;;;-*- Mode: LISP; Syntax: Common-Lisp; Base: 10; Package: COMMON-LISP-USER -*-

;;; $Id: solut1.lisp,v 1.1 1995/10/03 16:27:11 lyman Exp lyman $
;;; $Revision: 1.1 $

;;;; Overview
;;;
;;; Initial Author: Lyman Taylor ( lyman@cc.gatech.edu )
;;; For:    2360 Fall 95
;;; 
;;; Modification:
;;;             See RCS Log File.
;;;
;;; This file is a solution for assignment 1.  It contains the four prescribed 
;;;    functions and their associated helper functions.
;;; 
;;;  This file has 3 major sections after this Overview.
;;;
;;;           Section 1.   Questions 1-4
;;;
;;;           Section 2.   Misc. fcns.
;;;
;;;           Section 3.   Dribbled results. 
;;;
;;; 

;;;; Questions 1-4

;;; Question 1.
;;;

(defun era ( runs innings-pitched )
  "Calculate a ERA, earn run average, given runs given up and the number of 
   innings pitched.  WARNING: if latter is zero an error will result. "
   (* (runs-per-inning  runs innings-pitched )  9.0 ) )

(defun runs-per-inning ( runs innings )
 (/ runs innings ))


;;; Question 2
;;;

(defun circle-stuff ( radius )
 "Return a list of the circle's radius , area, and circumference given a radius."
 (list radius (circle-area radius ) (circle-circumference radius ) ) )

(defun circle-area ( radius )
  "Returns the area of a circle."
 (* pi (square radius )) )

(defun circle-circumference ( radius )
  "Returns the circumference of a circle. "
 (* 2  pi radius ) )


;;; Question 3
;;;

(defun hypotenuse ( side-1 side-2 )
 "Returns the length of the hypotenuse of a right triangle given the length of the
  two sides."
 (sqrt (sum-squares side-1 side-2 ) ) )

(defun sum-squares ( number-1  number-2  )
  "Return the sum of the squares of two nubmers."
  (+ (square number-1 ) (square number-2 )))



;;; Question 4
#| 
 The roots of the quadratic equation are found by:

                    ________
                    / 2
            -b +- \/ b  - 4ac
        x = _________________

                  2a
|#


(defun quadratic ( a b c )
 "Return a list of the quadratic equation's two roots given the coefficients a, 
  b, and c. "
 (list (pos-root a b c )
       (neg-root a b c ) ))

(defun pos-root ( a b c )
  (/ (pos-numerator  a b c )
     (my-denominator a   )))

(defun neg-root ( a b c )
  (/ (neg-numerator a b c )
     (my-denominator a )))

(defun my-denominator ( a ) 
  (*  2 a ) )


(defun pos-numerator ( a b c )
  ( + (- b )
      (discriminant a b c)))

(defun neg-numerator ( a b c)
( - (- b )
      (discriminant a b c)))
  

(defun discriminant ( a b c )
  (sqrt (- (square b )
           (* 4 a c ) )))



;;;; Misc. Fcns.

(defun square ( number )
  " Return the square of the given  number."
  (* number number ))


;;; Dribbled Results

#|  These results are actually cut and pasted out of the Lispworks listener...

CL-USER 2 > (era 1 9 )
1.0

CL-USER 3 > (era 9 1  )
81.0

CL-USER 8 > (circle-stuff 4 )
(4 50.26548245743669D0 25.132741228718345D0)

CL-USER 14 > (hypotenuse 3 4 )
5.0

CL-USER 17 > (quadratic 2 0 2 )
(#C(0.0 1.0) #C(0.0 -1.0))

CL-USER 18 > (quadratic 2 2 0 )
(0.0 -1.0)



|#


;;; EOF
;;;;;;;