ISSAC
2009
Springer
14 years 8 months ago
2009
Springer
We present a high performance algorithm for multiplying sparse distributed polynomials using a multicore processor. Each core uses a heap of pointers to multiply parts of the poly...
ISSAC
2009
Springer
14 years 8 months ago
2009
Springer
The computation of triangular decompositions involves two fundamental operations: polynomial GCDs modulo regular chains and regularity test modulo saturated ideals. We propose new...
ISSAC
2009
Springer
14 years 8 months ago
2009
Springer
We show that detecting real roots for honestly n-variate (n + 2)-nomials (with integer exponents and coefficients) can be done in time polynomial in the sparse encoding for any ...
CASC
2009
Springer
14 years 8 months ago
2009
Springer
We discuss the family of “divide-and-conquer” algorithms for polynomial multiplication, that generalize Karatsuba’s algorithm. We give explicit versions of transposed and sho...
CASC
2009
Springer
14 years 8 months ago
2009
Springer
We present lazy and forgetful algorithms for adding, multiplying and dividing multivariate polynomials. The lazy property allows us to compute the i-th term of a polynomial withou...
CASC
2009
Springer
14 years 8 months ago
2009
Springer
This work addresses the problem of computing a certified ǫ-approximation of all real roots of a square-free integer polynomial. We proof an upper bound for its bit complexity, b...
CASC
2009
Springer
14 years 8 months ago
2009
Springer
CASC
2009
Springer
14 years 8 months ago
2009
Springer
CASC
2009
Springer
14 years 8 months ago
2009
Springer
Abstract. We describe a symbolic framework for treating linear boundary problems with a generic implementation in the Theorema system. For ordinary differential equations, the ope...
CALCO
2009
Springer
14 years 8 months ago
2009
Springer
Abstract. We use coalgebraic methods to describe finitely generated free Heyting algebras. Heyting algebras are axiomatized by rank 0-1 axioms. In the process of constructing free...