# Finished GSoC project Expresso

GSoC ends today and I can announce the 0.2.0 version of the expresso library. It is build on top of core.logic and core.matrix and provides symbolic manipulation of algebraic expressions.

What's there?

- An api/dsl for manipulation of algebraic expressions which doesn't get in your way. Expresso's expressions are just clojure s-expressions and can be manipulated with rich set of clojure sequence functions
- useful manipulations for mathematical expressions: simplify, multiply-out, differentiate, …
- An equation solver which is capable of solving a single equation and multiple equations for unknowns.
- An optimizer which transforms a mathematical expression to a semantically equivalent but performanter one
- An expression compiler to compile an expression to an efficient clojure function
- A semantic rule based translator on top of which many of expresso's features are implemented

The code is fully documented and I wrote a tutorial and showcase of expresso, the expresso-tutorial.

GSoC has been a really fun and valuable time for me. I learned a lot. Of course I will continue developing expresso! Expresso and core.matrix are the first steps in the direction of a full computer algebra system for clojure. I hope that it will help clojure to be an attractive choice for scientific computing projects in the future.

Showcase:
Here are two examples of expresso's facility to manipulate mathematical expressions.
They can be found and are explained in the expresso-tutorial ^{1}.

- solving word problems:

(solve 'blue (ex (= pencils (+ green white blue red))) (ex (= (/ pencils 10) green)) (ex (= (/ pencils 2) white)) (ex (= (/ pencils 4) blue)) (ex (= red 45))) ;=> #{{blue 75N}}

- Analyzing roots and extremata of functions. This code shows how easy one can implement tasks involving symbolic manipulation with expresso:

(defn roots "returns the set of roots of the expression in regard to var" [var expr] (solve var (ex (= ~expr 0)))) (defn extremata "gets the extrema of the expression in regard to var. Returns a map with the keys :maxima and :minima" [var expr] (let [d1 (differentiate [var] expr) d2 (differentiate [var] d1) candidates (roots var d1)] (if (seq candidates) (let [extremata (->> candidates (map (fn [candidate] [candidate (evaluate d2 {var candidate})])) (remove #(== 0 (second %))) (group-by #(< 0 (second %))))] {:maxima (map first (get extremata false)) :minima (map first (get extremata true))})))) (defn analyse-function "returns a map with the :roots, the :maxima and the :minima of the expression in regard to var" [var expr] (assoc (extremata var expr) :roots (roots var expr))) (analyse-function 'x (ex (- (** x 4) (** x 2)))) ;=> {:roots #{0 -1 1}, ;; :maxima (0), ;; :minima (0.7071067811865476 -0.7071067811865476)}

Ideas/feedbacks etc are greatly appreciated! Enjoy, Maik

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