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I don't know if its appropriate question here...but I anyway want to try...

I have an algorithm in which I have a finite data in which each element is assumed as an element of a metric space with a metric defined. Now its mathematically possible to isometrically embed this specific metric space in an Hilbert space. So I do it on this data to get a vector representation although its infinite dimensional, mathematically, I do it in alogorithmic approximation to get a finite dimensional vector representation, for each data element. In theory, as per math, its possible to isometrically embedd this metric space into an Hilbert space, (metric meets required conditions, but approximation comes when we do it on real data with an algorithm).In practicality this isometric embedding on real data is an approximate one. (I do it via clustering the data with defined metric). Then we go on using this vector representation for further modeling as required by the application. The entire process is basically algorthimic, and the notions of metric space and its isometric embedding in a Hilbert space serves as a mathematical justification/motivation for the design of this particular algorithm.

Question : I am writing a patent on this algorithm on this, in which I need to submit a document to the patent attorney for her perusal. In this document should I just write the entire algorithm in a mechanical way, just as we write code, without giving any mathematical justification/motivation and without mentioning about the brand new mathematical metric space and its isometric embedding to an Hilbert space. Or should I also include a special section in the document giving all the mathematical justification in pure math terminology. (about metric space and isometric embedding).

If I write down only algorithm without explaining the math behind it, it sounds boring. But the attorney is not that math savvy to understand the math. Another point is that the mathematical metric space is something brand new, atleast as I searched on the internet, I couldn't find it anywhere the exact definition being used. So does this have any impact on the patent to mention this mathematical metric space in the patent? Should I mention this math in the document an an extra section?

PS : i basically did not know what to tag, so I added a few tags even though they dont seem to be appropriate. Please guide me to a site in case if its not valid here. But I'd like hear from math people what their opinion on this issue.

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The words algorithm and mathematics both reflexively make a patent practitioner think - unpatentable mathematical truth or abstract idea. I believe you will need to tie this to an application. –  George White Mar 29 at 21:34
    
@GeorgeWhite : The patent is on a practical application (software), I just did not mention it. –  Rajesh D Apr 1 at 12:28

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