D. Grigoriev

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20022008

most citedPolynomial-time computing over quadratic maps I: sampling in real algebraic sets

31 citations · 48 across the 11 of their papers we have counts for

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math.AP2008

Non-holonomic Ideals in the Plane and Absolute Factoring

D. Grigoriev, F. Schwarz

We study {\it non-holonomic} overideals of a left differential ideal $J \subset F [\partial_{x}, \partial_{y}]$ in two variables where $F$ is a differentially closed field of characteris…

math.AP2008★ 1 cited

Analogue of Newton-Puiseux series for non-holonomic D-modules and factoring

D. Grigoriev

We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series s…

math.AP2007★ 2 cited

Complexity of Janet basis of a D-module

Alexander Chistov, Dima Grigoriev

We prove a double-exponential upper bound on the degree and on the complexity of constructing a Janet basis of a $D$ -module. This generalizes a well known bound on the complexity o…