Interpolation of polynomials given by straight-line programs

Interpolation of polynomials given by straight-line programs

We give an algorithm for the interpolation of a polynomial A given by a straight-line program. Its complexity is polynomial in τ, log(d), L, n, where τ is an input bound on the number of terms in A, d is a bound on its partial degree in all variables, L is the length of the given straight-line program and n is the number of variables.

Factorization of Polynomials Given by Straight-Line Programs

An algorithm is developed for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors. The algorithm is in random polynomial-time as a function in the input size, total degree, and binary coefficient length for the usual coefficient fields and outputs a straight-line program, which with controllably high probability correctly determines...

Faster Sparse Interpolation of Straight-Line Programs

We give a new probabilistic algorithm for interpolating a “sparse” polynomial f given by a straight-line program. Our algorithm constructs an approximation f of f , such that f − f probably has at most half the number of terms of f , then recurses on the difference f−f. Our approach builds on previous work by Garg and Schost (2009), and Giesbrecht and Roche (2011), and is asymptotically more ef...

Integration of Multivariate Rational Functions Given by Straight-Line Programs

Integration of Multivariate Rational Functions Given by Straight-Line Programs

We present a well-parallelizable algorithm which, taking a straight-line program for the evaluation of a vectorial field of rational functions of Q(X1, . . . , Xn) as input, decides whether they allow a rational potential function and, in case of affirmative answer, computes it as output. We introduce a mixed model of representation of polynomials to allow the application of integration techniq...