[Om3] [Fwd: ISSUE-33 (statistical symbols): Kyle's Siegrist's request for new Content-MathML symbol]

[Professor James Davenport]

On Fri, October 24, 2008 8:07 am, Michael Kohlhase wrote:
> Dear all,
>
> there was a request for symbols in content MathML3, we should talk about
> what to do here from the CDs side. In particular, I know that binomial
> coefficient is in combinat1, but what about the others?
I enclose the original message, since it's hard to understand otehrwise.

> Here is what I would love to see added to Content MathML:

>  1. Binomial coefficient
As MK says, in combinat1
>  2. Permutation coefficient:  n(n -1)...(n - k + 1), usually
>  rendered P(n, k) or nPk or (n)k.
Personally, I've always written n!/k!, but if there's a call for it, I
could always add it to combinat1.
>  3. A probability operator with an optional "given" construction
>  (for conditional probability).  Typical rendering would be
>     P(A, B, ...) (without conditioning) or  P(A, B, ... | C, D, ...)
>  (with conditioning).
For the monadic versions P(A), or P(A|C D ...) I have no problem: I assume
their absence is due to the fact that we never had a probabilist on board
in OM. I assume the proposers P(A, B, ...) is P(A&B&...), and we MIGHT
want to see that represented explicitly.
>  4. An expected value operator with an optional "given" construction
>  (for conditional expected value).  Typical rendering would be E(A,
>  B, ...) (without conditioning) or  E(A, B, ... | C, D, ...) (with
>  conditioning).
Again, I hace no problem with E(A) or E(A|C ...).
I have no idea what is meant by E(A,B).
>  5. General union, to form the union of Ai over i = a to b, or the
>  union of Ai where i is in an index set I.  This would work just
>  like the sum construction, with a bound variable and with lower and
>  upper limits, or with a bound variable and with a condition.
I discussed this in Barcelona
(http://www.jem-thematic.net/files_private/Barcelona.pdf). As far as
MathML2 is concerned, I quoted
<apply> <union/> <bvar>i</bvar> <lowlimit>... </apply>
Hence it seems as if we are in the general 'condition in MathML3' debate.
For OpenMath I quoted 'big union on make_list' which I admitted was not as
satisfactory, especially as in the summation case one can write
<OMS name="sum" cd="arith1"/>
Maybe we shou;d bite the bullet and have the equuivalent of sum.
>  6. Exactly like 5, but with intersection.

> If I had these extensions, I think that I could do just a>bout
> everything that I wanted without going over to Presentation MathML.

>  Items 3 and 4 (with the "given" construction) are really important in
>  probability, statistics, and stochastic processes; conditional
>  probability and expected value are central notions.  Ordinary
>  probability and expected value can be done with the usual function
>  ("apply") construction, but there is no way to do the conditioning
>  without adding Presentation MathML as a kludge.

>  I am really surprised that items 5 and 6 are not already present;
>  they seem very natural and necessary for lots of areas of math."
True.

James Davenport
Hebron & Medlock Professor of Information Technology
Formerly RAE Coordinator and Undergraduate Director of Studies, CS Dept
Lecturer on CM30070, 30078, 50209, 50123, 50199
Chairman, Powerful Computing WP, University of Bath
OpenMath Content Dictionary Editor
IMU Committee on Electronic Information and Communication