We extend the theory of equitable decompositions introduced in [2], where it was shown that if a graph has a particular type of symmetry, i.e. a uniform or basic automorphism φ, it is possible to use φ to decompose ...
详细信息
This article is about applications of linear algebra to knot theory. For example, for odd prime p, there is a rule (given in the article) for coloring the arcs of a knot or link diagram from the residues mod p. This i...
详细信息
We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions;GCRD and LCLM;D-finite closure properties;natural transformations between related ...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions;GCRD and LCLM;D-finite closure properties;natural transformations between related algebras;guessing;desingularization;solvers for polynomials, rational functions and ( generalized) power series. This paper is a tutorial on how to use the package.
作者：
Huseynov, S. T.Ganja State Univ GSU
Natl Acad Aviat NAA Azerbaijan Fac Air Transport Dept Flying Apparat & Aviat Engines Ganja City Azerbaijan Ganja State Univ GSU
Fac Math & Informat Dept Informat Ganja City Azerbaijan
The paper mainly has devoted to the important fields of modern engineering education in the aerospace fields, particularly in such disciplines as structural mechanics and application of computer modeling there. The au...
详细信息
ISBN:
(纸本)9781509018413
The paper mainly has devoted to the important fields of modern engineering education in the aerospace fields, particularly in such disciplines as structural mechanics and application of computer modeling there. The author shares his experience in teaching and scientific research on some important issues about the role of modern software, which are concern to two different fields: CAD and computeralgebra. In the paper it has been showed relevant original graphical results of computer modeling in aerospace structural mechanics via Ansys CAD software and number of examples with original cods in Maple computer mathematics system for analytical researches in theory of mechanical equilibrium.
Let l a prime number and Phi(l)(X, Y) the modular polynomial of level l. Since this polynomial has integer coefficients one may compute it modulo primes. Petr Lisonek and Yung-Jung Kim compute the polynomial Phi(l)(X,...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
Let l a prime number and Phi(l)(X, Y) the modular polynomial of level l. Since this polynomial has integer coefficients one may compute it modulo primes. Petr Lisonek and Yung-Jung Kim compute the polynomial Phi(l)(X, Y) modulo 2 explicitly for several l and they conjecture that the coefficients under the diagonal vanish. In this note we prove their conjecture and that the same property holds modulo the primes 3 and 5.
The b-function and related invariants of the singularity z(1)(4) + z(2)(p) + z(1)z(2)(p-1) = 0 are determined. We exploit the theory of computeralgebra and Weyl algebra for the study of local b-function by T. Yano in...
详细信息
The b-function and related invariants of the singularity z(1)(4) + z(2)(p) + z(1)z(2)(p-1) = 0 are determined. We exploit the theory of computeralgebra and Weyl algebra for the study of local b-function by T. Yano in 1970s.
In the first part of this paper we present a short survey on the problem of the representation of rational normal curves as set-theoretic complete intersections. In the second part we use a method, introduced by Robbi...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
In the first part of this paper we present a short survey on the problem of the representation of rational normal curves as set-theoretic complete intersections. In the second part we use a method, introduced by Robbiano and Valla, to prove that the rational normal quartic is set-theoretically complete intersection of quadrics: it is an original proof of a classical result of Perron, and Gallarati-Rollero.
In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the computer Aided Geometric Design Community. The analysis of the validity o...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
In the nineties, several methods for dealing in a more efficient way with the implicitization of rational parametrizations were explored in the computer Aided Geometric Design Community. The analysis of the validity of these techniques has been a fruitful ground for Commutative algebraists and algebraic Geometers, and several results have been obtained so far. Yet, a lot of research is still being done currently around this topic. In this note we present these methods, show their mathematical formulation, and survey current results and open questions.
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric mo...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
In this expository article we give an introduction to Ehrhart theory, i.e., the theory of integer points in polyhedra, and take a tour through its applications in enumerative combinatorics. Topics include geometric modeling in combinatorics, Ehrhart's method for proving that a counting function is a polynomial, the connection between polyhedral cones, rational functions and quasisymmetric functions, methods for bounding coefficients, combinatorial reciprocity theorems, algorithms for counting integer points in polyhedra and computing rational function representations, as well as visualizations of the greatest common divisor and the Euclidean algorithm.
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime number Theorem and a classical result of Gauss count the remaining ones, approximately and exactly. For polynomi...
详细信息
ISBN:
(纸本)9783319150819;9783319150802
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime number Theorem and a classical result of Gauss count the remaining ones, approximately and exactly. For polynomials in two or more variables, the situation changes dramatically. Most multivariate polynomials are irreducible. This survey presents counting results for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones ( divisible by the sth power of a nonconstant polynomial), the relatively irreducible ones ( irreducible but reducible over an extension field), the decomposable ones, and also for reducible space curves. These come as exact formulas and as approximations with relative errors that essentially decrease exponentially in the input size. Furthermore, a univariate polynomial f is decomposable if f = g circle h for some nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small minority among all polynomials. The tame case, where the characteristic p of F-q does not divide n = deg f, is fairly well-understood, and we obtain closely matching upper and lower bounds on the number of decomposable polynomials. In the wild case, where p does divide n, the bounds are less satisfactory, in particular when p is the smallest prime divisor of n and divides n exactly twice. The crux of the matter is to count the number of collisions, where essentially different ( g, h) yield the same f. We present a classification of all collisions at degree n = p(2) which yields an exact count of those decomposable polynomials.
暂无评论