Juan Pablo

Hi, I’m Juan Pablo Gonzalez Trochez

I am currently a PhD candidate in the Department of Computer Science at the University of Western Ontario working under the supervision of Professor Marc Moreno Maza. I am a member of the Ontario Research Center for Computer Algebra (ORCCA). I have received a BSc in Mathematics from the Universidad del Norte.

My research interests lies in the field of computer algebra. To be precise, I have two main focuses: *regular chains* and * multivariate formal Puiseux series*.

Regular chains are triangular sets of polynomials used to solve systems of polynomial equations. My research mainly focus in the study one dimensional regular chains. That is, regular chains where the number of equations is one less than the number of variables. In particular, I am interested in computing the intersection between a one dimensional structure and a polynomial by means of evaluation and interpolation, under certain hypothesis.

Multivariate Puiseux series are a generalization of multivariate power series in which now we allow rational exponents to our variables. I am currently encoding Multivariate formal Puiseux series as an object inside of Maple by means of lazy-evaluation. I am also working in the Puiseux theorem, which allows us to factorize univaritate polynomials with Puiseux series coefficients.

### Projects

- I work on the
**Basic Polynomial Algebra Subprograms**(BPAS) library developing a modular version of the**Intersect**algorithm. - I am one of the developers of the
**Multivariate Power Series**package of Maple. ### Talks and posters

- Issac 2022 (poster): Algorithms for multivariate Laurent series.
- Master thesis defense 2022 (talk): Algorithms for Regular Chains of Dimension One.
- Maple conference 2021 (talk): A Maple implementation of a modular algorithm for computing the common zeros of a polynomial and a regular chain.
### Papers

**A Maple implementation of a modular algorithm for computing the common zeros of a polynomial and a regular chain.**

Matt Calder, Juan Pablo Gonzalez Trochez, Marc Moreno Maza, Erik Postma.

Proceedings of Maple Conference 2021,*Maple Transactions*, 2022.

Experience

- 2020-Current
- University of Western Ontario - CS Department
- Graduate Teaching Assistant

- 2021-2022
- MapleSoft
- Summer Intern

- 2019-2020
- University of Western Ontario - Math Department
- Graduate Teaching Assistant

- 2018-2019
- Universidad del Norte
- Lecturer

- 2017-2018
- Universidad del Norte
- Graduate Teaching Assistant

### University of Western Ontario

- PhD-Computer Science, Computer Algebra (2022-2026)
- MSc-Computer Science, Computer Algebra (2020-2022)
- MSc-Mathematics, course-based (2019-2020)
### Universidad del Norte

- Masters degree in Mathematics, Coding Theory (2016-2018)
- Mathematics (2011-2015)