[R] general inverse solver?

[Erich Neuwirth]

My main problem is that yacas can only factorize polynomials in one  
variable.
Any CAS which is not able to factor a^2 - b^2 into (a+b)*(a-B)
for me is less than satisfactory.



On Feb 10, 2009, at 1:51 PM, Gabor Grothendieck wrote:

> Yacas was completely rewritten in java (Ryacas interfaces to the
> C version) since the Ryacas project started so I would not exactly
> characterize yacas as dead.   The work that is going on in yacas
> may not have high visibility but that does not mean there is none.
>
> Also while Maxima is more sophisticated in terms of algorithms,
> yacas is actually more sophisticated from the viewpoint of its
> language  which borrows ideas from both imperative and prolog  
> programming
> and its interfaces are more sophisticated (it is one of the few CAS  
> systems
> that developed an OpenMath interface) and its socket server is
> used by the Ryacas interface.  yacas can also translate math  
> expressions
> to TeX and do exact arithmetic.
>
> Also to put this in the correct context, yacas does seem capable of
> answering the majority of questions that are posed on r-help that need
> a CAS in the answer. From a practical viewpoint it does seem to have
> the facilities that are most often needed.   The Ryacas vignette has
> a survey of some of its algebra capabilities.
>
> That being said, without taking away from yacas there is work going  
> on to
> interface R to a second CAS.
>
> On Tue, Feb 10, 2009 at 2:33 AM, Hans W. Borchers
> <hwborchers at googlemail.com> wrote:
>>
>> I know that Ryacas is promoted here whenever requests about  
>> symbolic algebra
>> or calculus appear on the R-help list. But to say the truth, Yacas  
>> itself is
>> a very very limited Computer Algebra System and looking onto its  
>> home page
>> it appears the development will stop or has stopped anyway.
>>
>> It would be fair to clearly state that there is no R package to solve
>> somewhat more involved symbolic mathematical problems. One could  
>> then point
>> the requestor to one of the open source Computer Algebra Systems   
>> (CAS) such
>> as Maxima or Axiom.
>>
>> Interestingly, the free Math Toolbox Euler by Grossmann has  
>> integrated
>> Maxima into its numerical environment in a way that is really  
>> useful for
>> numerical and symbolic computations. I could imagine that in a  
>> similar way
>> Maxima can be integrated into R bringing the full power of computer  
>> algebra
>> to the R community.
>>
>> Hans W. Borchers
>> ABB Corporate Research
>>
>> ----
>> Postscript
>>
>> "The Euler Mathematical Toolbox is a powerful, versatile, and open  
>> source
>> software for numerical and symbolic computations ... Euler supports  
>> symbolic
>> mathematics using the open algebra system Maxima."
>>
>> <http://mathsrv.ku-eichstaett.de/MGF/homes/grothmann/euler/>
>>
>>
>>
>> Gabor Grothendieck wrote:
>>>
>>> The forms of equations are limited but its not limited to just one:
>>>
>>>> library(Ryacas)
>>> Loading required package: XML
>>>> x <- Sym("x")
>>>> y <- Sym("y")
>>>> Solve(List(x+y == 2, x-y == 0), List(x, y))
>>> [1] "Starting Yacas!"
>>> expression(list(list(x == 2 - y, y == 1)))
>>>
>>>
>>> On Mon, Feb 9, 2009 at 7:45 PM, Carl Witthoft <carl at witthoft.com>  
>>> wrote:
>>>> Gabor G a ecrit:
>>>> Check out the Ryacas package.   There is a vignette with some
>>>> examples.
>>>>
>>>> ----
>>>> Which led me to the manuals for yacas itself.  I'm guessing there  
>>>> may be
>>>> a
>>>> way to use yacas'  "AND" construct to combine a few equations and  
>>>> then
>>>> hope
>>>> the Newton Solver can work with that, but it's not clear that  
>>>> will work.
>>>>
>>>> TK!Solver is nice because you aren't limited to linear equations,  
>>>> nor to
>>>> equations which "fit" into a matrix structure, and because it's  
>>>> legal to
>>>> have more than one unknown to be back-solved (assuming the  
>>>> problem is not
>>>> under- or over-defined, of course).
>>>>
>>>> ______________________________________________
>>>> R-help at r-project.org mailing list
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>>
>>>
>>
>> --
>> View this message in context: http://www.nabble.com/general-inverse-solver--tp21902788p21928972.html
>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

--
Erich Neuwirth, University of Vienna
Faculty of Computer Science
Computer Supported Didactics Working Group
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