Wikipedia:Reference desk/Archives/Mathematics/2012 October 16

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October 16

How it's called when equation gives 2 results for x?

For example ${\sqrt {x}}$ gives 2 results for any value (except 0), so it's not a function? If I want to plot a non-function, how do I call the equation I use to plot it?190.60.93.218 (talk) 17:50, 16 October 2012 (UTC)

You might want to look at the article Multivalued function. — Quondum 19:19, 16 October 2012 (UTC)

One quibble, ${\sqrt {x}}$ only gives 2 results for any value greater than 0, unless you include complex numbers in your solution set, for negative values of $x$. StuRat (talk) 08:39, 17 October 2012 (UTC)

Another quibble - the square root sign usually indicates the positive root (of a positive number), so it's not a multi-valued function onR+. AndrewWTaylor (talk) 09:09, 17 October 2012 (UTC)

Vaguely related: you may want to have a look at solution set (and perhaps analytic variety and algebraic variety).—Tobias Bergemann (talk) 10:08, 17 October 2012 (UTC)

Oh, and implicit function and implicit function theorem, of course. You mention function plotting in your question. I am surprised that we apparently don't have an article on the techniques used to plot the graph of a function or the contour plot of a function of two variables.—Tobias Bergemann (talk) 10:20, 17 October 2012 (UTC)

Ring theory applications

what are the applications of Rings .can any body give me name of a book about it — Precedingunsigned comment added by 182.187.60.87 (talk) 21:56, 16 October 2012 (UTC)

I am not sure whether you are asking for applications of ring theory outside of mathematics or not. Could you be more specific?

I don't know of any books that would discuss applications of rings outside of mathematics. (Quite unlike group theory. Groups play a central role in theoretical physics, and there are several books about the applications of groups and their representations to quantum field theory and the physics of condensed matter, for example.)

Furthermore, offhand I cannot think of a book that would specifically discuss applications of rings within mathematics, partly because rings are very general structures (whenever you extend an abelian group with another binary operation that is associative and isdistributive over the abelian group operation you get a ring) with many important specialisations that carry themselves theories rich enough to fill books. (You probably already know the following if you have read the Wikipedia articles ring (mathematics) and ring theory, but it wasn't clear to me from your question.) Many notions of ring theory carry over to field theory. Every field is a ring, and every finite division ring is a finite field. Finite fields are used in number theory and incryptography and coding theory. Every associative algebra is a ring, and this includes square matrices and operator algebras. The set of polynomials in one or more variables with coefficients in a given ring is another ring, see polynomial ring. Thinking about the factorization of polynomials leads to the fundamental theorem of algebra. Then there is algebraic number theory. And so on. —Tobias Bergemann (talk) 15:34, 17 October 2012 (UTC)