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general inverse solver?

10 messages · Carl Witthoft, Erich Neuwirth, Stavros Macrakis +3 more

Carl Witthoft
# 
Gabor G a ecrit:
Check out the Ryacas package.   There is a vignette with some
examples.

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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).
Gabor Grothendieck
# 
The forms of equations are limited but its not limited to just one:
Loading required package: XML
[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:
Hans W Borchers
# 
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:

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
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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:

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Erich Neuwirth
    

    

      
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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:

        

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

            

      
      
      
    

        

      
      
    

        
--
Erich Neuwirth, University of Vienna
Faculty of Computer Science
Computer Supported Didactics Working Group
Visit our SunSITE at http://sunsite.univie.ac.at
Phone: +43-1-4277-39464 Fax: +43-1-4277-39459

  
  


  


      

    

    

      
      

        


  

        

      Hans W Borchers
    

    

      
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Gabor Grothendieck <ggrothendieck <at> gmail.com> writes:

            

      
      
      
    

        
I do not agree with this statement. Looking back into some of the requests for
symbolic computations on this help list, [R]Yacas showed off weaknesses such as:

 - extremely slow in high-precision arithmetic
 - not solving very high-dimensional polynomials
 - does not simplify expressions in several variables
 - does not solve systems of equations except linear ones
 - does not symbolically solve medium to complex integrals
 - has very few special functions
 - therefore differentiation is unsatisfying

            

      
      
      
    

        
considering the requests it illustrates that Yacas is not providing necessary
CAS features. Especially the missing capabilities in symbolic integration can be
painful in a statistics environment.

Many times Ryacas was pointed out, it was actually not solving the problem.

The examples in the Ryacas vignette are -- in my opinion -- trivial ones and do
not display advanced capabilities.

This is not meant to diminish the efforts invested in the Yacas software over
the years. I know a bit how difficult it is to write software for symbolic
computations. But in my opinion it also is evidence that a more advanced
computer algebra module could be very valuable for extending and improving the R
system.

Hans W. Borchers

            

      
      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Stavros Macrakis
    

    

      
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On Tue, Feb 10, 2009 at 7:51 AM, Gabor Grothendieck

        
<ggrothendieck at gmail.com> wrote:

            

      
      
      
    

        
Glad to hear it... (I first worked on Maxima in 1971...)

            

      
      
      
    

        
It is true that Yacas has a nicer syntax for its pattern-matching
functionality than Maxima, but I think they are fundamentally very
similar.  In particular, as far as I can tell, neither does
backtracking or unification, so neither is very Prolog-like.

            

      
      
      
    

        
Maxima interfaces to a variety of other systems via sockets.  It does
not have an OpenMath interface (yet!), but I don't know how useful
that is compared to other linearized tree structures.

            

      
      
      
    

        
Maxima can also output TeX and do exact rational arithmetic and
arbitrary-precision floating-point arithmetic.  Maxima also handles a
variety of cases which apparently Yacas doesn't, like factorization of
multivariate polynomials (seems pretty basic!), many special
functions, etc.  Maxima also has an active user and development
community.

           -s

  
  


  


      

    

    

      
      

        


  

        

      Gabor Grothendieck
    

    

      
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I am not sure what the point of all this is.

This is an R list, not a CAS list.  The recommendation to use yacas is based on
the fact  that there is an interface between R and yacas.  There is no
interface between
R and Maxima so Maxima is not in the running.  Anyone who has used
Maxima knows that
is an impressive piece of software but that's not the point.

Regarding, why there is no interface to Maxima, its because its harder
to interface to
Maxima than yacas.   There are two problems here:

1. Maxima does not incorporate a socket server as far as I know.
You would have to write it and that may or may not need an in depth
understanding of Maxima to do so but in any case represents work.
With yacas you don't have to write a server since yacas itself already
contains a server. Just run:
  yacas --server .,.
and the server side is done. (In the case of yacas it would also be
possible to use its C interface for an in-process interface or presumably
the java interface of the new java version of yacas.  With Maxima
it would be more problematic since its written in Lisp.)

2. Once you have created some sort of communications channel
then what?  If you want more than a crude interface that passes
an unprocessed character string to the CAS and then passes one
back then you will want to translate between R and the CAS.  With
yacas, OpenMath facilitates this greatly.

The end result is that its more work to meaningfullly interface with
Maxima than with yacas yet yacas satisfies the majority of
needs of a CAS.  There is the minority who need more powerful
algorithms but I think it was a reasonable step to handle the 80%
that can be accommodated most easily first by using yacas. The
remaining 20%, which is what the other respondents to this thread
are discussing will in part be addressed in the future possibly, in
part, by the second project I am working on now.  Perhaps some
would quibble with the 80/20 and if you are in the 20 it probably
seems like 100 but we will never settle that question definitively.

  
  


  


      

    

    

      
      

        


  

        

      Hans W Borchers
    

    

      
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Gabor Grothendieck <ggrothendieck <at> gmail.com> writes:

            

      
      
      
    

        
The point of all this is:

1.  Some users of R here on the list apparently would like to have more powerful
CAS functionalities than Yacas can provide.

2. Many of the solution hints to Ryacas on this list were simply not solving the
resp. problem, so the 80/20 statement of yours may be downright wrong.

3. Maxima does incorporate a socket server and can be integrated into other
systems, see EULER (do you never listen?).

What are you mourning about? Of course, it was great that you made available
Yacas for R. But others have the right to discuss their wishes here w/o being
'slammed' every time with questionable hints to Ryacas.

I agree arguments have been exchanged and we should stop here. After this
discussion, I wish someone would think about an Rmaxima package (along the lines
of EULER, e.g.), I cant do it, unfortunately.

Hans Werner Borchers

            

      
      
      
    

  
  


  


      

    

    

      
      

        


  

        

      Baptiste Auguie
    

    

      
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In a different perspective the sage project might also be an option,  
it seems to interface to Maxima and R among other things. I haven't  
tested it myself though.

http://www.sagemath.org/index.html

Best wishes,

baptiste


PS:  sagemath.org is a well-thought website, perhaps a good  
inspiration for the new design discussed recently?

        
On 11 Feb 2009, at 07:56, Hans W. Borchers wrote:

        

            

      
      
      
    

        

      
      
    

        
_____________________________

Baptiste Augui?

School of Physics
University of Exeter
Stocker Road,
Exeter, Devon,
EX4 4QL, UK

Phone: +44 1392 264187

http://newton.ex.ac.uk/research/emag