Testing degenerate polynomials
✍ Scribed by Mihai Cipu; Ismaïla Diouf; Maurice Mignotte
- Book ID
- 105867592
- Publisher
- Springer
- Year
- 2011
- Tongue
- English
- Weight
- 160 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0938-1279
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let S = N" be a finite set (cq ..... %) of exponents. We construct explicitly a testing set Ts , N" with k elements t~ ..... tk (namely t~ = (2 ~l ..... 2~I')), such that if , a=X~e~[x, ..... x,.], then there exists i (1 \_< i < k) such that P(q) ~ O.
It is well known that the condition under which a quadratic in two variables reduces to a product of two linear factors is that the determinant of the associated quadratic form should be zero. This result is generalized to the case of a polynomial of degree n. For the degree n case there are 1 2 n À
Consider a system F of n polynomial equations in n unknowns, over an algebraically closed field of arbitrary characteristic. We present a fast method to find a point in every irreducible component of the zero set Z of F . Our techniques allow us to sharpen and lower prior complexity bounds for this