31 citations · 82 across the 22 of their papers we have counts for
29 papers
Deterministic identity testing paradigms for bounded top-fanin depth-4 circuits
Pranjal Dutta, Prateek Dwivedi, Nitin Saxena
Polynomial Identity Testing (PIT) is a fundamental computational problem. The famous depth- reduction result by Agrawal and Vinay (FOCS 2008) has made PIT for depth- circuits…
Computing Igusa's local zeta function of univariates in deterministic polynomial-time
Ashish Dwivedi, Nitin Saxena
Igusa's local zeta function is the generating function that counts the number of integral roots, , of , for all . It is a famous r…
Special-case Algorithms for Blackbox Radical Membership, Nullstellensatz and Transcendence Degree
Abhibhav Garg, Nitin Saxena
Radical membership testing, and the special case of Hilbert's Nullstellensatz (HN), is a fundamental computational algebra problem. It is NP-hard; and has a famous PSPACE algorithm…
Counting basic-irreducible factors mod in deterministic poly-time and -adic applications
Ashish Dwivedi, Rajat Mittal, Nitin Saxena
Finding an irreducible factor, of a polynomial modulo a prime , is not known to be in deterministic polynomial time. Though there is such a classical algorithm that {\em…
Efficiently factoring polynomials modulo
Ashish Dwivedi, Rajat Mittal, Nitin Saxena
Polynomial factoring has famous practical algorithms over fields-- finite, rational \& -adic. However, modulo prime powers it gets hard as there is non-unique factorization and…
Algebraic dependencies and PSPACE algorithms in approximative complexity
Zeyu Guo, Nitin Saxena, Amit Sinhababu
Testing whether a set of polynomials has an algebraic dependence is a basic problem with several applications. The polynomials are given as algebraic circuits. Algebra…