Great work Maik!
It's an impressive library - the fact that you can implement a general
purpose symbolic analysis technique like "extremata" in a dozen lines of
Clojure shows just how powerful this is.
On Monday, 23 September 2013 23:38:47 UTC+8, Maik Schünemann wrote:
>
> GSoC ends today and I can announce the 0.2.0 version of the expresso [1]
> library.
> It is build on top of core.logic and core.matrix and provides symbolic
> manipulation of algebraic expressions.
>
> What's there?
> 1. 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
> 2. useful manipulations for mathematical expressions: simplify,
> multiply-out, differentiate, ...
> 3. An equation solver which is capable of solving a single equation and
> multiple equations for unknowns.
> 4. An optimizer which transforms a mathematical expression to a
> semantically equivalent but performanter one
> 5. An expression compiler to compile an expression to an efficient clojure
> function
> 6. 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 [2].
>
> 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
> [2].
>
> 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}}
>
>
> 2. 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
>
> [1] https://github.com/clojure-numerics/expresso
> [2] https://github.com/mschuene/expresso-tutorial
>
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