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Generic polynomial
About: Generic polynomial is a research topic. Over the lifetime, 608 publications have been published within this topic receiving 6784 citations.
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TL;DR: In this article, the Sylvester resultant of f and g was considered, where f is a generic polynomial of degree 2 or 3 and g is a generative polynomial of degree n.
Abstract: Let n be a positive integer. We consider the Sylvester resultant of f and g, where f is a generic polynomial of degree 2 or 3 and g is a generic polynomial of degree n. If f is a quadratic polynomial, we find the resultant's height. If f is a cubic polynomial, we find tight asymptotics for the resultant's height.
2 citations
01 Jul 2014
2 citations
TL;DR: In this article, the 0,1 distribution in the highest level sequence of a primitive sequence over Z 2 e generated by a primitive polynomial of degree n has been studied, and it is shown that the larger n is, the closer to 1/2 the proportion of 1 will be.
Abstract: In this paper, we discuss the 0,1 distribution in the highest level sequence a e -1 of primitive sequence over Z 2 e generated by a primitive polynomial of degree n . First we get an estimate of the 0,1 distribution by using the estimates of exponential sums over Galois rings, which is tight for e relatively small to n . We also get an estimate which is suitable for e relatively large to n . Combining the two bounds, we obtain an estimate depending only on n , which shows that the larger n is, the closer to 1/2 the proportion of 1 will be.
2 citations
22 Aug 1995
TL;DR: For polynomials over the integers or rationals, it is known that this problem is exponential space complete as mentioned in this paper, and the complexity results known for a number of problems related to polynomial ideals are discussed.
Abstract: A polynomial ideal membership problem is a (w+1)-tuple P=(f, g1,g2, ..., g w ) where f and the g i are multivariate polynomials over some ring, and the problem is to determine whether f is in the ideal generated by the g i . For polynomials over the integers or rationals, it is known that this problem is exponential space complete. We discuss complexity results known for a number of problems related to polynomial ideals, like the word problem for commutative semigroups, a quantitative version of Hilbert's Nullstellensatz, and the reachability and other problems for (reversible) Petri nets.
2 citations
2 citations