Answer by Brendan McKay for Polynomials all of whose roots are rational
Robert Israel's comment about using Sturm sequences got me thinking about how it could be done using only the original polynomial $f(x)$ (assumed to have distinct rational zeros). If the degree is odd,...
View ArticleAnswer by Aaron Meyerowitz for Polynomials all of whose roots are rational
Random comments:The rational root test might be good for finding all rational roots but less so if one is happy to abort as soon as an irrational root is found (i.e one not of the form...
View ArticleAnswer by Daniel m3 for Polynomials all of whose roots are rational
It seems to me that the obvious algorithm via the rational root theorem is somewhat inefficient in at least two cases: $a_0$ or $a_n$ is BIG (so that we might not even be able to factor it), or they...
View ArticleAnswer by Robert Israel for Polynomials all of whose roots are rational
Given a bound for the possible denominators, small enough intervals containing each root will each contain at most one candidate for a rational root, and it is easy to find that candidate (e.g. using...
View ArticleAnswer by Felix Goldberg for Polynomials all of whose roots are rational
Maybe this book has pertinent information:http://www.springer.com/mathematics/algebra/book/978-3-540-40714-0?otherVersion=978-3-642-03979-9Alas, I have no access to a copy now.ALSO, MathSciNet has this...
View ArticlePolynomials all of whose roots are rational
I have two questions about the class of integer-coefficient polynomials all of whose roots are rational.I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!)Q1....
View Article
