; This demonstrates solving a system of nonlinear equations,
; and initializing the iterative solver.
; The equations are from a geometrical problems involving ladders.

; Problem: You have two ladders, one 35 feet long, the other 45 feet
; long.  You need to arrange them in an alley between two skyscrapers
; so that they cross 10 feet above the ground.  How wide should the
; alley be?

; Let:
;    x = width of the alley
;    a = height of the 45-foot ladder
;    b = height of the 35-foot ladder
;    P = point on ground below where ladders cross
;    y = distance along the ground between P and 35-foot ladder
;    z = distance along the ground between P and 45-foot ladder

{ These are the equations.}
 x^2 + a^2 = 45^2
 x^2 + b^2 = 35^2
 y / 10 = x / b
 z / 10 = x / a
 y + z = x

{ These are the initializations.}
 x := 20
 y := 20
 a := 20
 b := 20
 z := 20