2 files changed, 86 insertions, 0 deletions
diff --git a/shared/lists.rkt b/shared/lists.rkt
index f8d96d0..8437fcb 100644
--- a/shared/lists.rkt
+++ b/shared/lists.rkt
@@ -6,6 +6,7 @@
          flatmap
          enumerate-interval
          enumerate-windows)
+
 (define (append list1 list2)
   (if (null? list1)
     list2
diff --git a/shared/symbolic-differentiation.rkt b/shared/symbolic-differentiation.rkt
new file mode 100644
index 0000000..d76a7d1
--- /dev/null
+++ b/shared/symbolic-differentiation.rkt
@@ -0,0 +1,85 @@
+#lang racket
+(provide make-deriv
+         variable?
+         same-variable?
+         =number?)
+         
+(define (variable? x) (symbol? x))
+(define (same-variable? x y) (and (variable? x) (variable? y) (eq? x y)))
+
+(define (=number? x num)
+  (and (number? x) (= x num)))
+(define (make-sum a1 a2)
+  (cond ((=number? a1 0) a2)
+        ((=number? a2 0) a1)
+        ((and (number? a1)
+              (number? a2)) (+ a1 a2))
+        (else (list '+ a1 a2))))
+(define (make-product m1 m2)
+  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
+        ((=number? m1 1) m2)
+        ((=number? m2 1) m1)
+        ((and (number? m1) (number? m2)) (* m1 m2))
+        (else (list '* m1 m2))))
+(define (make-exponent e p)
+  (cond ((=number? p 0) 1)
+        ((=number? p 1) e)
+        (else (list '** e p))))
+
+(define (sum? x)
+  (and (pair? x) (eq? (car x) '+)))
+(define (addend s) (cadr s))
+(define (augend s) 
+  (cond ((null? (cdddr s)) (caddr s))
+        (else (cons '+ (cddr s)))))
+
+(define (product? x)
+  (and (pair? x) (eq? (car x) '*)))
+(define (multiplier p)
+  (cadr p))
+(define (multiplicand p)
+  (cond ((null? (cdddr p)) 
+         (caddr p))
+        (else (cons '* (cddr p)))))
+
+(define (exponent? x)
+  (and (pair? x) (eq? (car x) '**)))
+(define (base expo)
+  (cadr expo))
+(define (exponent expo)
+  (caddr expo))
+
+
+(define (make-deriv
+          make-sum
+          sum?
+          addend
+          augend
+          make-product
+          product?
+          multiplier
+          multiplicand)
+  (define (deriv expr var)
+   (cond ((number? expr) 0)
+         ((variable? expr)
+          (if (same-variable? expr var) 1 0))
+         ((sum? expr)
+          (make-sum (deriv (addend expr) var)
+                    (deriv (augend expr) var)))
+         ((product? expr)
+          (make-sum
+             (make-product 
+               (multiplier expr)
+               (deriv (multiplicand expr) var))
+             (make-product 
+               (deriv (multiplier expr) var)
+               (multiplicand expr))))
+         ((exponent? expr)
+          (make-product
+            (deriv (base expr) var)
+            (make-product
+              (exponent expr)
+              (make-exponent (base expr) (- (exponent expr) 1)))))
+         (else
+           (error "unkown expression type -- DERIV" expr))))
+  deriv)