If F is a field and n is a nonnegative integer, then a polynomial of degree n over F is a formal sum of the form $$P(x) = {a_0} + {a_1}x + \\\cdots + {a_n}{x^n}$$ With a i ∈ F for i = 0, .., n, a n ≠ 0 and x an indeterminate. A polynomial P(χ...
Define Polynomials. Polynomials synonyms, Polynomials pronunciation, Polynomials translation, English dictionary definition of Polynomials. adj. Of, relating to, or consisting of more than two names or terms. n. 1. A taxonomic designation consisting of m
A univariate, sparse, integer polynomial class. That is, a polynomial in only one indeterminate, X, that only tracks terms with non-zero coefficients, and all coefficients are BigInteger integers. NOTE: All arithmetic is done symbolically. That means the result a arithmetic operation on two poly...
Let K be a field and let N = {1,2,...} be the set of all positive integers. Let R_n = K[x_(ij)/1 ≤ i ≤ n, j ∈ N] be the ring of polynomials in x_(ij) (1 ≤ i ≤ n, j ∈ N) over K. Let S_n = Sym({l, 2,..., n}) and Sym(N) be the groups ...
POLYNOMIALS AND TRIGONOMETRIC POLYNOMIALS ORTHOGONAL ON THE UNIT CIRCLE An orthonormal basis of L2( ; ), a nonnegative Borel measure on the unit circle , consisting of trigonometric polynomials is presented which generalizes th... B Engelhardt - International Workshop on Orthogonal Polynomials...
[polynomials]In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer expone...Sign up to watch this tag and see more personalized contentWatch...
The meaning of POLYNOMIAL is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power (such as a + bx + cx2). How to use polynomial in a sente
At least one complex root exists for every non-constant single-variable polynomial with complex coefficients. Property 12: If P(x) is a polynomial with real coefficients and has one complex zero (x = a – bi), then x = a + biwill also be a zero of P(x). Also, x2– 2ax + a2...
A Nontrivial Lower Bound for an NP Problem on Automata Summary: An NP problem L is linearly NP-complete if each NTIME (n)-problem is reducible to L in linear time on a deterministic Turing machine. This implies... E Grandjean - 《Siam Journal on Computing》 被引量: 54发表: 1990年 ...
Finally, if a and b have a small number of non-trivial zeros, the complexity solving the IP instance is reduced to n 6 + q . This allows to break a public-key authentication scheme based on IP1S, and to break all the IP challenges proposed by Patarin in 1996 in practical time: ...