Roots of a function: Difference between revisions

=={{header|Tcl}}==

This simple brute force iteration marks all results, with a leading "~", as approximate.

<lang Tcl>

proc froots {lambda {start -3} {end 3} {step 0.0001}} {

set res {}

set lastsign [sgn [apply $lambda $start]]

for {set x $start} {$x <= $end} {set x [expr {$x + $step}]} {

set sign [sgn [apply $lambda $x]]

if {$sign ne $lastsign} {lappend res [format ~%.11f $x]}

set lastsign $sign

}

return $res

}

proc sgn x {expr {($x>0) - ($x<0)}}

froots {x {expr {$x**3 - 3*$x**2 + 2*$x}}}

</lang>

Result and timing:

<pre/Tcl $ time ./froots.tcl

~0.00000000000 ~1.00000000000 ~2.00000000000

real 0m0.368s

user 0m0.062s

sys 0m0.030s</pre>