Therefore, I figured I'd turn to the real pros here for assistance. Unfortunately, I was rather ill this week and unable to attend class, meaning I have only been able to use the textbook as a resource, so I'm pretty lost when it comes to writing this program. Combining our reduction method and the modified univariate Ben-Or and Tiwari algorithm, we give a Monte Carlo multivariate interpolation algorithm, which has better total complexity in most cases for sparse interpolation of black-box polynomial over finite fields.I'm looking for some assistance on an exercise for my C++ programming class. A modified univariate Ben-Or and Tiwari algorithm over the finite field is proposed, which has better total complexity than the Lagrange interpolation algorithm. The reduction algorithm leads to multivariate interpolation algorithms with better or the same complexities in most cases when combining with various univariate interpolation algorithms.
A new Monte Carlo method is given to reduce the black-box multivariate polynomial interpolation problem to the black-box univariate polynomial interpolation problem over any ring. The method is based on two main ingredients. for the polynomial given by an SLP over finite field (for large characteristic).read more read lessĪbstract: In this paper, a new reduction based interpolation algorithm for general black-box multivariate polynomials over finite fields is given. And we also show that the complexity of our deterministic algorithm is the same as the one of deterministic zero-testing of Blaser et al. Its arithmetic complexity is quadratic in $n,T,\log D$, i.e., quadratic in the size of the sparse representation. It has better complexity than existing deterministic algorithms over a field with large characteristic. The second one is a deterministic algorithm. If $q$ is $O((nTD)^)$, where $D$ is the partial degree bound, then our algorithm has better complexity than other existing algorithms. Its arithmetic complexity is linear in the number $T$ of non-zero terms of $f$, in the number $n$ of variables. The first one is a Monte Carlo randomized algorithm. Both of our algorithms work over any finite fields $F_q$ with large characteristic.
Abstract: In this paper, we propose two new interpolation algorithms for sparse multivariate polynomials represented by a straight-line program(SLP).
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