相关论文: Numerical Calculations Using Maple: Why & How?

The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…

Many real-world dynamic systems, both natural and artificial, are understood to be performing computations. For artificial dynamic systems, explicitly designed to perform computation - such as digital computers - by construction, we can…

An introduction to the Quantum Chemistry Package (QCP), implemented in the computer algebra system Maple, is presented. The QCP combines sophisticated electronic structure methods and Maple's easy-to-use graphical interface to enable…

The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…

In this paper, we present our ongoing work and initial results on the formal specification and verification of MiniMaple (a substantial subset of Maple with slight extensions) programs. The main goal of our work is to find behavioral errors…

Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods…

To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally…

We present celmech, an open-source Python package designed to facilitate a wide variety of celestial mechanics calculations. The package allows users to formulate and integrate equations of motion incorporating user-specified terms from the…

This paper summarizes a research program to express the organization of sensorimotor control by specifying physiological states and the conditions for transitions among them. By a slight change in standard notation, conditional dynamics…

We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…

Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…

A package of Maple 5.3 commands for doing calculations with anticommutative variables is presented.

Polynomial dynamical systems describing interacting particles in the plane are studied. A method replacing integration of a polynomial multi--particle dynamical system by finding polynomial solutions of a partial differential equations is…

Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…

In the spirit of "multi-culturalism", we use four kinds of computations: simulation, numeric, symbolic, and "conceptual" to explore some "games of pure chance" inspired by children board games like "Snakes and Ladders" (aka as "Chutes and…

We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…

In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…

Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…

Methods for the computation of invariants and symmetries of nonlinear evolution, wave, and lattice equations are presented. The algorithms are based on dimensional analysis, and can be implemented in any symbolic language, such as…