[Arjen Markus] (5 march 2009) Yesterday I spoke with [Kevin Kenny] and [Cameron Laird] about the possibilities
of developing an application a la XPPAUT ([http://www.math.pitt.edu/~bard/xpp/xpp.html]). The idea is to
use such packages as [Tclode] and [Plotchart] to solve systems of ordinary differential equations and plot 
the results.

These equations should be definable in a very similar way as XPPAUT allows. The user-interface should be
much more modern though.

Anyway, here is a very first (or should I say zeroth) shot at something like that. I have called it 
"Bernoulli" in honour of those great 17th-century mathematicians, Johan, Jacob and Daniel. (it is also 
a bit of nostalgia for me, as some 15-20 years ago I developed a similar program, also called bernoulli).

All it does now is present the graph of a function you define as an expression ...

----
======
# bernoulli.tcl --
#     Integrate systems of ordinary differential equations
#
#package require Tcl 8.5
package require Tk
package require Plotchart


# plotf --
#     Convenience procedure to plot a function of one variable
#
# Arguments:
#     range       Range over which to plot the function (x-axis)
#     expression  Expression by which the function is defined
#                 (independent variable: t)
#
proc plotf {range expression} {

    # Very simple for now: no parameters

    foreach {tmin tmax} $range {break}
    set nosteps 100
    set tstep [expr {($tmax-$tmin)/double($nosteps)}]

    if { ![winfo exists .c] } {
        pack [canvas .c]
    } else {
        .c delete all
    }

    set tvalues {}
    set xvalues {}
    set xmin    {}
    set xmax    {}

    for {set i 0} {$i < $nosteps+1} {incr i} {
        set t [expr {$tmin + $i*$tstep}]
        set x [expr $expression]
        lappend tvalues $t
        lappend xvalues $x

        if { $xmin == {} || $x < $xmin } {
            set xmin $x
        }
        if { $xmax == {} || $x > $xmax } {
            set xmax $x
        }
    }

    set tscale [::Plotchart::determineScale $tmin $tmax]
    set xscale [::Plotchart::determineScale $xmin $xmax]

    set p [::Plotchart::createXYPlot .c $tscale $xscale]

    foreach t $tvalues x $xvalues {
        $p plot function $t $x
    }
}

# main --
#     Test the stuff
#
plotf {0 10} {exp(-$t)*cos(2.0*$t)}
after 3000 {
    plotf {0.0001 100} {sin($t)/$t} ;# Avoid t=0 of course
}
======
----
!!!!!!
%| [Category Mathematics] |%
!!!!!!