Re: CAS for the "masses" (was RE: how to calculate Ricci...)

As a simple example - if it is not able to simplify simple powers or
to do a simple limit (see my older emails on that), then it's not for
me.

Ondrej

On 3/27/07, Ondrej Certik <[email protected]> wrote:
> > Anyway, I'm hopeful that someday "CAS for the masses" will consist of
> > not a whole new simplified system but of defining in Axiom or something
> > like it a set of assumptions and constraints that creates the
> > simplified environment.  To me that makes the most sense for both
> > correctness and "expandibility" - as people need new ideas they can
> > incrementally add them, examining the consequences of each (for
> > example, expanding the domain of numbers under consideration from Reals
> > to Reals+Imaginary).  There's no particular reason I can see to abandon
> > rigor for simplicity - if the mathematics is valid it should be just a
> > question of defining the assumptions made to "simplify" the notation
> > for new users.
>
> Hi CY,
>
> you got precisely to the point. And, getting back to my original
> email, my first sentences were about mathematicians looking at the
> mathematics completely differently.
>
> I, personally, don't know, if it is possible to have a simple CAS for
> masses and also being it able to build on it more rigorous and
> abstract mathematics. As you said, what is really needed in physics is
> a very limited subset of mathematics (basically just calculus,
> integrals on k-manifolds in n-dimensions, differential equations,
> matrices, noncommutative algebras like Pauli or Dirac, series, limits,
> asymptotic expansion, complex numbers, but that's all). Ok, then some
> stuff like recurence relations, tensors, etc., but all of this I just
> call a simple calculus. I want the CAS for masses to be really good at
> this simple calculus.
>
> If someones finds a way how to do more advanced stuff, why not, but I
> am not interested in that primarily, as it is not needed. And if the
> more advanced stuff renders this basic calculus less usable, then I am
> completely against it. On the other hand, you have exactly the
> opposite opinion - if something is not exact, let's not talk about it.
> If, as a side effect, the CAS could also be used for masses, then why
> not, but primarily you are concerned with mathematical formalism.
>
> So I think this is the core difference between me and most developers of Axiom.
>
> I am not saying that you or me should be wrong - this is just the
> basic difference between mathematicians and physicists.
>
> Ondrej
>