Mailing-List: contact issues-help@commons.apache.org; run by ezmlm
Precedence: bulk
Reply-To: issues@commons.apache.org
Message-ID: <897348554.1237423670646.JavaMail.jira@brutus>
Date: Wed, 18 Mar 2009 17:47:50 -0700 (PDT)
From: =?utf-8?Q?Bernhard_Gr=C3=BCnewaldt_=28JIRA=29?= <jira@apache.org>
To: issues@commons.apache.org
Subject: [jira] Commented: (MATH-250) Solver for rational and other
 equations
In-Reply-To: <521929053.1237366190412.JavaMail.jira@brutus>
MIME-Version: 1.0
Content-Type: text/plain; charset=utf-8
Content-Transfer-Encoding: quoted-printable


    [ https://issues.apache.org/jira/browse/MATH-250?page=3Dcom.atlassian.j=
ira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=3D126832=
60#action_12683260 ]=20

Bernhard Gr=C3=BCnewaldt commented on MATH-250:
------------------------------------------

Here is a short summary what my approach is:

https://www.gruenewaldt.net/2009/03/using-maxima-to-derivate-rational-funct=
ions-and-solve-equations/

I want to do the same thing mentioned in the blog entry with commons math.


> Solver for rational and other equations
> ---------------------------------------
>
>                 Key: MATH-250
>                 URL: https://issues.apache.org/jira/browse/MATH-250
>             Project: Commons Math
>          Issue Type: Improvement
>    Affects Versions: 2.0
>            Reporter: Bernhard Gr=C3=BCnewaldt
>            Priority: Minor
>             Fix For: 2.0
>
>
> In addition to the existing PolynomialFunction class a RationalFunction c=
lass would be a good idea.
> http://en.wikipedia.org/wiki/Rational_function
> For package:
> http://commons.apache.org/math/userguide/analysis.html
> The goal should be to calculate derivates of functions like:
> f(x) =3D [ x + 2*x^3 ] / [ x -1]
> or=20
> f(x) =3D [ e^x + 2*x ] / [ cos(x) ]
> Therefore it would be best to have classes for all the inner equations li=
ke "e", "sin,cos,tan ...", "sqrt", a.s.o
> These inner equations would then be put together to an outer equation.=20
> This outer equation can then be derived using the "chain rule", "product =
rule" and all other rules for getting the derivative.
> One of this inner classes is the existing PolynomialFunction class from t=
he analysis package.
> For easy rational functions the outer equation is of the form:
> f(x) =3D PolynomialFunction / PolynomialFunction
> Now just use the rule to derive it:
> f(x) =3D g(x) / h(x)   =3D>  f'(x) =3D [h(x) * g'(x) - g(x) * h'(x) ] / [=
 h(x) ]^2
> Here we can use the inner derivate of the PolynomialFunction by calling P=
olynomialFunction.derivative()
> That's the idea, now the topics that have to be discussed:
> 1. We should have a parser that can parse the "standard mathematical nota=
tion" into a tree of function classes.
>     http://en.wikipedia.org/wiki/Mathematical_notation
> 2. A class for every type of function should be implemented with an inter=
face that has the common methods like:
>     add(Object o)
>     subtract(Object o)
>     multiply(Object o)
>     divide(Object o)
>     derivative(Object o)
>     a.s.o
> 3. We need to implement Excptions that are thrown for sqrt(-1) a.s.o
> 4. We need a mother class that implements all the complex derivation rule=
s like:
>     http://en.wikipedia.org/wiki/Chain_rule
>     http://en.wikipedia.org/wiki/Product_rule
>     a.s.o.
>     the sub classes the PolynomialFunction or the RationalFunction just i=
mplement their derivation rules, but the mother class implements the comple=
x rules to derivate a complex structure of any type of equation by using th=
e inner derivation rules and the complex chain rules a.s.o

--=20
This message is automatically generated by JIRA.
-
You can reply to this email to add a comment to the issue online.