Related papers: An algorithm for computing Grobner basis and the c…
We give an effective method to compute the entropy for polynomials orthogonal on a segment of the real axis that uses as input data only the coefficients of the recurrence relation satisfied by these polynomials. This algorithm is based on…
Let $I_1\subset I_2\subset\dots$ be an increasing sequence of ideals of the ring $\Bbb Z[X]$, $X=(x_1,\dots,x_n)$ and let $I$ be their union. We propose an algorithm to compute the Gr\"obner base of $I$ under the assumption that the…
It is shown that the methods and algorithms, developed in (A. Capani et al., Computing minimal finite free resolutions, {\it Journal of Pure and Applied Algebra}, (117& 118)(1997), 105 -- 117; M. Kreuzer and L. Robbiano, {\it Computational…
We present an effective method for computing parametric primary decomposition via comprehensive Gr\"obner systems. In general, it is very difficult to compute a parametric primary decomposition of a given ideal in the polynomial ring with…
Based on a theorem by Vasconcelos, we give an algorithm for equidimensional decomposition of algebraic sets using syzygy computations via Gr\"obner bases. This algorithm avoids the use of elimination, homological algebra and processing the…
We obtain two new algorithms for partial fraction decompositions; the first is over algebraically closed fields, and the second is over general fields. These algorithms takes $O(M^2)$ time, where $M$ is the degree of the denominator of the…
An algorithm to compute a good basis of the Brieskorn lattice of a cohomologically tame polynomial is described. This algorithm is based on the results of C. Sabbah and generalizes the algorithm by A. Douai for convenient Newton…
Consider a sparse polynomial in several variables given explicitly as a sum of non-zero terms with coefficients in an effective field. In this paper, we present several algorithms for factoring such polynomials and related tasks (such as…
A new version of the Graeffe algorithm for finding all the roots of univariate complex polynomials is proposed. It is obtained from the classical algorithm by a process analogous to renormalization of dynamical systems. This iteration is…
Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct…
Determining visibility in planar polygons and arrangements is an important subroutine for many algorithms in computational geometry. In this paper, we report on new implementations, and corresponding experimental evaluations, for two…
In this paper we describe a combination of ideas to improve incremental signature-based Groebner basis algorithms having a big impact on their performance. Besides explaining how to combine already known optimizations to achieve more…
Given a parametric polynomial ideal I, the algorithm DISPGB, introduced by the author in 2002, builds up a binary tree describing a dichotomic discussion of the different reduced Groebner bases depending on the values of the parameters,…
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature…
We discuss the problem of constructing differential operators for the generalized IBP reduction algorithms at the 2-loop level. A deeply optimized software allows one to efficiently construct such operators for the first non-degenerate…
Combinatorial algorithms for minimization of functions of many variables, which take their values in finite totally ordered sets, are developed. For that the decomposition of the functions by Boolean polynomials is used. The modified SFM…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…