General Purpose Systems

ALJABR

Contents

• Short Description

• Availability

• Long Description

Short Description

Availability

Apple Macintosh:

all platforms but 8MB RAM recommended.

Silicon Graphics:

Indigo, Personal IRIS and 4D Series.

Sun:

Sun4 and SparcStations.

ALJABR can be ordered at

Fort Pond Research
15 Fort Pond Road
Acton, Massachusetts 01720
E-mail aljabr@fpr.com
Phone 508-263-9692

For full product and pricing information contact Fort Pond Research.

Long Description

General Description

ALJABR users can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, and manipulate matrices and tensors. ALJABR also offers a high level programming language permitting the user to write his own functions or packages for transforming symbolic expressions. ALJABR's data base of symbol properties enable it to handle exceptional cases correctly and adds to the user's programming power.

Features

Arithmetic

Exact arbitrary length integers, rationals, arbitrary-precision floating point, CPU compatible floating point, exact algebraic arithmetic, complex numbers, relational and logical operators.

Algebra

Factor, expand and simplify multivariate expressions, solve systems of algebraic real and transcendental equations, compute with trigonometric and other elementary functions, algebraic integers, factorials, binomials, Bernoulli, Euler, and Fibonacci numbers, modular arithmetic, Bernoulli polynomials, random numbers, GCD, Jacobi symbols, factors and sum of divisors, totient function, definite summation using Gosper algorithm.

Graphics

Basic 2D graphics including x-y plots, polar plots, contour plots, and parametric plots.

Calculus

Limits, including directional limits, differentiation, definite and indefinite integration, definite integration includes existence analysis, principal value integrals, Romberg numerical integration, ordinary differential equations, initial and boundary values, Laplace and inverse Laplace transforms, Taylor, Laurent, Poisson, and power series expansions, asymptotic expansions and Pade approximants.

Matrix, Vector, and Tensor Calculus

matrix addition, multiplication, exponentiation, scalar multiplication, generalized inverses, minors, adjoint, rank, transpose, determinant, permanent, eigenvectors, eigenvalues, triangularization, row or column extraction, coefficient matrices, characteristic polynomials, orthogonalization,gradient, divergence, curl, Laplacian, coordinate transforms, Christoffel symbols, Einstein, Ricci, Riemann, Euler-Lagrange, d'Alembertian and Wehl tensors, Kronecker delta function.

List Handling

array to list conversion, joining lists, sublist extraction, list arithmetic, sorting, membership, apply mathematical functions to list elements.

Simplification

Pinpoint user control of expression simplification; simplification of rational and nonrational expressions, radicals, logs, exponentials and trigonometric functions.

Conversions

trigonometric to exponential, inverse trigonometric to logarithmic, square-free form, Horner form polynomials, continued fractions.

Internal Representations

General, rational canonical form, Taylor and Poisson series.

Symbols Database

Property and relations specification querying for mathematical and non mathematical facts. User defined CONTEXTS. ALJABR database includes some deductive skills. For example, if A>B and B>C, then the database concludes A>C.

Expression Control

expression part selection and substitution, minimum, maximum, absolute value, extraction of denominator or numerator, extraction by degree, polynomial quotient and remainder, GCD, resultant, polynomial discriminant, factoring.

Pattern Matching

testing for syntactic and semantic patterns, replacement/simplification rule definition and application.

Functions, Macros, Packages

recursive and mutually recursive function definitions, lambda expressions, function mapping on expression parts, arrays of functions, user macro definition and expansion.

Language

Blocks, compound statements, Conditionals IF..THEN..ELSE, Iterative DO constructs (including THRU, WHILE, FOR, UNLESS) Goto, local and nonlocal return.

Debugging

error condition handling, execution tracing with print level control, user interrupts and break points, variable binding tracing.

Input/Output

Interactive command entry, batched ALJABR commands, lisp source and object files. session transcripts (commands and evaluated results), saved user environments and selected user command sets optimized FORTRAN source, TEX and ASCII data in user-defined formats.

General Purpose Systems

Last updated: November 15, 1994