Disputatio:Polynomium
Latest comment: abhinc 8 annos by Amahoney
Not only is that word very strange the declension suggested appears even strange: n polyonomon, gen polyonomou : huh? Why not the standard polynomium from Lectiones elementares mathemaicae: seu, elementa algebrae, et geometriae By Nicolas Louis de La Caille?--Rafaelgarcia 23:58, 23 Octobris 2009 (UTC)
- I found this word in a Latin-German dictionary of classical Latin, where there are no such Neo-Latin words like polynomium(see the footnote) and I didn't even know, that there are words like polynomium in Neo-Latin. As the word polyonymon derives from a Greek adjective I thought the greek genitive would be suitable. Monkeypoo 19:48, 25 Octobris 2009 (UTC)
- Polyonymus,-a,-um is an adjective used by grammarians (Donatus, Diomedes, Consentius) to denote synonymous words (e.g., terra, humus, tellus count as polyonyma). This adjective is also used in the sense of 'having many names'. Not being a methamatician, I'm unable to take a normative stand to its applicability in the case of polynoms (though personally, I seem to have nothing against it -- but in that case, I'd prefer the Latinised form polyonymum). BTW, in "pure" Latin, polyonymus is plurinomius (e.g., Isidorus). --Neander 20:18, 25 Octobris 2009 (UTC)
- When writing about mathematical topics, rather than coin terms, we should differ to the established and copious Latin mathematical literature, much of which is available on the web. Most mathematical terminology can be found in the works of Leibnitz, Euler and Newton who upon discovering calculus and functional analysis established most of the terminology. There are also a dozen or so Latin textbooks teaching these topics.
- In that literature, the latin term for a polynomial function in mathematics is evidently polynomium, not polyonymon. It is a terminus technicus that has absolutely nothing to do with synonyms. Rather it names a function having multiple terms inside it consisting of different powers of its variables with coefficients. You can't expect to find such terms in a classical dictionary because the math didn't exist then. These are technical terms and to find them you have to look at the latin mathematical literature.
- Unfortunately, there are parts of mathematics for which the literature is either missing or not easily found on the web, and those are modern set theory and abstract algebra; in these cases it is prudent and acceptable to either borrow terms from Romance languages, latinizing them as needed or possibly in some cases borrowing from Greek or perhaps something else.
- What is important however, is not to cite a source for a mathematical term when the source is not giving the term as a mathematical term. When you cite a source for a mathematical term, the casual reader will naturally assume that this is a source for the term with the purported meaning, not a classical term adapted by the author for a new purpose. But in this case, evidently the word polyonymon evidently has nothing to do with mathematics, which is explained by the fact that the source is a classical dictionary referring to a period over a millenium before algebra and functional theory were invented. And this is terribly misleading!!--Rafaelgarcia 03:20, 2 Novembris 2009 (UTC)
- Polyonymus,-a,-um is an adjective used by grammarians (Donatus, Diomedes, Consentius) to denote synonymous words (e.g., terra, humus, tellus count as polyonyma). This adjective is also used in the sense of 'having many names'. Not being a methamatician, I'm unable to take a normative stand to its applicability in the case of polynoms (though personally, I seem to have nothing against it -- but in that case, I'd prefer the Latinised form polyonymum). BTW, in "pure" Latin, polyonymus is plurinomius (e.g., Isidorus). --Neander 20:18, 25 Octobris 2009 (UTC)
To say the terms could be part of any group (corpus) isn't quite correct. More correctly, they must be elements of the set of complex numbers (arguably, also quaternions or octonions), but it would be strange to say that they could be part of the symmetries (which constitutes a group under the operation of combining any two symmetry). A group is a slightly different structure than the number sets. It is defined as a set of elements together with a binary operation satisfying the group axioms (closure, associativity, identity and inverse). -Vegarius- 16:07, 14 Aprilis 2016 (UTC)
- The math is above my level, but note that according to the Wikidata links, corpus = field, copia = set, and caterva = group. These terms aren't set in stone, but as they are, you actually changed "field" to "set." Amahoney may have something to say. Lesgles (disputatio) 18:56, 14 Aprilis 2016 (UTC)
- Actually, the coefficients can be in any field. It's perfectly reasonable to talk about solving polynomials over, say, (field of integers mod 5). In fact, polynomials can be defined over a ring (say, the ring of non-singular matrices of order n), though in general what you want is an algebraically complete field. A polynomial defined over the complex numbers will have as many roots as its degree (counting multiplicity of course); the same polynomial over the reals may have fewer because some of the roots may not be real. It is certainly wrong to talk about a polynomial defined over a "set" (copia), because a mere set of numbers does not have operations defined on it. A. Mahoney (disputatio) 19:15, 14 Aprilis 2016 (UTC)
- Ah, yes i see my misunderstanding. I'm not sure why i read corpus as group. It was correct in the first place. Sorry about that. As a side note, it's perfectly ok to say the coefficients should be elements of a set of numbers, but to define a polynomial over a set would indeed be inaccurate.-Vegarius- 19:36, 14 Aprilis 2016 (UTC)
- Clearly! But for non-specialist readers I think it's easier to leave the underlying set out of it: of course a field, ring, group, or whatever is a set, with extra stuff, but in a general encyclopedia it seems easier just to say "field" here and let them go look up what a field is if they don't remember. A. Mahoney (disputatio) 19:47, 14 Aprilis 2016 (UTC)
- Ah, yes i see my misunderstanding. I'm not sure why i read corpus as group. It was correct in the first place. Sorry about that. As a side note, it's perfectly ok to say the coefficients should be elements of a set of numbers, but to define a polynomial over a set would indeed be inaccurate.-Vegarius- 19:36, 14 Aprilis 2016 (UTC)
- Actually, the coefficients can be in any field. It's perfectly reasonable to talk about solving polynomials over, say, (field of integers mod 5). In fact, polynomials can be defined over a ring (say, the ring of non-singular matrices of order n), though in general what you want is an algebraically complete field. A polynomial defined over the complex numbers will have as many roots as its degree (counting multiplicity of course); the same polynomial over the reals may have fewer because some of the roots may not be real. It is certainly wrong to talk about a polynomial defined over a "set" (copia), because a mere set of numbers does not have operations defined on it. A. Mahoney (disputatio) 19:15, 14 Aprilis 2016 (UTC)
