TUsolveCubic TCL UTILITIES USER MANUAL TUsolveCubic
SYNOPSIS
Solve a cubic equation of the form: Ax3 + Bx2 + Cx + D = 0
PACKAGE
TCLUTILS
NAME
TUsolveCubic
USAGE
set rV  [TUsolveCubic  A B C D]
INPUT DEFINITIONS
A - The coefficient of the cubic term in the equation.
B - The coefficient of the quadratic term in the equation.
C - The coefficient of the linear term in the equation.
D - The constant term in the equation.
RETURN DEFINITION
rV - Solutions of the equation as a list. If the list length is 3 there are three real solutions. If the list length is 5 then there is one real solution and 2 imaginary solutions. Imaginary solutions are stored as the two real components followed by the two imaginary components. The single real solution is always the first in the list.
DESCRIPTION
TUsolveCubic solves for the three roots of the equation: 
            Ax3 + Bx2 + Cx + D = 0
The roots are returned through the list variable rV. When the roots are real rV has the form: 
            set rV [list R1 R2 R3]
with R1 being the minumum root value and R3 the maximum root value. When there are imaginary roots rV has the form: 
            set rV [list R1 R2 R3 I2 I3]
ERRORS
None Generated
C BACKING
No
EXAMPLE(S) 
set A 5.0
set B 2.0
set C 10.0
set D -1.0
set rV [TUsolveCubic $A $B $C $D]
if { [llength $rV] == 3 } {
   puts stderr "REAL SOLUTIONS"
   puts stderr "  S1 = [lindex $rV 0]"
   puts stderr "  S2 = [lindex $rV 1]"
   puts stderr "  S3 = [lindex $rV 2]"
} else {
   puts stderr "REAL SOLUTION"
   puts stderr "  S1 = [lindex $rV 0]"
   puts stderr "IMAGINARY SOLUTIONS"
   if { [lindex $rV 3] < 0.0 } { set SgN - } else { set SgN + }
   puts stderr "  S2 = [lindex $rV 1] $SgN i[expr abs([lindex $rV 3])]"
   if { [lindex $rV 4] < 0.0 } { set SgN - } else { set SgN + }
   puts stderr "  S3 = [lindex $rV 2] $SgN i[expr abs([lindex $rV 4])]"
}

> REAL SOLUTION
>   S1 = 0.0976284722457
> IMAGINARY SOLUTIONS
>   S2 = -0.248814236123 + i1.40949430059
>   S3 = -0.248814236123 - i1.40949430059
Setting C to -10.0 gives the result: 

> REAL SOLUTIONS
>   S1 = -1.58336053902
>   S2 = -0.0985364793555
>   S3 = 1.28189701838
Apr 17, 2003