next up previous contents index
Next: 1.2 Installation Up: 1. Description and installation Previous: 1. Description and installation   Contents   Index

Subsections

1.1 Introduction

The program funct can be used to study real or complex functions $f(x)$ of one real variable $x$, and use them in geometry. It accepts commands given interactively by the user or programs that are sequences of commands. It can produce graphics on a X11 window, and files in various graphic formats.

funct uses the command interpreter library interpcom (see 1.2). It may be useful to read at least a part of the documentation of interpcom before using funct, especially chapters 4 ("Programming with the command interpreter") and 11 ("List of available commands"). Functions, or geometric objects, like points, lines, polygons, are created by appropriate commands and are given names which are used to refer to them in subsequent commands. funct can be used interactively and run programs.

funct can be built with several graphic libraries, in 3 ways :

-
with the libplot library, which is a part of GNU-plotutils. This is the simplest and preferred way. It provides X11, Postscript, PNG, GIF and FIG formats.

-
with the allegro library for X11, and g2, gd forPNG and Postscript graphics.

-
with the ggi library for X11, and g2, gd for PNG and Postscript graphics.




1.1.1 Functions

Functions are defined by a finite number of $x$ and the corresponding values of $f(x)$. We do not assume that these $x$ are equally spaced, but this case is also considered, since it simplifies sometimes the definition of functions or their computation. We assume that the functions are continuous, linear between two successive $x$ where they are defined, and constant before the first $x$ and after the last one. However, for Fourier or Bessel transforms we assume that the functions vanish after the last $x$ and before the first.

The program is able to make operations (such as sum, products, composition, derivation, integration, convolution) on functions which are not necessary defined on the same $x$. For example if we want to compute the sum of $f_1(x)$ and $f_2(x)$ we will define a new function $g(x)$ (with a well defined x-range) and the sum of the two first functions will be computed exactly at the points of the x-range of $g$ and stored in this function.

Two kinds of tranforms are implemented in funct : Fourier transforms and Bessel transforms. There are two kinds of Fourier tranforms : the FFT transform, and the precise Fourier transform (cf. 3.3.1). Here also we don't assume that the x-ranges of a function and of its transform are related.

The expression evaluator accepts in funct 81 numerical functions. Those who are not in the standard math library come from the cephes package (see 1.2). These numerical functions can of course be used to define or modify the functions in funct.




1.1.2 Graphics

It is possible to draw graphics with funct, on a X11 window or in files, in various formats. In particular there is a command to plot functions.

There are two ways of drawing graphics : the raw way, where the coordinates are given in pixels, or it is possible to use frames, where the user defines the coordinates (i.e the minimal and maximal values for x,y).




1.1.3 Geometry

It is possible to define, use and draw several geometrical objects : points, lines, circles, polygons. Polygons are sequences of points. It is possible to associate a polygon to a pair of functions, so it is possible to define parametric curves. The converse is also possible and can be used to define and study geometric locus.


next up previous contents index
Next: 1.2 Installation Up: 1. Description and installation Previous: 1. Description and installation   Contents   Index
jmdr 2003-10-01