Related papers: Computing preimages of points and curves under pol…
We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined…
Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…
We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.
In this note, we are interested in the Jacobian Conjecture. Following the results of L.M.~Dru$\dot{\rm z}$kowski, we consider some vector fields depending on a certain \'etale polynomial map. From results of semialgebraic geometry with the…
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
We determine the precise bifurcation diagrams of the apparent contours of generic crosscaps, which contain the information of bifurcations with respect to the images of the singular sets of crosscaps: crosscap points and double point…
Elliptic curves over finite fields with predefined conditions in the order are practically constructed using the theory of complex multiplication. The stage with longest calculations in this method reconstructs some polynomial with integer…
We derive a formula for the number of pre-images under a non-degenerate harmonic mapping $f$, using the argument principle. This formula reveals a connection between the pre-images and the caustics. Our results allow to deduce the number of…
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
We describe an explicit method for constructing pseudo-automorphisms of a space $X$ which is obtained by blowing up points of $P^k$ (or a product $P^k \times \cdots \times P^k$). The centers of blowup are chosen to lie on an elliptic normal…
We implement an algorithm to compute the number of points over finite fields for the Shimura curves $X_0^D(N)$ and their Atkin--Lehner quotients. Our computations result in many examples of curves which attain the largest known point counts…
Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Kedlaya's algorithm (Kedlaya, J. Ramanujan Math. Soc 16, 2001) can be used to count the points of arbitrary hyperelliptic curves over finite fields of characteristic p, where p is an odd prime. The algorithm uses the cohomology of a p-adic…
We compute the virtual Poincar\'e polynomials of the configuration space of $n$ ordered points on an elliptic curve with sum 0.