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:
“Every boy was supposed to come into the world equipped with a father whose prime function was to be our father and show us how to be men. He can escape us, but we can never escape him. Present or absent, dead or alive, real or imagined, our father is the main man in our masculinity.”
—Frank Pittman (20th century)
“Auden, MacNeice, Day Lewis, I have read them all,
Hoping against hope to hear the authentic call . . .
And know the explanation I must pass is this
MYou cannot light a match on a crumbling wall.”
—Hugh MacDiarmid (1892–1978)