252:(Dis. - I am neither a mathematician nor an experienced Wiki user) I'm quite sure the editor-by-author is adequately versed on the subject, and as a student the information doesn't seem at all odd. However, I still feel that the problem remains concerning the article's method of conveying the information. Knowledge's math section has many great broad-topic articles, and a recurring theme I notice is that the simplified approach is always put first. As of now, this is not the case for this article, and this is a considerably important subject. Yes, it may be somewhat informal to refer "a polynomial whose coefficients are themselves rational-coefficient polynomials", given a rigorous context of algebra. However, an even more intuitive approach would rather refer "a function which can be represented using only addition, multiplication, division, and root-taking in a finite number of steps", or something of the like. This is more easily understood to non-mathematicians, and less intimidating than the approach provided now. From there, one may clarify any shortcomings or technicalities for due formalism, and then continue with the more technical and rigorous definitions. This is simply a conventional standard that seems ubiquitous in math entries, so I'm just suggesting a rearrangement.
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equation of degree n has n roots, a polynomial equation does not implicitly define a single function, but n functions, sometimes also called branches". This is not true, as infinitely many functions satisfying the same equation can be built by exploiting tricks similar to the one adopted for constructing the example function above. Additional requirements about continuity could fix the issue. --
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This article fails to convey any clear concept of what an algebraic expression is to non-mathematicians. Relying on even more obscure definitional technicalities is not good enough. I am no mathematician, but I am trained in analytic philosophy and formal logic, and I cannot understand what the hell
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Is this actually correct? The wikipedia definition of a "transcendental function" explicity requires the function to be analytic, which is very strong... Doesn't the "algebraic" concept (which should be more strict) need some continuity specification? Furthermore, the article affirms that "As an
633:. Good catch. As an algebraic equation has, in general, several solutions, one can get a lot of uninteresting functions by jumping many times from solution to another one. If continuity is assumed, it can be proved that the solution is analytic at any point where the root is not multiple.
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I have attempted to clarify parts of the article. Part of it was done after the first comment above but before the second. I also rephrased the lead in line with the ideas in the second comment. Hopefully the article is a bit more comprehensible now.
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OOOPS, this function is not the Bring radical. I have edited the article for taking the Bring radical as an example, and linking to it. I have also changed the link for the impossibility of solving by radicals.
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you people are talking about at all. One suspects that the authors of this article don't have a full grasp of their topic. If you do, then prove it, and make it clear to all of us.
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Though I'm not deeply into the field, I fear that something is missing in the current definition of "algebraic function" here. According to the definition, something like
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Knowledge. If you would like to participate, please visit the project page, where you can join
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It would be useful with a definition of an algebraic expression. The article
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