It is proved that for every k there exist k triples of positive integers with the same sum and the same product. In this paper we solve the problem D.16 from the book [1] by proving the following Theorem. For every k there exist infinitely many primitive sets of k triples of positive integers with the same sum and the same product. (A set S of triples is called primitive if the greatest common ...

A domain of semantic analysis is presented: invoices. This domain has been successfully tackled by us with a practical system. The analysis of scenario and system yield, first, ideas how to decompose a scenario or domain and, second, concepts resulting from the decomposition. It is then shown how to further develop the concepts found, and how to enter into a system design and implementation. Th...

We notice that some recent explicit results about linear recurrent sequences over a ring R with 1 were already obtained by Agou in a 1971 paper by considering the euclidean division of polynomials over R. In this paper we study an application of these results to the case when R = Fq [t] and q is even, completing Agou’s work. Moreover, for even q we prove that there is an infinity of indices i s...

The main purpose of this paper is to prove an important generalization of the construction of the Incidence Divisor given in [BMg1] in the case of an ambient manifold. Let us first recall briefly the setting : let Z be a complex manifold and (X s) s∈S an analytic family of (closed) n−cycles in Z parametrized by a reduced complex space S. To a (n+1)−codimensional subspace Y in Z, which is assume...

A b s t r a c t . The fastest known algorithms in classical algebra make use of signature functions. That is, reducing computat ion with formulae to computing with the integers modulo p, by substi tut ing random numbers for variables, and mapping constants modulo p. This idea is exploited in specific algorithms in computer algebra systems, e.g. algorithms for polynomial greatest common divisors...

This paper continues the series of papers on Inverse Additive Number Theory published in 1955–1964 (see references [84]–[92], [98] in [2]). Throughout the paper, we work with the set A ⊂ Z of cardinality |A| = k ≥ 3. We assume that A = {a0 = 0 < a1 < · · · < ak−1} and that the greatest common divisor of the numbers from A is 1. Let T denote the cardinality of the set 2A = A + A of all pairwise ...

1. Linear series on curves 1.1. Terminology and notation 1.2. Morphisms from linear series; Castelnuovo’s genus bound 1.3. Linear series from morphisms 1.4. Relation between linear series and morphisms 1.5. Hermitian invariants; Weierstrass semigroups I 2. Weierstrass point theory 2.1. Hasse derivatives 2.2. Order sequence; Ramification divisor 2.3. D-Weierstrass points 2.4. D-osculating spaces...

Given n polynomials in n variables of respective degrees d1, . . . , dn, and a set of monomials of cardinality d1 . . . dn, we give an explicit subresultant-based polynomial expression in the coefficients of the input polynomials whose non-vanishing is a necessary and sufficient condition for this set of monomials to be a basis of the ring of polynomials in n variables modulo the ideal generate...