4 papers · 1 filter
Sparse Polynomial GCD Cannot Be Computed in Fixed-output Polynomial Time
Ruichen Qiu, Yichuan Cao, Qiao-Long Huang +2
This paper shows that, assuming , sparse univariate polynomial GCD cannot be computed in fixed-output polynomial time over any fixed computable field. Pre…
Sparse Polynomial Divisibility Test over Finite Field is CoNP-hard
Yichuan Cao, Ruichen Qiu, Qiao-Long Huang +2
In this paper, we show that deciding whether a sparse polynomial does not divide another sparse polynomial exactly over finite fields is NP-hard under BPP many-one reductions. Equi…
Quasi-linear Time Multiplication of Sparse Polynomials with Integer Coefficients
Qiao-Long Huang, Yichuan Cao, Ruichen Qiu +1
Sparse polynomial multiplication is a fundamental problem in computer algebra and the theory of computation, and the development of a quasi-linear time output-sensitive multiplicat…
Deterministic Interpolation of Sparse Black-box Multivariate Polynomials using Kronecker Type Substitutions
Qiao-Long Huang, Xiao-Shan Gao
In this paper, we propose two new deterministic interpolation algorithms for a sparse multivariate polynomial given as a standard black-box by introducing new Kronecker type substi…