arXiv subjects

Mahsa Kazemi

Publications and source records attributed to Mahsa Kazemi.

3 recordsLinked to original sources

arXiv2021

Multivariate Power Series in Maple

We present MultivariatePowerSeries, a Maple library introduced in Maple 2021, providing a variety of methods to study formal multivariate power series and univariate polynomials over such series. This library offers a simple and easy-to-use user interface. Its implementation relies on lazy evaluation techniques and takes advantage of Maple's features for object-oriented programming. The exposed methods include Weierstrass Preparation Theorem and factorization via Hensel's lemma. The computational performance is demonstrated by means of an experimental comparison with software counterparts.

cs.SC↗

arXiv2018

Symbolic local bifurcation analysis of scalar smooth maps

The local zero structure of a smooth map may qualitatively change, when the map is subjected to small perturbations. The changes may include births and/or deaths of zeros. The qualitative properties are defined as the invariances of an appropriate equivalence relation. The occurrence of a qualitative change in the zero structures is called a bifurcation and the map is named a singularity. The local bifurcation analysis of singularities has been extensively studied in singularity theory and many powerful algebraic tools have been developed for their study. However, there does not exist any symbolic computer-library for this purpose. We suitably generalize some powerful tools from algebraic geometry for correct implementation of the results from singularity theory. We provide some required criteria along with rigorous proofs for efficient and cognitive computer-implementation. We have accordingly developed a Maple end-user friendly library, named Singularity, for an efficient and complete local bifurcation analysis of real zeros of scalar smooth maps. We have further written a comprehensive user-guide for Singularity. The main features of Singularity are briefly illustrated along with a few examples.

math.DS↗

arXiv2018

A user guide for Singularity

This is a user guide for the first version of our developed Maple library, named Singularity. The first version here is designed for the qualitative study of local real zeros of scalar smooth maps. This library will be extended for symbolic bifurcation analysis and control of different singularities including autonomous differential singular systems and local real zeros of multidimensional smooth maps. Many tools and techniques from computational algebraic geometry have been used to develop Singularity. However, we here skip any reference on how this library is developed. This package is useful for both pedagogical and research purposes. Singularity will be updated as our research progresses and will be released for public access once our draft paper [4] is peer-reviewed in a refereed journal.

math.DS↗