Re: complexity of numerical software

Jean-Claude Arbaut wrote: 
Jaap Spies wrote:

[...] 

I you write a new CAS, it would be silly to use only those "standard"
libraries: they compute with IEEE754, hence the precision is very
limited for a CAS. You'd probably prefer a multiprecision library,
but I don't know of a standard one... GMP and others only compute
with integers, but you need approximate values of many transcendental
functions.


Yes, GMP and
MPFR: http://www.mpfr.org/
are the candidates.

I will never, never make the mistake, as I did some 20 years ago to
write my own multiprecision software! At that time there was no real
alternative, but ...

You'll also need to write special algorithms for that, since the problem
of computing with high precision numbers or with rationnals have its own difficulties: among others, how do you reduce the size of numbers (to
increase speed) appearing in computations, like the solution of a linear system of equations. These are also numerical computations, though not
the classical "number crunching" BLAS.


Sure!

Oh, and just an idea: what is *really* a CAS ? I have already used Maple, Mathematica and MuPAD, and then I discovered GAP: no more
"formal" computations, but "true" mathematical objects :-) I mean,
it looks like in Maple, the elementary object is an "expression",
which can be almost anything. In GAP, there are no expressions, only
values: polynomials, finite groups, matrices, are _values_. That makes
a great difference I think. Maybe I'm wrong... 

Values -- Objects. The design of Maple (and Mathematica) is flawed. OK,
understandable seeing the history, but opening new ways cost a lot.
Are we prepared to pay for it?

Bringing together the good stuff is a possibility, as I mentioned
in the original thread:

    http://modular.ucsd.edu/sage/index.html

Good for doing mathematics, but not for engineering applications
as RJF pointed out! And supposedly to die soon!?

Jaap
.

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