Arjen Markus (22 november 2002) It must be the time of year, but I felt very mathematical this week. So I sat down and wrote a little script that does a mathematical job: it allows you to define polynomial functions and (truncated) power series. Obviously, this is just a quick version and a full-blown package should include such things as:

- Adding, multiplying polynomials (division with remainder)
- Differentiation, integration (the result being another polynomial function)
- Scaling
- Introspection and error estimates
- Numerous other fascinating operations

Nevertheless, if you have a need for other functions than the ones offered by expr, this may give you some idea. The proof of the pudding is usually in the eating - so the example includes the zeroth order Bessel function of the first kind, J0. It is my favourite :)

AM A more direct evaluation of Bessel functions can be found at: Bessel functions

# polynoms.tcl -- # # Package for handling polynoms and power series # (sample Workbench module) # # Notes: # This package is a quick hack to get started only # # Version information: # version 0.1: initial implementation, november 2002 package provide Polynoms 0.1 namespace eval ::polynoms { namespace export polynom powerseries # powerseries -- # Construct a procedure that implements a power series # and return its name # # Arguments: # name Name of the new procedure # nterms Number of terms # calcterm Procedure to calculate a term # # Result: # Name of procedure that will calculate the power series # proc powerseries {name nterms calcterm} { set terms {} for { set n 0 } { $n <= $nterms } { incr n } { lappend terms [$calcterm $n] } polynom $name $terms } # polynom -- # Construct a procedure that implements a polynom # and return its name # # Arguments: # name Name of the new procedure # terms Coefficients (from degree 0 to degree n) # # Result: # Name of procedure that will calculate the polygon # proc polynom {name terms} { set first [lindex $terms end] set rterms {} for { set n [expr {[llength $terms]-2}] } { $n >= 0 } { incr n -1 } { lappend rterms [lindex $terms $n] } interp alias {} $name {} [namespace current]::EvalPolynom \ $first $rterms return $name } # EvalPolynom -- # Calculate the value of a polynom # # Arguments: # rterms Coefficients from degree n to degree 0 # x Value of the argument # # Result: # Value of the polynom at x # proc EvalPolynom {first rterms x} { set value $first foreach term $rterms { set value [expr {$value*$x+$term}] } return $value } } ;# End of namespace # # Run the program # namespace import ::polynoms::* puts "Simple parabola" polynom parabola {0.0 0.0 1.0} for { set i 0 } { $i < 10 } { incr i } { puts [parabola $i] } puts "Exponential function" proc exp_terms {n} { set fac 1 for {set i 1} {$i <= $n} {incr i} { set fac [expr {$fac*$i}] } expr {1.0/$fac} } powerseries exp 10 exp_terms for { set i 0 } { $i < 10 } { incr i } { puts "[exp $i] [expr {exp($i)}]" } puts "Bessel function J0" proc J0_terms {n} { if { $n%2 == 1 } { return 0.0 } else { set fac 1 set sign [expr {$n%4==2?-1:1}] for {set i 1} {$i <= $n/2} {incr i} { set fac [expr {$fac*$i}] set sign [expr {$sign/4.0}] } expr {$sign/($fac*$fac)} } } powerseries J0 10 J0_terms for { set x 0.0 } { $x < 2.0 } { set x [expr {$x+0.2}] } { puts "$x [J0 $x]" }

AM (13 july 2004) A more mature package is on its way for Tcllib. See Evaluating polynomial functions for some numerical experiments.