tag:blogger.com,1999:blog-12604614.post1870103610906752903..comments2017-04-01T04:56:50.736-07:00Comments on Math Refresher: Nonzero Polynomials with Distinct ParametersLarry Freemanhttp://www.blogger.com/profile/06906614246430481533noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-12604614.post-49645429134896603032009-11-12T21:07:54.424-08:002009-11-12T21:07:54.424-08:00Larry,
Thinking about this further, there seems t...Larry,<br /><br />Thinking about this further, there seems to be an interesting corollary to this theorem: <br /><br />If one takes the argument further from the n_th parameter backward to the first, it seems that it should be true that: <br /><br /> G(x_r,1,1,1,...,1) <> 0, where x_r is an element of K that is not a root of the polynomial in A that one derives by setting all the other variables to 1.<br /><br />Neat!<br /><br />Richardrasrasterhttp://www.blogger.com/profile/04466375608443743070noreply@blogger.comtag:blogger.com,1999:blog-12604614.post-9746375386328696992009-11-12T21:00:29.099-08:002009-11-12T21:00:29.099-08:00Hi Larry,
This is a really nice and concise proof...Hi Larry,<br /><br />This is a really nice and concise proof. <br /><br />Edwards indicates the general direction the proof should go (induction, starting with A). But since the function in question involves polynomials with mixed terms (e.g., k *(A^2)*(B^3)*(C^4)), I really wasn't sure how to get from (n-1) to n. Your proof is nice and clean and simple and doesn't require imagining how to solve the mixed terms.<br /><br />Thanks!rasrasterhttp://www.blogger.com/profile/04466375608443743070noreply@blogger.com