SENAC .0

A Software Environment for Numeric and Algebraic Computation

Short Description
SENCORE: An interactive computer algebra host language for SENAC modules
SENPACK: Numerical Recipes, large sparse linear programming, the finite element method
SENGRAPH: A graphics library with PostScript output
NUMLINK: A fully automated symbolic numeric interface to the NAG Library
GRAFLINK: A symbolic graphic interface to the NAG Graphics Library
SENAC Documentation
Portable Code
SENAC Address

Short Description

SENAC stands for Software Environment for Numeric and Algebraic Computation.

SENAC is a modular software system for Scientists, applied mathematicians and engineers. It integrates numeric, symbolic and graphical features, it interfaces to existing libraries, and is portable.

SENCORE is a special purpose symbolic manipulation language which provides an interactive, easy to use software host within which the symbolic form of mathematical modelling problems can be easily represented and numeric and

SENCORE features

an easy to learn and use stand-alone natural user interface with extensive error checking
interactive input of symbolic and numeric expressions
symbolic expression output formatting
full featured floating point number formatting
probabilistic and deterministic algorithms for integer primality testing a factoring
list, matrix and sparse matrix data types
a wide range of matrix transformation functions
monomial and recursive polynomial representations
Zippel's probabilistic GCD and multinomial-factorisation
canonical rational simplification of SENAC expressions
user defined functions and programs for symbolic and numeric transformation
differentiation of expressions and undefined functions
symbolic integration by pattern matching or the Risch algorithm
translation of user defined functions into Fortran for SENAC calculation or external use
access to common blocks in Fortran code from SENAC
callbacks to SENAC from Fortran code for function evaluation
command timing and interruption
internal form of SENAC expressions
compiler for SENAC functions [Jan 1993]
array data types [Jan 1993]
a commentary feature to describe the progress of algorithms
optional interfaces to graphical and numeric subroutine libraries, online help for the host language and each interface included as a standard feature

Interfaces and Modules

In addition to the host module SENCORE, there are available with SENAC two optional modules and two optional interfaces: an interactive numeric library SENPACK and graphics library SENGRAPH, and the interfaces NUMLINK to the NAG Library of numeric subroutines and GRAFLINK to the NAG Graphics Library.

SENPACK

SENPACK consists of three main sections: basic numeri- cal algorithms, optimization, and solving partial differen- tial equation models using the finite element method.

Basic Numerical Algorithms

SENPACK includes functions for solving problems using tools from numerical analsis. These consist of an easy to use Senac adaptation of the widely used set of programs Numerical Recipes in Fortran by Willam H. Press, Brian P. Flannery, Saul A. Teukolsky and William T. Vetterling, published by Cambridge University Press and translated with permission. It includes about 170 functions covering the areas: solution of linear equations interpolation and extrapolation, integration of functions , evaluation of functions, special functions, random numbers, sorting, root finding and nonlinear sets of equations, minimization and maximization of functions, eigensystems, fourier, transform spectral methods, statistics, modelling of data, integration of ordinary, differential equations, two point boundary value problems, partial differential equations.

Optimization

This section includes a set of Senac functions for large scale linear real and integer program- ming with natural algebraic expression input for con- straints, non-linear integer programming, zero-one linear integer programming, simulated annealing integer program- ming, knapsack problem, assignment problem, global optimiza- tion, and portfolio analysis and investment prediction.

Finite Element Method

self-adjoint equations in one and two space dimensions for boundary value problems and eigen problems and the time dimension for initial boundary value problems. Eight element types and four mesh generation techniques are available: manual mesh input, structured mesh construction using grids, automatic quadrilateral mesh gen- eration through solutions to the Laplace equation, and automatic triangulation for regions which may contain sub- regions and holes. Paramatrized boundary descriptions and boundary conditions are available.

The basic numerical algorithms and optimization sec- tions of SENPACK do not require any other software than Sen- core. The finite element method section requres access to SENGRAPH, described below.

SENGRAPH

The graphics module is smoothly integrated into the Senac environment. SENGRAPH provides a bridge between Sen- core and PostScript As well as lowlevel PostScript functions like lineto and moveto, it provides elements of computa- tional geometry (such as triangulations, convex hull compu- tations, contouring of scattered data) and three dimensional graphics (views, clipping into a bounding box and hidden surface removal). Curve drawing features include functions for plotting data, curves, polygons, b-splines, Bezier curves, least squares approximations, polar curves, phase space plots, etc.

SENGRAPH requires SENCORE and a PostScript interpreter, but no other software.

NUMLINK

NUMLINK is a comprehensive interface between the symbolic host language SENCORE and the NAG Library of numeric subroutines. The advantage of using a Library routine is its efficiency, robustness and correctness. The disadvantgage is the time required to solve problems. Finding the routine, analysing the documentation, writing code including subprograms for function and derivative evaluation and formatting input and output are all and time consuming and give rise to errors.

