Arjen Markus At the third European Tcl/Tk meeting I presented a "mathematical workbench". This page shows a small example of this work. The idea is described in the abstract:
A handheld calculator is a great way to do all kinds of ad hoc calculations. You do not write a C or Fortran program with hard-coded numbers to add them for balancing your books. In a similar way doing mathematics - for instance solve some geometrical problem - requires a handheld calculator suitable for that type of calculations. The essential ingredients are an interactive program that interprets dedicated commands, and a few conventions to make its use more or less uniform. This paper describes the application of Tkcon and such a set of conventions to provide the interface. It illustrates the concepts with three different mathematical tools: complex numbers, ordinary differential equations and (statistical) optimisation.
The script below contains a few commands that illustrate the idea compactly:
If you run the script from within Tkcon or a similar shell, you can experiment with it.
(Note: the full workbench contains much more convenient commands)
# functions.tcl -- # # Package for analysing real functions # (sample Workbench module) # # Notes: # This package provides basic analysis functionality for real # functions of one variable. # # Version information: # version 0.1: initial implementation, july 2002
package provide Functions 0.1
namespace eval ::Workbench {
variable nextID 0
# uniqueID -- # Create a unique ID (private) # # Arguments: # expression Expression using "x" as independent variable # evaluating to the function value # # Result: # Name of a new command implementing the function # # Side effect: # Create a new command that takes one argument, x, and # returns the function value # proc uniqueID {typename} {
variable nextID
incr nextID
return "${typename}##$nextID"} } ;# End of namespace
namespace eval ::Functions {
namespace export func deriv
# func -- # Create a new function # # Arguments: # expression Expression using "x" as independent variable # evaluating to the function value # # Result: # Name of a new command implementing the function # # Side effect: # Create a new command that takes one argument, x, and # returns the function value # proc func {expression} {
set name [::Workbench::uniqueID "X-FUNCTION"]
interp alias {} $name {} [namespace current]::xfunc_impl $expression
return $name}
# xfunc_impl -- # Implementation of an "x function" # # Arguments: # expression Expression using "x" (hidden via interp alias) # x Independent variable # # Result: # Function value # proc xfunc_impl {expression x} {
expr $expression
}
# deriv -- # Create a new function that evaluates to the derivative of the given # function # # Arguments: # funcname Name (!) of the function # step Step for the numerical derivation # # Result: # Name of a new command implementing the function's derivative # # Side effect: # Create a new command that takes one argument, x, and # returns the original function's derivative # proc deriv {funcname {step 0.01} } {
upvar $funcname fname
set name [::Workbench::uniqueID "X-DERIVATIVE"]
set expression [lindex [interp alias {} $fname] 1]
interp alias {} $name {} [namespace current]::xderiv_impl $expression $step
return $name}
# xderiv_impl -- # Implementation of the derivative of an "x function" # # Arguments: # expression Expression using "x" (hidden via interp alias) # step Step size for numerical derivation # xv Independent variable # Result: # Value of derivative # proc xderiv_impl {expression step xv} {
set x [expr {$xv-$step}]
set fx1 [expr $expression]
set x [expr {$xv+$step}]
set fx2 [expr $expression]
expr {($fx2-$fx1)/(2.0*$step)}}
} ;# End of namespace
# # Import the functions procedures # namespace import ::Functions::*
# # Simple demo # if { file tail [info script] == [file tail $::argv0 } {
puts "Simply a parabola: y = x^2"
set f [func {$x*$x}]
set df [deriv f]
set x 0.0
while { $x < 10.1 } {
puts "[$f $x] [$df $x]"
set x [expr {$x+1.0}]
}
puts "A more complex function"
set f [func {sin($x)*$x}]
set df [deriv f]
set x 0.0
while { $x < 10.1 } {
puts "[$f $x] [$df $x]"
set x [expr {$x+0.1}]
}}