[R] general inverse solver?

Hans W. Borchers hwborchers at gmail.com
Tue Feb 10 23:02:47 CET 2009

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

> 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.

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

>From a statistics point of view or application this may not be so relevant, but
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

Hans W. Borchers

> 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
> >

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