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Reports tagged with algebraic independence:
TR11-022 | 14th February 2011
Malte Beecken, Johannes Mittmann, Nitin Saxena

Algebraic Independence and Blackbox Identity Testing

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials $\{f_1,\ldots, f_m\} \subset \mathbb{F}[x_1,\ldots, x_n]$ are called algebraically independent if there is no non-zero polynomial $F$ such that $F(f_1, \ldots, f_m) = 0$. The transcendence degree, $\mbox{trdeg}\{f_1,\ldots, f_m\}$, is the maximal ... more >>>

TR12-014 | 20th February 2012
Johannes Mittmann, Nitin Saxena, Peter Scheiblechner

Algebraic Independence in Positive Characteristic -- A p-Adic Calculus

A set of multivariate polynomials, over a field of zero or large characteristic, can be tested for algebraic independence by the well-known Jacobian criterion. For fields of other characteristic $p>0$, there is no analogous characterization known. In this paper we give the first such criterion. Essentially, it boils down to ... more >>>

TR15-194 | 30th November 2015
Mrinal Kumar, Shubhangi Saraf

Arithmetic circuits with locally low algebraic rank

Revisions: 1

In recent years there has been a flurry of activity proving lower bounds for
homogeneous depth-4 arithmetic circuits [GKKS13, FLMS14, KLSS14, KS14c], which has brought us very close to statements that are known to imply VP $\neq$ VNP. It is a big question to go beyond homogeneity, and in ... more >>>

TR18-212 | 26th December 2018
Prerona Chatterjee, Ramprasad Saptharishi

Constructing Faithful Homomorphisms over Fields of Finite Characteristic

We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken, Mittmann and Saxena (Information and Computing, 2013), and exploited by them, and Agrawal, Saha, Saptharishi and Saxena (Journal of Computing, 2016) to design algebraic independence based identity tests ... more >>>

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