From: <njh_at_cs.monash.edu.au>

Date: Wed, 8 Sep 1999 08:34:45 +1000 (EST)

Date: Wed, 8 Sep 1999 08:34:45 +1000 (EST)

On Tue, 7 Sep 1999, Squeak wrote:

*> how much symbolic math do you want? like Integral(x^3,x,0,1)=1/4 ? or
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*> merely having place holders that are manipulated in simple ways.
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I was aiming for a similar level of ability to mathematica, at least as

powerful as mupad.

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

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