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> I wonder if you're trolling or just clueless

Given the curious interpretation of ‘polynomial’ by means of an only somewhat correct translation, I’d tend to the latter.




Well I admit I don't understand it fully. That is no reason to accuse me of trolling or downvote my comments.

http://en.wikipedia.org/wiki/Polynomial

Is Wikipedia not correct on this issue? I was told on one hand to look stuff up on Wikipedia, and on another I found out it is not always correct.


‘poly’ means many, yes, and ‘nomial’ in this context can stand for ‘terms’ or ‘expressions’ (not really numbers, but maybe formulae as you said). However, ‘polynomial’ does not mean ‘many terms’ when used by mathematicians and, in extension, computer scientists.

A polynomial function, in this context, means a function that is/can be expressed as a sum of powers (usually restricted to a finite number of addends) of its input variables with appropriate prefactors. For example,

  f(x) = 1
is a polynomial function, but it certainly does not have many terms (nor numbers). That the finiteness of the sum is an important requirement when it comes to complexity can be seen by the fact that the exponential function can be expressed as an infinite polynomial:

  exp(x) = 1 + x + 1/2 x² + 1/6 x³ + …
In other areas, where people are more concerned with nondivergent or differentiable functions, this requirement is often dropped and nearly everything that doesn’t have poles in x is called ‘polynomial’.

Furthermore, you didn’t only get downvoted for misinterpreting polynomial, but also for the strange mixing of theoretical CS, which is concerned with the complexity of algorithms at hand, and real-world effects such as slowdowns due to other programs multitasking, CPU caches etc. etc. which are rarely taken into account when deciding whether a given algorithm is remotely feasible to implement (runs in time, say, n^10 or faster) or just too slow.


Ah I see, I am exploring theoretical areas of computer science for which there are no clear answers yet. Downvotes for you, bad HN user for making us try to think of new theories. :)

So a Polynomial doesn't need be many of them, it can be just one of them. The poly in the name threw me off I admit. I would have assumed that was a mononomial for just one and two of them are a binomial but apparently polynomial is used instead even for only one or two? I hope you understand my confusion there. Thank you for clearing that up.


Ah I see, I am exploring theoretical areas of computer science for which there are no clear answers yet. Downvotes for you, bad HN user for making us try to think of new theories. :)

In science in general, including computer science, "theoretical" doesn't mean fringe or unexplored, it means foundational and abstract. CS theory uses the word "theory" in the same sense as music theory. CS theory deals with well-defined, rigorous analysis of computation in abstract or mathematical terms.

I would have assumed that was a mononomial for just one and two of them are a binomial but apparently polynomial is used instead even for only one or two?

A two-termed polynomial is also called a binomial. "Binomial" and "monomial" are special cases of the more general term "polynomial".


Just as poly- and mono- are prefixes of Greek origin[0], you’d probably use ‘di-’ rather than ‘bi-’ here (binomials are a little different, again), just as you have monosaccharides, disaccharides and polysaccharides[1] (aka carbohydrates).

The relevant point is that it usually doesn’t matter whether you have one, five or 500 terms in a polynomial, as the largest one will certainly dominate for sufficiently large input sizes[2] and all terms in a polynomial essentially behave the same way (being differentiable, having no poles etc.).

[0] The only thing wrong with homosexuality is smashing a Greek prefix onto a Latin root.

[1] Latin: uno-, bi-, pauc-, multi-, Greek: mono-, di-, oligo-, poly-

[2] cf. http://www.wolframalpha.com/input/?i=x%5E20%3B+x%5E20%2Bx%5E...




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