NUMLINK retains the advantages and all but eliminates the coding problem by using interface routines to automatically perform all steps in the coding exercise which could possibly be automated.

NUMLINK features

Complex calls to subroutine library routines can be made in minutes rather than days without loss in functionality.
The scope and power of the NAG Library become available to users in a way that has not until now existed.
Input and output variables are classified into two types: those relating to the problem to be solved such as the name of an input function, endpoints of a function's domain and so on, and those relating to algorithm tuning or analysis which the user may not need to change frequently. These latter variables are placed in the environment and need never be looked at unless the user wishes. There is a significant reduction in the complexity of the subroutine call which, through NUMLINK, reflects the essence of the problem in a natural manner.
Input and output data are always valid SENAC data types and so may be manipulated interactively - in particular the output from one call becomes the input for another with no special formatting.

All the features of the NAG Library become accessible to the user through SENAC:

Complex arithmetic,
zeros of polynomials,
roots of non-linear equations,
summation of series,
quadrature,
fourier transforms,
special functions,
matrix inversion,,
simultaneous linear equations,
eigenvalue and eigenvectors,
determinants,
linear algebra operations,
orthogonalisation,
ordinary differential equations,
stiff ordinary differential equations,
integral equations,
partial differential equations,
interpolation,
curve and surface fitting,
polynomial zeros,
non-linear optimization,
linear programming,
basic statistics,
non-parametric statistics,
analysis of variance,
correlation,
random number generators,
contingency table analysis,
univariate estimation,
multivariate regression,
time series analysis,
operations research,
sorting real data.

GRAFLINK

GRAFLINK is an interface between SENCORE and the NAG Graphical Supplement. The same function call argument rationalizations employed with NUMLINK are applied to the plotting of functions. The user need only be concerned with the essence of a problem to obtain graphs. Implementation details and low level FORTRAN program writing tasks are performed by SENAC internally.

GRAFLINK features

Calls to plot routines are significantly simplified. The features of the NAG Graphical Library become available to the user interactively in the SENAC environment:
plotting of axes and grids
point plotting and straight line drawing
curve drawing
ode graphics
general and special function drawing
function plots with error bars
fitting of single and
multiple valued curves
Chebyshev and B-spline interpolation
contouring over grids or user defined functions
isometric and perspective surfaces
two and three dimensional vector field plotting
histograms
data presentation graphics
statistical graphics

The following plot output devices may be interfaced to SENAC through GRAFLINK:

GHOST80
GINO-F
CalComp
GKS
Lineprinter
HPGL
DEC Regis
Tektronix Plot 10 IGL
Adobe PostScript
DEC UIS
UNIRAS

SENAC Documentation

SENAC documentation comes in printed and on-line forms. All of the on-line documentation is included in the system, no matter what interface options are chosen by the user. The documentation for SENPACK and SENGRAPH is not on-line. The on-line help of each VMS implementation is structured in the form of a VMS help library and can be accessed from the command interpreter (DCL) as well as from SENAC. The Unix versions are accessed using the Unix function "more".

The SENAC printed manual set is as follows:

SENCORE Manual
SENPACK Manual
SENGRAPH Manual
NUMLINK Manual
GRAFLINK Manual

The GRAFLINK manual can in general be used independently of the corresponding NAG documentation. The NUMLINK Manual requires access to the NAG printed or On-line Information Supplement for variable interpretations where this is not fully defined in the Manual. There is also a document called the Wslink manual, for the NAG Workstation subset of the full NAG Library which can be used independenly of the NAG documentation. There are over 1300 symbolic, numeric and graphical functions in SENAC. Each function comes with an example program which is included in the printed documentation.

Portable code

Versions of SENAC and the interfaces to numeric and graphical libraries are written in Allegro CL or VAX LISP. SENAC may be ported to any system with a supported version of Common Lisp. Current implementations are listed below. Other are under development: Microsoft Windows (PCs), Unix workstations (DEC, HP, IBM, Sun, SGI), Convex, and Cray. For other implementations please contact the SENAC Address For further information in the UK/Europe:

University of London Computer Centre (ULCC)
20 Guilford Street
London WC1N 1DZ
FAX (071)242-1845
Tel (071)405-8400
e-mail: senac@ulcc.ac.uk

All other regions:

Associate Professor Kevin Broughan
Mathematical Software Project Director
Department of Mathematics and Statistics,
University of Waikato, Private Bag 3105
Hamilton 2001, New Zealand
Telephone: -64(7)856-2889x8330 or -64(7)856-6358
Fax: -64(7)838-4155
e-mail: senac@waikato.ac.nz

SENAC Home Page.

webmaster@can.nl