NetNews Usenet Archive 1992 #16/NN_1992_16.iso/spool/sci/math/symbolic/2082

Text File | 1992-07-26 | 1.7 KB | 46 lines

Newsgroups: sci.math.symbolic
Path: sparky!uunet!cs.utexas.edu!qt.cs.utexas.edu!yale.edu!ira.uka.de!fhg!iitb!dsd1!kir
From: [e-mail] (Harald Kirsch)
Subject: sigma-algebras and probability spaces
Message-ID: <[e-mail]>
Sender: [e-mail]
Organization: Institut fuer Informations- und Datenverarbeitung
Date: Mon, 27 Jul 1992 07:48:30 GMT
Lines: 35



Dear Netters,

I am looking for a sw package that can do symbolic computations in
$\sigma-$algebras (set theory). In the moment I have access only to
Maple and it looks like it can not do what I need:

I simply want to tell the sw that e.g. A and B are sets and that they
are disjoint without saying s.th. about the contents of A and B. Then
the SW should be able to derive that e.g. the following holds:
     $A \subset   A\cup B$
     $A \setminus B = \emptyset$
     $A \subset \C{B}$ (where \C{B} denotes the complement of B
                        relative to a set which contains A and B as
                        subsets.)
     etc.

In the next step I need to do symbolic math with probabilities. To
continue the example above, I tell the computer the probabilities
P(A) and P(B) and it should be able to derive that
    $P(A\cup B) = P(A)+P(B)$  (because $A\cap B=\emptyset$)
    (etc. with more A's and B's and more known probability values)

Does anybody out there know about a sw package able to solve those
problems. If not, it would also help to get some pointers to
literature with algorithms dealing with symbolic computation in
$\sigma-$algebras and probability spaces. (No pointers to Bayesian
Networks please, I know them already.)

Please send your answers to  [e-mail]

Thanks in advance,
  Harald Kirsch