Re: [genius-list] Genius Future:

On Wed, 8 Sep 1999, Squeak wrote:

> URL on mupad?

Excite found: www.mupad.de

> Also I think this goal is very lofty, definately should look into open
> source solutions already available, andtake as much from their experience
> as we can. As late as '95 mathematica did some integrals incorrectly. They
> have worked very hard to get their product as good as it is, AND got
> paid :) Does "yacas" or "rlab" do this sort of thing?

Yes, but only a small number of people got paid.

> On the subject of complexity, sparse matricies might better be written
> as hash's (glib hash seems fine). Then sets would be pretty easy
> to extend to hash's whose values were either 1 or 0. To demonstrate
> need: "a@(10000,10000)=4" hangs genius, and "a=[0] ; a@(100,100)=4 ;
> a@(10000,10000)=5" gets a fatal memory error.

Yep, but what if you want to do something useful, like reduce to upper
triangular form? You will need to store lots of intermediate values.
There are nice algorithms for this and looking around wouldn't hurt.

> Partial orders would definately be better as a tree. I'm thinking the
> problem is so low level multiple solutions might be neccessary?

Except there is nothing that a partial order adds beyond a semigroup :-)
Hence my working on semigroups...

> What is an element by the way? Integers, real numbers, complex numbers,
> sets there of? You might want to check out ghc (the glorious glasgow
> haskell compiler) for some ideas as well. SuSe linux came with some
> finite element software.

Presumably an element is anything which could be entered at the top level.

> ** Important question: is the source available? cvs or something?

For what, symbolic.guile:
http://hawthorn.cs.monash.edu.au/~njh/symbolic.guile

> If i could see what's being written (even if it doesnt work) I would have
> a clue about which of my ideas to put into code. Things on the todo list
> (with more notes than code)

Could you make a list on a web page listing each item and what operations
you would have.

> Polynomial rings,
Is Eisenstein irreducibility computable? This would be useful.

> quotient spaces,
What about them?

> finite fields
Fits under semigroups

> Inteval arithmetic
That would be very useful!

> Recursion
? You mean f(x) = x*f(x-1) - doesn't genius already do this

> infinite (really infinite in the greek sense) sequences,
Presumably defined as f(i)?

> basic algebraic stuff (variables are treated like unknown quantities
> and kept throughout a calculation, first step imho).

Done.

> Functionals
? Aren't they just a special form of function(\omega->R ?)

> curryable functions
? Aren't all functions curryable - once you have variable argument lists.

> functions as transformation rules
? explain

> quarternions, matricies over skew fields
c.v. fields :-)

> And of course: a couple graphing type extensions that are total hack.
Why would they need to be hacks? Could a graph be simply a
function(called graph) which returns an image?

> As it is right now, I'm just slowly writing my own (GPL) sub-genius
> (to learn compiler design I guess) so most of the junk I've written
> either has problems or is already done by genius (hence its just a
> subgenius).

Ok, well tell me when you finish it, and we'll start on the genius
sym-manip.

njh
Received on Tue Sep 07 1999 - 22:15:27 CDT