fixup

9 files changed, 356 insertions, 22 deletions

diff --git a/coding-exercises/2/10.rkt b/coding-exercises/2/10.rkt
index 20c70b0..ae68781 100644
--- a/coding-exercises/2/10.rkt
+++ b/coding-exercises/2/10.rkt
@@ -1,8 +1,5 @@
 #lang racket
-(require 
-  "7.rkt"
-  "8.rkt"
-  "9.rkt")
+(require "../../shared/intervals.rkt")
 
 (define (div-interval x y)
   (if (and (< 0 (lower-bound y)) (> 0 (upper-bound y)))
diff --git a/coding-exercises/2/11.rkt b/coding-exercises/2/11.rkt
new file mode 100644
index 0000000..d81d33a
--- /dev/null
+++ b/coding-exercises/2/11.rkt
@@ -0,0 +1,90 @@
+#lang racket
+(require "../../shared/intervals.rkt")
+
+;; Could be written to use less comparisons with nested cond, but this is more readable.
+(define (pos? x)
+  (> x 0))
+(define (neg? x)
+  (< x 0))
+(define (mul-interval x y)
+  (cond
+    ;; 1. all positive
+    ((and
+       (pos? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 2. one lower-bound neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (upper-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 3. one lower-bound neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 4. one interval neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 5. one interval neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 6. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 7. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 8. all neg
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 9. both crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval ((lambda (a b) (if (< a b) a b))
+                     (* (lower-bound x) (upper-bound y))
+                     (* (upper-bound x) (lower-bound y)))
+                    ((lambda (a b) (if (> a b) a b))
+                     (* (upper-bound x) (upper-bound y))
+                     (* (lower-bound x) (lower-bound y)))))))
+
+(mul-interval
+  (make-interval -3 3)
+  (make-interval -4 4))
diff --git a/coding-exercises/2/12.rkt b/coding-exercises/2/12.rkt
new file mode 100644
index 0000000..c977436
--- /dev/null
+++ b/coding-exercises/2/12.rkt
@@ -0,0 +1,29 @@
+#lang racket
+(require "../../shared/intervals.rkt")
+
+(define (make-center-width c w)
+  (make-interval (- c w) (+ c w)))
+
+(define (center i)
+  (/ (+ (lower-bound i) (upper-bound i)) 2))
+
+(define (make-center-percent c p)
+  (let ((toler (* c (/ p 100.0)))) 
+    ((lambda (a b) 
+       (if (> a b) 
+         (make-interval b a)
+         (make-interval a b)))
+     (- c toler) 
+     (+ c toler))))
+
+(define (percent i)
+  (abs (* 100 (/ (width i) (center i)))))
+
+(define (print)
+ (define t (make-center-width 10.0 6.1))
+ (define tp (make-center-percent -10.0 50.0))
+ (print-interval t)
+ (print-interval tp)
+ (println (percent t))
+ (println (percent tp)))
+(print)
diff --git a/coding-exercises/2/13.rkt b/coding-exercises/2/13.rkt
new file mode 100644
