ISSAC
2009
Springer
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 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
13 years 11 months ago
2009
Springer
CASC
2009
Springer
13 years 11 months ago
2009
Springer
CASC
2009
Springer
13 years 11 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
13 years 11 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...