Geodesic
An effective construction of a small number of equations defining an algebraic variety
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 140-156 Cet article a éte moissonné depuis la source Math-Net.Ru

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Consider a system of polynomial equations in $n$ variables of degrees at most $d$ with the set of all common zeros $V$. We suggest subexponential time algorithms (in the general case and in the case of zero characteristic) for constructing $n+1$ equations of degrees at most $d$ defining the algebraic variety $V$. Further, we construct $n$ equations defining $V$. We give an explicit upper bound on the degrees of these $n$ equations. It is double exponential in $n$. The running time of the algorithm for constructing them is also double exponential in $n$. 
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A. L. Chistov. An effective construction of a small number of equations defining an algebraic variety. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIII, Tome 507 (2021), pp. 140-156. http://geodesic.mathdoc.fr/item/ZNSL_2021_507_a7/

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