index 0000000..bc4cf09
--- /dev/null
+++ b/coding-exercises/2/13.rkt
@@ -0,0 +1,10 @@
+#lang racket
+(require "../../shared/intervals.rkt")
+
+(define (print)
+  (let ((i1 (make-center-percent 12.0 5.0))
+        (i2 (make-center-percent 12.0 5.0)))
+    (print-interval (mul-interval i1 i2))
+    (println (percent (mul-interval i1 i2)))))
+  
+(print)
diff --git a/coding-exercises/2/14.rkt b/coding-exercises/2/14.rkt
new file mode 100644
index 0000000..50d28fc
--- /dev/null
+++ b/coding-exercises/2/14.rkt
@@ -0,0 +1,66 @@
+#lang racket
+(require "../../shared/intervals.rkt")
+
+(define (print-interval-percent i)
+  (newline)
+  (display "interval{")
+  (display (center i))
+  (display ",")
+  (display (percent i))
+  (display "}")
+  (newline))
+
+(define (lem1 i1 i2)
+  (div-interval (mul-interval i1 i2)
+                (add-interval i1 i2)))
+
+(define (lem2 i1 i2)
+  (let ((one (make-center-percent 1.0 0)))
+    (div-interval 
+      one
+      (add-interval 
+        (div-interval one i1)
+        (div-interval one i2)))))
+
+;; adding scales the heighest percent to the new center
+(define (print-add)
+  (let ((i1 (make-center-percent 100.0 2.0))
+        (i2 (make-center-percent 200.0 3.0)))
+    (newline)
+    (println "*** add")
+    (print-interval-percent i1)
+    (print-interval-percent i2)
+    (print-interval-percent (add-interval i1 i1))
+    (print-interval-percent (add-interval i1 i2))
+    (print-interval-percent (sub-interval i1 i1))
+    (print-interval-percent (sub-interval i1 i2))))
+
+;; multiplication and addition of positive intervals
+;; adds percentage from both intervals
+(define (print-mul)
+  (let ((i1 (make-interval 2.0 8.0))
+        (i2 (make-interval 2.0 8.0)))
+    (newline)
+    (println "*** mul")
+    (print-interval-percent i1)
+    (print-interval-percent i2)
+    (print-interval-percent (div-interval i1 i1))
+    (print-interval-percent (div-interval i1 i2))
+    (print-interval-percent (mul-interval i1 i1))
+    (print-interval-percent (mul-interval i1 i2))))
+  
+;; There are at least some problems as I understand:
+;; 1. Repeated intervals in an equation are dependent on each other
+;; 2. Multiplicative identity is undefined and should not be uncertain
+(define (print-lem)
+  (let ((i1 (make-center-percent 100.0 2.0))
+        (i2 (make-center-percent 200.0 3.0)))
+    (newline)
+    (println "*** lem")
+    (print-interval-percent i1)
+    (print-interval-percent i2)
+    (print-interval-percent (lem1 i1 i2))
+    (print-interval-percent (lem2 i1 i2))))
+(print-add)
+(print-mul)
+(print-lem)
diff --git a/coding-exercises/2/7.rkt b/coding-exercises/2/7.rkt
index 13f28a6..462a58e 100644
--- a/coding-exercises/2/7.rkt
+++ b/coding-exercises/2/7.rkt
@@ -1,12 +1,4 @@
 #lang racket
-(provide
-  make-interval
-  upper-bound
-  lower-bound
-  add-interval
-  mul-interval
-  div-interval
-  print-interval)
 
