General Theory of Algebraic Equations
Theory of equations
Wikipedia says that similar methods can be used for higher degree polynomials, but I'm struggling on finding resources on the general theory of using special functions in addition to radicals to solve polynomial equations. I tried looking up "hyperradicals", but this name seems to be used for other purposes.
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Is there a name for this general theory? Has the theory I am speaking of even been developed much at all?
Sign up using Facebook. Ratings and Reviews 0 0 star ratings 0 reviews. Please review your cart. Please help improve this article by adding citations to reliable sources. Probability for Statistics and Machine Learning. Since then algebra has been dramatically enlarged to include many new subareas, and the theory of algebraic equations receives much less attention. Amazon Restaurants Food delivery from local restaurants.
The theory of elliptic functions in general is sufficient to solve polynomials of any order, as is shown in Jordan's Treatise on Substitutions and Algebraic Equations. This is discussed here , for example. By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. Home Questions Tags Users Unanswered. The solution of the general quadratic equation was known as early as the ninth century; that of the general cubic and quartic equations was discovered in the sixteenth century.
During the succeeding two centuries many imsuccessful attempts were made to solve the general equations of the fifth and higher degrees. In Lagrange analyzed the methods of I iis predecessors and traced all their results to one principle, that of rational resolvents, and proved that the general quintic equation cannot be solved hy rational resolvents.
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The impossibility of the algebraic solution of the general equation of degree nfn 4 , whether by rational or irrational resolvents, was then proved by A bel, Wantzel, and Galois. Out of these algebraic investigations grew the theory of substitutions and groups. The subject is here presented in the historical order of its development.
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The First Part pp. The Second Part pp. The aim has been to make the presentation strictly elementary, with practically no dependence upon any branch of mathematics beyond elementary algebra.
This book provides the first English translation of Bezout's masterpiece, theGeneral Theory of Algebraic Equations. It follows, by almost two hundred years. This book provides the first English translation of Bezout's masterpiece, the General Theory of Algebraic Equations. It follows, by almost two.
There occiu niunerous illustrative examples, as well as sets of elementary exercises. Typographical errors above are due to OCR software and don't occur in the book. About the Publisher Forgotten Books is a publisher of historical writings, such as: Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings.
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Not to be confused with equational theory. This article does not cite any sources.
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