This paper presents a new algorithm for computing the Hermite form of a polynomial matrix. Given a nonsingular n x n matrix A filled with degree d polynomials with coefficients from a field, the algorithm computes the Hermite form of A using an expected ...

Based on Eisenbud's idea (see [Eisenbud, D., Evans, G., 1973. Every algebraic set in n-space is the intersection of n hypersurfaces. Invent. Math. 19, 107-112]), we present an algorithm for computing set-theoretic generators for any algebraic variety in ...

Let f ∈ Q[X_1,...,X_n] be of degree D. Algorithms for solving the unconstrained global optimization problem f*=inf_x∈Rⁿ f(x) are of first importance since this problem appears frequently in numerous applications in engineering sciences. This can be ...

Let I in K[x1,...,x_n] be a 0-dimensional ideal of degree D where K is a field. It is well-known that obtaining efficient algorithms for change of ordering of Gröbner bases of I is crucial in polynomial system solving. Through the algorithm FGLM, this ...

Let L be a second order linear ordinary differential equation with coefficients in C(x). The goal in this paper is to reduce L to an equation that is easier to solve. The starting point is an irreducible L, of order two, and the goal is to decide if L ...

Abstract This paper describes a Buchberger-style algorithm to compute a Gröbner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for the new ...

A finite number of rational functions are compatible if they satisfy the compatibility conditions of a first-order linear functional system involving differential, shift and q-shift operators. We present a theorem that describes the structure of ...

We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a weakened notion of a polynomial GCD modulo a regular chain, which permits to greatly ...

This article is a continuation of our earlier work [3], which introduced triangular decompositions of semi-algebraic systems and algorithms for computing them. Our new contributions include theoretical results based on which we obtain practical ...

In this paper, we introduce a new method to avoid zero reductions in Gröbner basis computation. We call this method LASyz, which stands for Lineal Algebra to compute Syzygies. LASyz uses exhaustively the information of both principal syzygies and non-...

Enumerating all 3-manifold triangulations of a given size is a difficult but increasingly important problem in computational topology. A key difficulty for enumeration algorithms is that most combinatorial triangulations must be discarded because they ...

The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (n_i/d)_{1≤ i≤ n} from their images (a_i)_{1≤ i≤ n} mod M, subject to a condition such as 0 < d ≤ N and N_i}≤ N for a given magnitude bound ...

We study generalized log-sine integrals at special values. At π and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at ±1. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms ...

In this tutorial we will focus on the solution of polynomial systems given with inexact coefficients using hybrid symbolic-numeric methods. In particular, we will concentrate on systems that are over-constrained or have roots with multiplicities. These ...

We give an overview over computer algebra algorithms for dealing with symbolic sums, recurrence equations, generating functions, and asymptotic estimates, and we will illustrate how to apply these algorithms to problems arising in discrete mathematics.

Condition numbers are well known in numerical linear algebra. It is less known that this concept also plays a crucial part in understanding the efficiency of algorithms in linear programming, convex optimization, and for solving systems of polynomial ...

A general goal concerning fundamental linear algebra problems is to reduce the complexity estimates to essentially the same as that of multiplying two matrices (plus possibly a cost related to the input and output sizes). Among the bottlenecks one ...

ISSAC 2011 is a continuation of a well-established series of international conferences for the presentation of the latest advances in the field of Symbolic and Algebraic Computation. The first meeting of the series (1966) was held in Washington, DC, and ...