The program funct can be used to study real or complex
functions
of one real variable
, 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 :
Functions are defined by a finite number of
and the corresponding values of
. We do not
assume that these
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
where they
are defined, and constant before the first
and after the last
one.
However, for Fourier or Bessel transforms we assume that the functions
vanish after the last
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 . For example if
we want to compute the sum of
and
we will define a new
function
(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
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.
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).
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.