 (define (add-interval x y)
   (make-interval (+ (lower-bound x) (lower-bound y))
diff --git a/coding-exercises/2/8.rkt b/coding-exercises/2/8.rkt
index 1a205fd..61ea92c 100644
--- a/coding-exercises/2/8.rkt
+++ b/coding-exercises/2/8.rkt
@@ -1,7 +1,5 @@
 #lang racket
-(provide
-  sub-interval)
-(require "7.rkt")
+(require "../../shared/intervals.rkt")
 
 (define (sub-interval x y)
   (make-interval (- (lower-bound x) (upper-bound y))
diff --git a/coding-exercises/2/9.rkt b/coding-exercises/2/9.rkt
index 0525802..e85b77d 100644
--- a/coding-exercises/2/9.rkt
+++ b/coding-exercises/2/9.rkt
@@ -1,14 +1,9 @@
 #lang racket
-(provide
-  width)
-(require 
-  "7.rkt"
-  "8.rkt"
-  "9.rkt")
+(require "../../shared/intervals.rkt")
 
 (define (width x)
   (/ (- (upper-bound x) (lower-bound x)) 2))
- 
+
 (define (print-sum)
   (newline)
   (println "*** (width SUM) == (SUM width) ***")
diff --git a/shared/intervals.rkt b/shared/intervals.rkt
new file mode 100644
index 0000000..270be51
--- /dev/null
+++ b/shared/intervals.rkt
@@ -0,0 +1,157 @@
+#lang racket
+(provide
+  width
+  make-center-width
+  center
+  make-center-percent
+  percent
+  pos?
+  neg?
+  mul-interval
+  div-interval
+  sub-interval
+  add-interval
+  make-interval
+  upper-bound
+  lower-bound
+  print-interval)
+(define (width x)
+  (/ (- (upper-bound x) (lower-bound x)) 2))
+(define (make-center-width c w)
+  (make-interval (- c w) (+ c w)))
+(define (center i)
+  (/ (+ (lower-bound i) (upper-bound i)) 2))
+(define (make-center-percent c p)
+  (let ((toler (* c (/ p 100.0)))) 
+    ((lambda (a b) 
+       (if (> a b) 
+         (make-interval b a)
+         (make-interval a b)))
+     (- c toler) 
+     (+ c toler))))
+(define (percent i)
+  (let ((w (width i))
+        (c (center i)))
+    ;; (newline) (print c)(println w)
+    ;; not defined: percent of interval centered at zero
+    (if
+      (<= c 0)
+      0
+      (abs (* 100 (/ w c))))))
+(define (pos? x)
+  (> x 0))
+(define (neg? x)
+  (< x 0))
+(define (mul-interval x y)
+  (cond
+    ;; 1. all positive
+    ((and
+       (pos? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 2. one lower-bound neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (lower-bound x) (upper-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 3. one lower-bound neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 4. one interval neg
+    ((and
+       (neg? (lower-bound x))
+       (pos? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 5. one interval neg
+    ((and
+       (pos? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (lower-bound x) (lower-bound y))))
+    ;; 6. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 7. one interval neg, one interval crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (upper-bound x) (upper-bound y))
+                    (* (upper-bound x) (lower-bound y))))
+    ;; 8. all neg
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (neg? (upper-bound x))
+       (neg? (upper-bound y)))
+     (make-interval (* (lower-bound x) (lower-bound y))
+                    (* (upper-bound x) (upper-bound y))))
+    ;; 9. both crossing zero
+    ((and
+       (neg? (lower-bound x))
+       (neg? (lower-bound y))
+       (pos? (upper-bound x))
+       (pos? (upper-bound y)))
+     (make-interval ((lambda (a b) (if (< a b) a b))
+                     (* (lower-bound x) (upper-bound y))
+                     (* (upper-bound x) (lower-bound y)))
+                    ((lambda (a b) (if (> a b) a b))
+                     (* (upper-bound x) (upper-bound y))
+                     (* (lower-bound x) (lower-bound y)))))
+    ;; 10. The case where one of the endpoints is neither negative or positive, 0
+    (else (mul-interval-min-max x y))))
+(define (mul-interval-min-max x y)
+  (let ((p1 (* (lower-bound x) (lower-bound y)))
+        (p2 (* (lower-bound x) (upper-bound y)))
+        (p3 (* (upper-bound x) (lower-bound y)))
+        (p4 (* (upper-bound x) (upper-bound y))))
+    (make-interval (min p1 p2 p3 p4)
+                   (max p1 p2 p3 p4))))
+(define (div-interval x y)
+  (if (and (< 0 (lower-bound y)) (> 0 (upper-bound y)))
+    (error "Division by interval spanning zero")
+    (mul-interval 
+      x
+      (make-interval 
+        (/ 1.0 (upper-bound y))
+        (/ 1.0 (lower-bound y))))))
+(define (sub-interval x y)
+  (make-interval (- (lower-bound x) (upper-bound y))
+                 (- (upper-bound x) (lower-bound y))))
+(define (add-interval x y)
+  (make-interval (+ (lower-bound x) (lower-bound y))
+                 (+ (upper-bound x) (upper-bound y))))
+(define (make-interval a b) (cons a b))
+(define (lower-bound x) (car x))
+(define (upper-bound x) (cdr x))
+(define (print-interval x)
+  (newline)
+  (display "interval{")
+  (display (lower-bound x))
+  (display ",")
+  (display (upper-bound x))
+  (display "}")
+  (newline))
+