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.