符号计算

For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n)…

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…

We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n x n matrix of degree d over a field K we give a rank and nullspace algorithm using about…

This tutorial presents features of the new and improved TeXmacs-maxima interface. It is designed for running maxima-5.9.2 from TeXmacs-1.0.5 (or later).

GPL Maxima is an open-source computer algebra system based on DOE-MACSYMA. GPL Maxima included two tensor manipulation packages from DOE-MACSYMA, but these were in various states of disrepair. One of the two packages, CTENSOR, implemented…

In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential…

We continue the study of counting complexity begun in [Buergisser, Cucker 04] and [Buergisser, Cucker, Lotz 05] by proving upper and lower bounds on the complexity of computing the Hilbert polynomial of a homogeneous ideal. We show that the…

So far, the scope of computer algebra has been needlessly restricted to exact algebraic methods. Its possible extension to approximate analytical methods is discussed. The entangled roles of functional analysis and symbolic programming,…

We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…

We examine two associative products over the ring of symmetric functions related to the intransitive and Cartesian products of permutation groups. As an application, we give an enumeration of some Feynman type diagrams arising in Bender's…

In this paper, we present a determinist Jordan normal form algorithms based on the Fadeev formula: \[(\lambda \cdot I-A) \cdot B(\lambda)=P(\lambda) \cdot I\] where $B(\lambda)$ is $(\lambda \cdot I-A)$'s comatrix and $P(\lambda)$ is $A$'s…

In this paper we present our recent work in developing a computer-algebra tool for systems of partial differential equations (PDEs), termed "Kranc". Our work is motivated by the problem of finding solutions of the Einstein equations through…

The article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology

After an introduction to the sequential version of FORM and the mechanisms behind, we report on the status of our project of parallelization. We have now a parallel version of FORM running on Cluster- and SMP-architectures. This version can…

We present a partial proof of van Hoeij-Abramov conjecture about the algorithmic possibility of computation of finite sums of rational functions. The theoretical results proved in this paper provide an algorithm for computation of a large…

A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…

We want to achieve efficiency for the exact computation of the dot product of two vectors over word-size finite fields. We therefore compare the practical behaviors of a wide range of implementation techniques using different…

Given a quadratic map Q : K^n -> K^k defined over a computable subring D of a real closed field K, and a polynomial p(Y_1,...,Y_k) of degree d, we consider the zero set Z=Z(p(Q(X)),K^n) of the polynomial p(Q(X_1,...,X_n)). We present a…

Let $\{w_{i,j}\}_{1\leq i\leq n, 1\leq j\leq s} \subset L_m=F(X_1,...,X_m)[{\partial \over \partial X_1},..., {\partial \over \partial X_m}]$ be linear partial differential operators of orders with respect to ${\partial \over \partial…

OTTER is a resolution-style theorem-proving program for first-order logic with equality. OTTER includes the inference rules binary resolution, hyperresolution, UR-resolution, and binary paramodulation. Some of its other abilities and…