incanter.symbolic — incanter/incanter-core 1.9.3

A library for performing symbolic math, a port from SICP (http://mitpress.mit.edu/sicp/).

all-fn-list clj

chain-list clj

deriv clj/s macro

(deriv exp v)

(deriv exp v degree)

Macro for symbolic differentiation. with 2 args, takes 1st degree deriv. with 3, takes arbitrary degrees. contains all deriv rules for basic funcs.

Examples:

(use '(incanter core symbolic))

(deriv (+ x 3) x) ; => 1 (deriv (* x y) x) ; => y (deriv (* (* x y) (+ x 3)) x) ; => (+ (* (+ x 3) y) (* x y)) (deriv (* (* x y) (+ x 3)) y) ; => (* (+ x 3) x)

(deriv (* x y (+ x 3)) x) ; => (+ (* y (+ x 3)) (* y x)) (deriv (* x y (+ x 3)) y) ; => (* (+ x 3) x)

(deriv (sin x) x) ; => (cos x) (deriv (cos x) x) ; => (* -1 (sin x))

(deriv (sin (* x y)) y) ; => (* x (cos (* x y)))

(deriv (pow x 3) x) ; => (* 3 (pow x 2)) (deriv (** x 3) x) ; => (* 3 (pow x 2))

(deriv (pow x 3) x 2) ; => (* 3 (* 2 x))

(deriv (* x y (+ x 3)) x 2) ; => (+ y y) (deriv (* x y (+ x 3)) x 3) ; => 0

(deriv (+ (* 3 x) (* 8 x)) x) ; => 11

;; NOT WORKING YET

(deriv (/ 1 x) x) ; => (* (deriv* (* (x)) x) (* -1 (pow (* (x)) -2))) ^-- need to fix

deriv* clj

(deriv* exp v)

(deriv* exp vr degree)

Main sub-function for differentiation. with 2 args, takes 1st degree deriv. with 3, takes arbitrary degrees. contains all deriv rules for basic funcs.

Examples:

(use '(incanter core symbolic))

(deriv* '(+ x 3) 'x) (deriv* '(* x y) 'x) (deriv* '(* (* x y) '(+ x 3)) x) (deriv* '(* (* x y) (+ x 3)) 'y)

(deriv* '(* x y (+ x 3)) 'x) (deriv* '(* x y (+ x 3)) 'y)

(deriv* '(* x y (+ x 3)) 'x 2) (deriv* '(* x y (+ x 3)) 'x 3)

deriv-fn clj/s macro

(deriv-fn [& args] expr v)

(deriv-fn [& args] expr v degree)

Examples: (use '(incanter core symbolic))

(deriv-fn [x y] (+ (* x y) x) x)

((deriv-fn [x y] (+ (* x y) x) x) 5 9)

(use 'incanter.charts) (doto (function-plot sin -5 5) (add-function (deriv-fn [x] (sin x) x) -5 5) (add-function (deriv-fn [x] (sin x) x 2) -5 5) view)

(let [f (fn [x] (pow x 2)) df (deriv-fn [x] (pow x 2) x)] (doto (function-plot f -5 5) (add-function df -5 5) view))

(let [f (fn [x] (pow x 3)) df (deriv-fn [x] (pow x 3) x)] (doto (function-plot f -5 5) (add-function df -5 5) view))

;; NOT WORKING YET

(let [f (fn [x] (/ 1 x )) df (deriv-fn [x] (/ 1 x) x)] (doto (function-plot f 0.5 5) (add-function df 0.5 5) view))

deriv-fn* clj

(deriv-fn* [& args] expr v)

(deriv-fn* [& args] expr v degree)

Examples: (use '(incanter core symbolic))

(deriv-fn* '[x y] '(+ (* x y) x) 'x)

((deriv-fn* '[x y] '(+ (* x y) x) 'x) 5 9)

fn-list clj