> I would be interested to hear what the MathMorphs folks would have to say
about this, or anyone familiar with, eg, MathLab or the good Lisp math
libraries.
>
> - Dan
>

For the MathMorphs guys, Squeak has been a source of inspiration in the
field of (high and pure) Mathematics. Given that mathematicians are
interested in abstract concepts, they are rather reluctant to limit what is
unlimited in nature. Any limitation is an obstacle that prevents the
development of further interesting concepts.

For instance, LargeIntegers are interesting because they correspond to the
fact that integer numbers are unlimited. With unlimited integers one can
define unlimited Fractions, and with unlimited Fractions one can define
unlimited AlgebraicNumbers.

AlgebraicNumbers are an extension of rational numbers (fractions). They
consist of all zeros of all polynomials with rational coefficients. In
Squeak, AlgebraicNumbers can be represented with unlimited precision, just
because Integers and Fractions exist and are unlimited.

Integer, Fractions, AlgebraicNumbers and ModularIntegers are by far much
more interesting for mathematicians than Floats. You can also extend these
quantities introducing the Complex number i. Following this path you can
build Polynomials in several variables with coefficients in any of these
algebraic systems, in the Real or Complex field. You can also build all
concepts found in LinearAlgebra, not just vector and matrices, but abstract
linear spaces, subspaces, linear bases, tensors, homomorphisms, duals, etc.
With all this background other constructions as quadratic forms become
possible and, what is more important, natural.

Now, would Squeak be the same if the answer to the message 1 / 3 were
different from 1/3? I don't think so. For the MathMorphs guys, nothing is
nicer than discovering that Squeak is able to incarnate definitions and
notations with simplicity and accuracy, and with the same naturalness than
mathematicias are used to think about them.

/Leandro