Abstract
Given a set of polynomials, P 1(x),⋯, P m(x), one of the most basic questions one can ask about them is whether they have common zeros or not. Hilbert gave a comprehensive answer to this sort of question in his famous theorem. To state it, we will use the following notation:
NOTATION. Let % be the polynomial ideal generated in R := k[x 1,⋯, x n] by the polynomials P 1,⋯P m of respective degrees D 2(=: D) ≥ D 3 ≥ D m ≥ D 1.
Keywords
- Polynomial Ideal
- Common Zero
- Diophantine Approximation
- Homogeneous Ideal
- Algebraic Independence
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
[Hil] D. Hilbert. Über die vollen Invariantensysteme. Math. Ann. 42, (1883), 313-373
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© 2001 Springer-Verlag Berlin Heidelberg
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(2001). The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence. In: Nesterenko, Y.V., Philippon, P. (eds) Introduction to Algebraic Independence Theory. Lecture Notes in Mathematics, vol 1752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44550-1_16
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DOI: https://doi.org/10.1007/3-540-44550-1_16
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