Re: [genius-list] Genius Future: Dr.Genius (Dr.Geo+Genius)

On Tue, 7 Sep 1999, Squeak wrote:

> how much symbolic math do you want? like Integral(x^3,x,0,1)=1/4 ? or
> merely having place holders that are manipulated in simple ways.

I was aiming for a similar level of ability to mathematica, at least as
powerful as mupad.

> Small idea:
>
> Sets could be implemented as characteristic functions ( if A is a set, chi
> sub A is a primitive (logical not set-theoretic) function such that chi
> sub A of x is 1 iff x is in A, and chi sub A of x is 0 iff x is not in A).
>
> A union B = chiA + chiB (chiA | chiB)
> A intersect B = chiA * chiB (chiA & chiB)
> A - B = chiA & ~chiB

Yup, that's a good idea, it leaves the problem of defining the universe
alone(i.e. ~chiA is well-defined) but it still doesn't give a good
internal representation. Common internal reps I've looked at are
bit-set(one bit per element), Linear array(probably the best solution -
not complex), tree(The most efficient - there are log/linearithmic time
algos for many set ops).

Anyway, I'm working on a somewhat broader problem of manipulating
relations; which can include congruences, partial orders, sets, groups
etc. I had some code, but I accidentaly deleted my linux partition(while
debugging a scanner driver - oops!) so I will start from scratch(probably
a good thing!).

njh
Received on Tue Sep 07 1999 - 15:37:32 CDT