SIGSAM

In his 1999 SIGSAM BULLETIN paper [7], H. J. Stetter gave an explicit formula for finding the nearest polynomial with a given zero. This present paper revisits the issue, correcting a minor omission from Stetter's formula and explicitly extending the ...

Determining the topology of an algebraic surface is not only an interesting mathematical problem, but also a key issue in computer graphics and CAGD. An algorithm is proposed to determine the intrinsic topology of an implicit real algebraic surface f(x,...

We consider the evaluation of the truncated hypergeometric series

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to high precision, where <i>a, b, p</i>, and <i>q</i> are polynomials with integer coefficients, and <i>a</i>(<i>n</i>), <i>b</i>(<i>n</i>), <i>p</i>(<i>n</i>), <i>q</i>(<i>n</i>) have ...

A multivariate hyperexponential function is a function whose "logarithmic derivatives" are rational. Examples of hyperexponential functions include rational functions, exponential functions, and hypergeometric terms. Hyperexponential functions play an ...

Group actions are ubiquitous in mathematics. They arise in diverse areas of applications, from classical mechanics to computer vision. A classical but central problem is to compute a generating set of invariants.

We consider a rational group action on the ...

The offset hypersurface O_d(V), at distance d, to an irreducible hypersurface V is essentially the envelope of the system of spheres centered at the points of V with fixed radius d (for a formal definition, and for basic properties of offsets, see [2] ...

Numerical matrix methods are increasingly popular for polynomial root-finding. This approach usually amounts to the application of the QR algorithm to the highly structured Frobenius companion matrix of the input polynomial. The structure, however, is ...

Let G be a finite dimensional torus acting diagonally on the smooth affine variety X = k^r x (k^x)^s, with k an algebraically closed field k of characteristic 0. We denote the ring of regular functions on X by O(X) and the ring of differential operators by ...

The Stewart Platform (SP) is a parallel manipulator consisting of a moving platform and a base. The position and orientation (pose) of the base are fixed. The base and platform are connected with six extensible legs. The SP has been studied extensively ...

We explore the notion of generalization in the setting of symbolic mathematical computing. By "generalization" we mean the process of taking a number of instances of mathematical expressions and producing new expressions that may be specialized to all ...

Let F(x,u), with (u) = (u₁,...,u_ℓ), be an irreducible multivariate polynomial over C, having singularity at the origin, and let F_New(x,u) be the so-called Newton polynomial for F(x,u). The extended Hensel construction (EHC in short) of F(x,u) allows us ...

We give a new bound for the number of recursive subdivisions in the Descartes method for polynomial real root isolation. Our proof uses Ostrowski's theory of normal power series from 1950 which has so far been overlooked in the literature. We combine ...

The program CRACK is a computer algebra package written in REDUCE for the solution of over-determined systems of algebraic, ordinary or partial differential equations with at most polynomial non-linearity. It is available as part of version 3.8 of the ...

Performing calculations modulo a set of relations is a basic technique in algebra. For instance, computing the inverse of an integer modulo a prime integer or computing the inverse of the complex number 3 + 2<i>t</i> modulo the relation &ell;² + ...

The standard approach for computing with an algebraic number is through the data of its irreducible minimal polynomial over some base field k. However, in typical tasks such as polynomial system solving, involving many algebraic numbers of high degree, ...

In this paper we present two algorithms for irreducible decomposition of monomial ideals. We first use staircase structures to study the monomial ideals. We generalize the shifting degrees rule from two variables to three variables and then arbitrary ...

We present a system [1] that allows wireless smartphones to be used for mathematics communication, that is, for the creation and exchange of mathematical formulas, diagrams, and text between two or more participants. The system enables two or more persons ...