In this paper we present algorithmic and complexity results for polynomial sign evaluation over two real algebraic numbers, and for real solving of bivariate polynomial systems. Our main tool is signed polynomial remainder sequences; we exploit recent advances in univariate root isolation as well as multipoint evaluation techniques.

The library fast polynomial for Sage compiles multivariate polynomials for subsequent fast evaluation. Several evaluation schemes are handled, such as Hörner, divide and conquer and new ones can be added easily. Notably, a new scheme is introduced that improves the classical divide and conquer scheme when the number of terms is not a pure power of two. Natively, the library handles polynomials ...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

The cryptographic literature contains many provably secure highspeed authenticators. Some authenticators use n multiplications for length-n messages; some authenticators have the advantage of using only about n/2 multiplications. Some authenticators use n variables for length-n messages; some authenticators have the advantage of using only 1 variable. This paper, after reviewing relevant polyno...

The Heuristic Polynomial GCD procedure (GCDHEU) is used by the Maple computer algebra system, but no other. Because Maple has an especially eecient kernel that provides fast integer arithmetic, but a relatively slower interpreter for non-kernel code, the GCDHEU routine is especially eeective in that it moves much of the computation into \bignum" arithmetic and hence executes primarily in the ke...

We define a two-variable polynomial fa(t, z) for a greedoid G which generalizes the standard one-variable greedoid polynomial A<j(f). Several greedoid invariants (including the number of feasible sets, bases, and spanning sets) are easily shown to be evaluations of fG(t, z). We prove (Theorem 2.8) that when G is a rooted directed arborescence, fo(t, z) completely determines the arborescence. We...