Topic
Divisor
About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.
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TL;DR: In this article, it was shown that any divisor on the chain of loops that is rational over the value group lifts to a divisors of the same rank on, confirming a conjecture of Cools, Draisma, Robeva, and the third author.
Abstract: Let be a curve over a complete valued field having an infinite residue field and whose skeleton is a chain of loops with generic edge lengths. We prove that any divisor on the chain of loops that is rational over the value group lifts to a divisor of the same rank on , confirming a conjecture of Cools, Draisma, Robeva, and the third author.
40 citations
TL;DR: In this article, the authors studied the problem of parametrizing the points (s,yx,..., y) such that y is a (possibly infinitely near) m-fold point of D. They obtained a general formula which yields, as special cases, the formula of de Jonquieres and other classical results of Enumerative Geometry.
Abstract: Given a family of divisors {/),} in a family of smooth varieties { Ys} and a sequence of integers mx, . . . , m,, we study the scheme parametrizing the points (s,yx, . . . ,y,) such that^, is a (possibly infinitely near) m,-fold point of D,. We obtain a general formula which yields, as special cases, the formula of de Jonquieres and other classical results of Enumerative Geometry. We also study the questions of finiteness and the multiplicities of the solutions.
39 citations
TL;DR: The architecture presented for the proposed algorithm is faster than previously proposed radix-4 dividers, which require at least four digits of the partial remainder to be observed to determine quotient digits.
Abstract: In this paper we present a fast radix-4 division algorithm for floating point numbers. This method is based on Svoboda's division algorithm and the radix-4 redundant number system. The algorithm involves a simple recurrence with carry-free addition and employs prescaling of the operands. In the proposed divider implementation, each radix-4 digit (belonging to set {-3,...,+3}) of the quotient and partial remainder is encoded using two radix-2 digits (belonging to the set {-1,0,+1}) and this leads to hardware simplicity. The quotient digits are determined by observing three most-significant radix-2 digits of the partial remainder and independent of the divisor. The architecture presented for the proposed algorithm is faster than previously proposed radix-4 dividers, which require at least four digits of the partial remainder to be observed to determine quotient digits. >
39 citations
TL;DR: For any odd prime p, using the cyclotomic classes of order 2 and 4 with respect to GF(p), the perfect and odd perfect Gaussian integer sequences of length p are proposed.
Abstract: A Gaussian integer is a complex number whose real and imaginary parts are both integers. A Gaussian integer sequence is called perfect (odd perfect) if the out-of-phase values of the periodic (odd periodic) autocorrelation function are equal to zero. In this letter, for any odd prime p, using the cyclotomic classes of order 2 and 4 with respect to GF(p), we propose perfect and odd perfect Gaussian integer sequences of length p. Several examples are also given.
39 citations
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TL;DR: Lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors were obtained in this paper for two-point codes on general Hermitian and Suzuki curves.
Abstract: For a given curve X and divisor class C, we give lower bounds on the degree of a divisor A such that A and A-C belong to specified semigroups of divisors. For suitable choices of the semigroups we obtain (1) lower bounds for the size of a party A that can recover the secret in an algebraic geometric linear secret sharing scheme with adversary threshold C, and (2) lower bounds for the support A of a codeword in a geometric Goppa code with designed minimum support C. Our bounds include and improve both the order bound and the floor bound. The bounds are illustrated for two-point codes on general Hermitian and Suzuki curves.
39 citations