✦ LIBER ✦

Symbolic computer vector analysis

✍ Scribed by David R. Stoutemyer

Publisher: Elsevier Science
Year: 1979
Tongue: English
Weight: 679 KB
Volume: 5
Category: Article
ISSN: 0898-1221
DOI: 10.1016/0898-1221(81)90133-4

No coin nor oath required. For personal study only.

✦ Synopsis

A MACSYMA program is described which performs symbolic vector algebra and vector calcuhrs. The program can combine and simplify symbolic expressions including dot products and cross products, together with the gradient, divergence, curl and Laplacian operators. The distribution of these operators over sums or products is under user control, as are various other expansions, including expansion into components in any specific orthogonal curvilinear co-ordinate system. There is also a capability for deriving the scalar or vector potential of a vector field. Examples include derivation of the partial differential equations describing fluid flow and magnetohydrodynamics, for 12 different classic orthogonal curvilinear co-ordinate systems.

📜 SIMILAR VOLUMES

Symbolic vector analysis in plasma physi

Symbolic vector analysis in plasma physics

✍ H. Qin; W.M. Tang; G. Rewoldt 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 1012 KB

Many problems in plasma physics involve substantial amounts of analytical vector calculation. The complexity usually originates from both the vector operations themselves and the underlying coordinate systems. A computer algebra package for symbolic vector analysis in general coordinate systems, Gen

Symbolic Reachability Computation for Fa

Symbolic Reachability Computation for Families of Linear Vector Fields

✍ Gerardo Lafferriere; George J. Pappas; Sergio Yovine 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 391 KB

The control paradigm of physical processes being supervised by digital programs has lead to the development of a theory of hybrid systems combining finite state automata with differential equations. One of the most important problems in the verification of hybrid systems is the reachability problem.

Computable symbolic dynamics

✍ Douglas Cenzer; S. Ali Dashti; Jonathan L. F. King 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 149 KB

## Abstract We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π^0^~1~ class __P__ is a subshift if and only if there exists a computable function __F__ mapping 2^ℕ^ to 2^ℕ^ such that __P__ is the set of itineraries of elements of 2

SYMBOLIC EQUATION PROCESSING UTILIZING V

SYMBOLIC EQUATION PROCESSING UTILIZING VECTOR/DYAD NOTATION

✍ A.A. Barhorst 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 228 KB

In previous work the author has presented a methodology for obtaining closed form equations of motion for general non-holonomic hybrid parameter multiple body systems (HPMBS). It is well known that generating closed form symbolic equations of motion for HPMBS of few degrees of freedom rapidly degene

Rigorous Error Analysis of Numerical Alg

Rigorous Error Analysis of Numerical Algorithms via Symbolic Computations

✍ MARIAN MROZEC 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 646 KB

We present a symbolic technique of error analysis of numerical algorithms, which acts as a preprocessor to the actual numerical computation. The technique provides rigorous, a priori bounds which are universal for inputs in a prescribed domain. The method is an alternative to interval arithmetic in

Symbolic computation with fermions

✍ D.I. Hughes 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 368 KB

A set of REDUCE routines for manipulating operators which anticommute amongst themselves is described. These routines have applications in theories such as supergravity where anticommuting operators are used to represent ferminns. The Dirae bracket of the supersymmetry constraints arising in a quant