lt;i>n . We prove an effective affine Nullstellensatz of the following particular formdoi:10.1007/bf01200407Marc GiustiJoos HeintzJuan SabiaBirkhäuser-VerlagComputational ComplexityM. Giusti, J. Heintz, J. Sabia. “On the efficiency of effective Nullstellensätze”, Computational Complexity 3 pp....
With that, one may decide if $(*)$ has a solution by linear algebra, since $(*)$ is a finite-dimensional linear system with the $g_i$'s as unknowns. This procedure is called the "effective nullstellensatz". To say what "intractable" means in our conjecture, it is necessary to ...
On the effective Nullstellensatz Let K be an algebraically closed field and let X subset of K-m be an n-dimensional affine variety. Assume that f(1),..., f(k) are polynomials which have no common zeros on X. We estimate the degrees of polynomials A(i) is an element of K... Z ...
Stéphane Gaubert - The Nullstellensatz and Positivstellensatz for Sparse Tropica 45:37 Marek Bożejko - Fock spaces associated with Coxeter groups of type B 49:09 Marek Kuś - Perception of visual art and topological data analysis 43:00 Mikhael Gromov - 16 Probability, symmetry, linearity...
01 Stéphane Gaubert - The Nullstellensatz and Positivstellensatz for Sparse Tropica 45:37 Marek Bożejko - Fock spaces associated with Coxeter groups of type B 49:09 Marek Kuś - Perception of visual art and topological data analysis 43:00 Mikhael Gromov - 16 Probability, symmetry, linearity...
Nullstellensatz,O Sánchez,A Ovchinnikov 摘要: Understanding bounds for the effective differential Nulls tellensatz is a central problem in differential algebraic g eometry. Recently, several bounds have been obtained using Dic ksonian and antichains sequences (with a given growth rate). In the ...
At the end, while we proved that Schubert positivity is in AM (assuming GRH) using the Hilbert’s Nullstellensatz, a key problem in AG. Faced with a clash of core beliefs, Colleen and I needed to completely rethink the strategy and try to explain what do our results really mean?
then the complex number identity is generated by the elimination method; finally, the closure property under all four operations of real numbers is employed to prove the proposition. A test on more than 300 geometric problems shows that the proposed method is highly effective, and the corresponding...
We correct a small gap found in the paper. This gap is due to an inequality that does not generally hold. However, under one additional assumption, it does hold. In this note, we provide a detailed proof of this. We then point out that this assumption is satisfied in all instances in...
We correct a small gap found in the authors' paper 'On bounds for the\neffective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is\ndue to an inequality that does not generally hold. However, under one\nadditional assumption, it does hold. In this note, we provide...