Related papers: Computing invariants of cubic surfaces
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
The invariant theory for conformal hypersurfaces is studied by treating these as the conformal infinity of a conformally compact manifold: For a given conformal hypersurface embedding, a distinguished ambient metric is found (within its…
We introduce the notion of matrices graph, defining continued fraction algorithms where the past and the future are almost independent. We provide an algorithm to convert more general algorithms into matrices graphs. We present an algorithm…
Modeling electronic systems is an important application for quantum computers. In the context of materials science, an important open problem is the computational description of chemical reactions on surfaces. In this work, we outline a…
In this paper we discuss two different existing algorithms for computing topological entropy and we perform one of them in order to compute the isentropes for cubic polynomials.
Using equivariant geometry, we find a universal formula that computes the number of times a general cubic surface arises in a family. As applications, we show that the PGL(4) orbit closure of a generic cubic surface has degree 96120, and…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
We define a differential graded algebra associated to Legendrian knots in thickened convex surfaces $\Sigma\times \mathbb{R}$. The algebra is defined in the same spirit as the Chekanov-Eliashberg DGA for Legendrians in $\mathbb{R}^3$, but…
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
We compute the critical surface for the existence of invariant tori of a family of Hamiltonian systems with two and three degrees of freedom. We use and compare two methods to compute the critical surfaces: renormalization-group…
We study homological invariants of smooth families of real quadratic forms as a step towards a "Lagrange multipliers rule in the large" that intends to describe topology of smooth maps in terms of scalar Lagrange functions.
The aim of this note is to give a formula expressing the trace form associated with the 27 lines of a cubic surface.
In this paper we describe the algebra of differential invariants for GL(n,C)-structures. This leads to classification of almost complex structures of general positions. The invariants are applied to the existence problem of…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
We consider ruled surfaces with finite multiplicity. We study behaviors of the striction curves and the singularities of the ruled surfaces. We also give geometric meanings of invariants related to the ruled surfaces.
The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems, for instance, spectral submanifolds have emerged as useful…
Cylindrical algebraic decompositions (CADs) are a key tool for solving problems in real algebraic geometry and beyond. We recently presented a new CAD algorithm combining two advances: truth-table invariance, making the CAD invariant with…
We study the moduli space $\widetilde{\calM}$ of marked cubic surfaces. By classical work of A.\,B. Coble, this has a compactification $\widetilde{M}$, which is linearly acted upon by the group $W(E_6)$. $\widetilde{M}$ is given as the…