All reports by Author Pranjal Dutta:

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TR20-039
| 25th March 2020
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Pranjal Dutta, Nitin Saxena, Thomas Thierauf#### Lower bounds on the sum of 25th-powers of univariates lead to complete derandomization of PIT

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TR17-153
| 9th October 2017
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Pranjal Dutta, Nitin Saxena, Amit Sinhababu#### Discovering the roots: Uniform closure results for algebraic classes under factoring

Pranjal Dutta, Nitin Saxena, Thomas Thierauf

We consider the univariate polynomial $f_d:=(x+1)^d$ when represented as a sum of constant-powers of univariate polynomials. We define a natural measure for the model, the support-union, and conjecture that it is $\Omega(d)$ for $f_d$.

We show a stunning connection of the conjecture to the two main problems in algebraic ... more >>>

Pranjal Dutta, Nitin Saxena, Amit Sinhababu

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the ... more >>>