Hello,
I was working on a project to build a small computer algebra system in Squeak, and have just updated the package that I made available on the web at http://cage.rug.ac.be/~stes/squeak.html.
(I think this would be a good application of Squeak, in mathematics, and I've also added the URL of my package to the Squeak Swiki server at http://minnow.cc.gatech.edu/squeak.20)
There's already some simple things you can do with the package (and more to come) :
Create a BigInt instance,
one := BigInt int:1 1
Make a polynomial z+1,
p := Polynomial scalar:one 1 t := Term scalar:one symbol:'z'exponent:1 'z' p insertTerm:t 'z' + 1
Square the polynomial,
q := p square 'z'^2 + 2 'z' + 1
Add a term in a different variable (to get a multivariate polynomial)
t := Term scalar:one symbol:'a' exponent:1 'a' q insertTerm:t 'z'^2 + 2 'z' + 'a' + 1 q := q square 'z'^4 + 4 'z'^3 + (2 'a' + 6) 'z'^2 + (4 'a' + 4) 'z' + 'a'^2 + 2 'a' + 1
Now convert the polynomial from the recursive representation (where coefficients are polynomials) to the expanded representations, where the polynomial is an (expanded) sum of monomials,
p := q makeExpanded 'z'^4 + 4 'z'^3 + 6 'z'^2 + 4 'z' + 'a'^2 + 2 'a' 'z'^2 + 4 'a' 'z' + 2 'a' + 1
The total degree and order of the polynomial,
p degree 4 q order 0
Get the leading monomial (or term etc.)
p leadingMonomial 'z'^4
Convert back to recursive representation
p makeRecursive 'z'^4 + 4 'z'^3 + (2 'a' + 6) 'z'^2 + (4 'a' + 4) 'z' + 'a'^2 + 2 'a' + 1
I hope to eventually have a good set of 'building blocks' for algebra in Squeak, and then you could use Squeak for other computations as well (group theoretical, for instance).
David.