Related papers: A Macaulay2 package for computations with rational…
Given a birational map in the three dimensional projective space defined by monomials of degree $d$, we prove that its inverse is defined by monomials of degree at most $d^2-d+1$.
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…
We offer a Maple package SL\_2\_Inv\_Ker for calculating of minimal generating sets for the algebras of joint invariants/semi-invariants of binary forms and for calculations of the kernels of Weitzenb\"ock derivations.
We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…
We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimensional radical ideals depending on algebraically independent…
Two birational subvarieties of P^n are called Cremona equivalent if there is a Cremona modification of P^n mapping one to the other. If the codimension of the varieties is at least 2 then they are always Cremona Equivalent. For divisors the…
A geometric realization of a birational map $\psi$ among two complex projective varieties is a variety $X$ endowed with a $\mathbb{C}^*$-action inducing $\psi$ as the natural birational map among two extremal geometric quotients. In this…
In this paper, we propose a feasible algorithm to give an explicit basis of the space of regular differential forms on the nonsingular projective model of any given plane algebraic curve. The algorithm is demonstrated for concrete examples,…
We discuss the computational complexity and feasibility properties of scenario based techniques for uncertain optimization programs. We consider different solution alternatives ranging from the standard scenario approach to recursive…
The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a…
Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…
We compute the presentations of fundamental groups of the complements of a class of rational cuspidal projective plane curves classified by Flenner, Zaidenberg, Fenske and Saito. We use the Zariski-Van Kampen algorithm and exploit the…
Cubic spline interpolation on Euclidean space is a standard topic in numerical analysis, with countless applications in science and technology. In several emerging fields, for example computer vision and quantum control, there is a growing…
We have developed a Python package ZMCintegral for multi-dimensional Monte Carlo integration on multiple Graphics Processing Units(GPUs). The package employs a stratified sampling and heuristic tree search algorithm. We have built three…
For any given natural $d\ge 1$ we provide examples of rational self-maps of complex projective plane $\pp^2$ of degree $d$ without (holomorphic) fixed points. This makes a contrast with the situation in one dimension. We also prove that the…
The Package Miura contains functions that compute divisor class group arithmetic for nonsingular curves. The package reduces computation in a divisor class group to that in the ideal class group via the isomorphism. The underlying quotient…
We look at sequences of positive integers that can be realized as degree sequences of iterates of rational dominant maps of smooth projective varieties over arbitrary fields. New constraints on the degree growth of endomorphisms of the…
We construct a birational map of $\mathbb{P}^d$ ($d\geq6$) whose intermediate dynamical degrees are all trancendental.
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is…
The open-source Python package Gammapy, developed for the high-level analysis of gamma-ray data, requires gamma-like event lists combined with the corresponding instrument response functions. For a morphological analysis, these data have to…