What is this symbol that looks like an O with a small n or r in it?

November 2, 2007 8:54 AM

What is this logical/matrix/algorithm symbol?

I'm trying to implement an algorithm for manipulating matrices and I think I understand the equation described, but I don't know what the symbol that looks like a big O with a small n or r in it is called, or what it really means.

The actual computation seems to be a calculation of Minkowski distance having exactly i+1 links, and that it relies on knowing the distance having i links. I've never seen that symbol before, and would like to know what it means

posted by i love cheese to computers & internet (12 comments total)

could that be some fucked-up rendering of the tensor multiplication symbol? that would make sense based on the context, if W is a matrix.
posted by sergeant sandwich at 9:01 AM on November 2, 2007

yes, i was thinking that too. maybe it's a kronecker product, or maybe they're using that symbol (looks like an r circled) to denote the operation is being done in that certain metric?
posted by virga at 9:19 AM on November 2, 2007

If I had to guess, I'd say they're making up their own notation here - W (circled-r) W^i means "compute this formula with respect to some r", where the r is that exponent you see over on the right there. So if you were using, say, the square root of the sum of squares, r would be 2, and you'd write that as W (circled-2) W^i.
posted by wanderingmind at 9:30 AM on November 2, 2007

W^(i+1) is the same dimension as W^i so it can't be a tensor product...

I think it's definitely an 'r' for the 'r-metric' and that it is made up notation for taking the r'th root of the min of the sum...
posted by geos at 9:44 AM on November 2, 2007

Well, they're giving a definition in your example. Maybe they're making it up right there. I think it's a shorthand for something to be used soon, not something you should remember past the next few pages.
posted by cmiller at 9:56 AM on November 2, 2007

Well, they're giving a definition in your example.

QED
posted by Chuckles at 10:01 AM on November 2, 2007

Yes, it says "Definition 5" and then proceeds to say that the symbol is "computed as follows". What is not clear about this?
posted by number9dream at 10:35 AM on November 2, 2007

I don't know myself.

cmiller might be right in saying that the author might be defining a new operator here, designated by that symbol. However: why would an author define a new oprerator that he never again uses? (Does this symbol appear elswhere in the text?)

I've never seen that symbol before. If it were a "standard" mathematical symbol, even one used only in some obscure backwater subfield, I would have expected someone would have chimed in by now. (One hour, at midday in N. America, is a long time by my reckoning.)

My thought: maybe it's a typo of some sort? If I had to put money down, though, I'd say wanderingmind and/or geos are closest to the truth.

(an aside: Chuckles' comment helps no-one, is confusing, and should be removed!)
posted by funkbrain at 10:44 AM on November 2, 2007

number9dream: apparently you read that text and the idea the author meant to convey was clear to you. It's not clear to me, and apparently, that idea is not clear to "i love cheese", either.

to answer this question, we askmefites only have the context provided in that image (maybe some clever askmefite will find the original source). It would be easier to address the original question if we had more context...

A -good- author would say: "Here we introduce the FOO operation, represented by the symbol BAR... ", etc. Of course, this is all IMHO.
posted by funkbrain at 10:54 AM on November 2, 2007

Agreed that the notation is not a standard, widely-known operation you're supposed to recognize; the notation is being introduced and defined on the spot. The r is included in the notation to indicate its dependence on the value of r; something like x2297;_r might just as well have been used, but with the circled times sign used in its "generic binary operation that I need a symbole for" role as opposed to its "I specifically mean tensor product" role. People come up with all kinds of (mostly circular, but occasionally quite fanciful) symbols to use for their operations they're making up.
posted by Wolfdog at 11:57 AM on November 2, 2007

Well, it worked in the preview. ⊗_r is what I meant, and if that doesn't show, the hell with it.
posted by Wolfdog at 11:58 AM on November 2, 2007

Thanks for everyone's input. It appears that the PDF I used (of an out of print book here's the .zip) rendered an uppercase theta incorrectly.

So, they were simply defining theta as an operator. (although, perhaps they were pulling a Prince move, and creating the symbol formerly known as theta).

I discovered this in a later paper by some other authors that used Theta in the same definition. These other authors either made a really plausible guess, or had access to the physical book, which likely rendered the symbol appropriately.

Sorry for the confusion. Thanks again for the suggestions.
posted by i love cheese at 12:48 PM on November 2, 2007