Symmetric Function Explanation
In the context of a valuation, we are given certain information in the form of the valuations of elementary symmetric functions of the roots of a polynomial, and require information on the valuations of the actual roots, in an algebraic closure. This has aspects both of ramification theory and singularity theory. The valid inferences possible are to the valuations first of the power sums, by means of Newton's identities.
Read more about this topic: Newton Polygon
Famous quotes containing the words function and/or explanation:
“Our father has an even more important function than modeling manhood for us. He is also the authority to let us relax the requirements of the masculine model: if our father accepts us, then that declares us masculine enough to join the company of men. We, in effect, have our diploma in masculinity and can go on to develop other skills.”
—Frank Pittman (20th century)
“How strange a scene is this in which we are such shifting figures, pictures, shadows. The mystery of our existence—I have no faith in any attempted explanation of it. It is all a dark, unfathomed profound.”
—Rutherford Birchard Hayes (1822–1893)