Wang:The Generalized Rabinowitsch’s Trick. pdf

## Schedule

Thursday 2309:00 – 09:30 Gregory Bard - A Brief Introduction to the Extended Linearization Method (or XL Algorithm) for Solving Polynomial Systems of Equations. 09:30 – 10:00 Jean-Charles Faugère - Gröbner Bases and Structured Systems: an Overview. 10:00 – 10:30 Joris van der Hoeven - On the Complexity of Polynomial Reduction. 10:30 – 11:00 Dingkang Wang - The Generalized Rabinowitsch’s Trick. 11:00 – 11:30 Break 11:30 – 12:00 Anna Karasoulou - Resultant of an Equivariant Polynomial System with Respect to the Symmetric Group. 12:00 – 12:30 Robert Lewis - Symbolic Solution of Parametric Polynomial Systems with the Dixon Resultant. 12:30 – 13:00 Manfred Minimair - Design of a Maple Package for Dixon Resultant Computation. 13:00 – 15:00 Lunch 15:00 – 15:30 Manuel Kauers - Integral Bases for D-Finite Functions. 15:30 – 16:00 Suzy Maddah - LINDALG: Mathemagix Package for Symbolic Resolution of Linear Differential Systems with Singularities. 16:00 – 16:30 Dimitrios Poulakis - Bezout Matrices and Roots of Quaternion Polynomials. 16:30 – 17:00 Elias Tsigaridas - Nearly optimal bit complexity bounds for computations with structured matrices 17:00 – 17:30 Erol Yilmaz - Linear Algebraic Approach to H-Basis Computation.

## Local Information

For travel, housing and related information, please refer to the ACA 2015 homepage.

## ACA 2015 - Applications of Computer Algebra

GBReLA 2 will take place as a special session in the context of the ACA - "Applications of Computer Algebra" conference. We believe that ACA is an ideal venue for GBReLA, since many top researchers on the topics of GBReLA as well as young researchers and students will be present.

## Organization

- Maximilian Jaroschek: mjarosch an_at mpi-inf.mpg a_dot de
- Zafeirakis Zafeirakopoulos: zafeirakopoulos an_at gmail a_dot com