What is Differenciation and How Does It Verify Finite Polynomials?

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Discussion Overview

The discussion revolves around the concept of "differenciation" as proposed by a participant, which they claim can be used to verify finite polynomials. The scope includes theoretical exploration and potential applications of this method, as well as comparisons to established mathematical concepts like the Newton series.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant introduces "differenciation" as a personal method for verifying finite polynomials and invites feedback on their explanation.
  • Another participant expresses confusion about the meaning of the term and speculates that it may relate to difference equations or Newton series.
  • A participant acknowledges that their method is akin to the Newton series, clarifying that it can be used to derive formulas for finite polynomials with rational inputs and outputs.
  • One participant praises the clarity of the document provided and emphasizes the importance of personal derivation in understanding mathematical concepts.
  • There is a mention of the usefulness of differences in discrete mathematics and an interest in the analogies with differentials.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement regarding the concept of "differenciation." While some recognize its connection to established theories like the Newton series, there is no consensus on the originality or implications of the proposed method.

Contextual Notes

The discussion includes assumptions about the definitions and applications of "differenciation" and the Newton series, which remain unresolved. The relationship between the proposed method and established mathematical theories is not fully clarified.

Who May Find This Useful

Readers interested in mathematical methods for verifying polynomials, difference equations, or those exploring discrete mathematics may find this discussion relevant.

Eynbanoiqvs
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The above is not a spelling mistake as I am referring to differenciation rather than differentiation. As to the best of my knowledge, no one else has used the same term nor developed a similar method; and so I claim it as my own till challenged.
Using differenciation, one can verify the expression of any finite polynomial.

I put a lot of work in trying to write up an explanation for my method...so it's best seen in the word document attached. But I still don't think it's perfect.
Please post your views and understanding of this. I would like any feedback.
 

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Using differenciation, one can verify the expression of any finite polynomial.
I can't figure out what this sentence is supposed to mean.
I haven't tried downloading your zip file. I'm guessing you're reproducing the theory of difference equations, or possibly have rediscovered some form of Newton series.
 
Yes; it is the Newton series...but in a primitive form. Thanks for telling me. I didn't know how to search for it or identify it.

That sentence means that you can use the Newton series method to check the formula for any function; assuming it is a finite polynomial and has rational inputs and outputs.
For example, the sum of natural numbers. If one didn't know any theory behind the derivation; this method could yield n^2 /2 +n/2 by calculation with minimum logic involved.
So simple that a computer could derive the formula.

Thanks again for identifying it! I was hoping I was the first...but I guess Newton bet me! :)
 
I've looked at the article, I'll say it's much better written than I expected from a *.doc file posted on the internet!

There's no better way to understand (and to eventually further) a subject than to derive it for yourself, so hopefully you'll continue your study / research, and a lead on existing knowledge will surely help. Sometimes just having good notation makes all the difference!

If nothing else, I think differences are fun -- and the fact of analogies with differentials is interesting -- although I've only spent a little bit of time with them. And they certainly can be very useful in discrete math.
 
Thanks! I actually used the latest Word 2007 to design the document, and then converted it into the old format for uploading.
 

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