Related papers: Solvable Sextic Equations

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete.

We obtain various irreducibility criteria for pairs of polynomials $(f(X),g(X))$ with integer coefficients whose resultant $Res(f,g)$ is a prime number, or is divisible by a sufficiently large prime number, and also for some of their linear…

For the solvable polynomial algebras introduced and studied by Kandri-Rody and Weispfenning [J. Symbolic Comput., 9(1990)], a constructive characterization is given in terms of Gr\"obner bases for ideals of free algebras, thereby solvable…

We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…

Let $P(T,X)$ be an irreducible polynomial in two variables with rational coefficients. It follows from Hilbert's Irreducibility Theorem that for most rational numbers $t$ the specialized polynomial $P(t,X)$ is irreducible and has the same…

We study the determinisation and unambiguisation problems of weighted automata over the rational field: Given a weighted automaton, can we determine whether there exists an equivalent deterministic, respectively unambiguous, weighted…

We extend the classification of solvable Lie algebras with abelian nilradicals to classify solvable Leibniz algebras which are one dimensional extensions of an abelian nilradicals.

We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…

We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…

In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…

In this paper we give an algorithm to calculate the coefficients of the p-adic expansion of a rational numbers, and we give a method to decide whether this expansion is periodic or ultimately periodic.

We classify order $3$ linear difference operators over $\mathbb{C}(x)$ that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion of absolute irreducibility for difference modules, and…

We demonstrate a polynomial approach to express the decision version of the directed Hamiltonian Cycle Problem (HCP), which is NP-Complete, as the Solvability of a Polynomial Equation with a constant number of variables, within a bounded…

We complete the proof of Oka's conjecture on the Alexander polynomial of an irreducible plane sextic. We also calculate the fundamental groups of irreducible sextics with a singular point adjacent to $J_{10}$.

Let $R(x)=g(x)/h(x)$ be a rational expression of degree three over the finite field $\mathbb{F}_q$. We count the irreducible polynomials in $\mathbb{F}_q[x]$, of a given degree, which have the form $h(x)^{\mathrm{deg}\, f}\cdot…

Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.

The number of rational points of a plane non-singular algebraic curve X defined over a finite field is computed, provided that the generic point of X is not an inflexion and that X is Frobenius non-classical with respect to conics.

We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse…

We show that the intersection of the rational derived series of a one-relator group is rationally perfect and is normally generated by a single element. As a corollary, we characterise precisely when a one-relator group is residually…