An algorithm is discussed to compute the exponential representation of principal units in a finite extension field F of the p-adic rationals. Also is discussed the computation of roots of unity... Show moreAn algorithm is discussed to compute the exponential representation of principal units in a finite extension field F of the p-adic rationals. Also is discussed the computation of roots of unity contained in F and a special kind of principal unit, which is called a distinguished unit. The properties of norm residue symbols are given and also an algorithm to compute the norm residue symbol. Moreover a strongly distinguished unit is defined and an algorithm is given to compute such a unit. All the algorithms are polynomial time algorithms. Show less
The importance and character of exchange in the Carolingian period has long been a subject of academic debate. There is much discussion on the relative importance of local, regional and... Show moreThe importance and character of exchange in the Carolingian period has long been a subject of academic debate. There is much discussion on the relative importance of local, regional and international exchange, the role of various groups of actors, and the nature of exchange. What is largely lacking is a consideration of non-elite rural dwellers as constitutive elements in the economy. The present study focusses on the role of rural communities in the development of exchange systems during the Carolingian period. To what extent did the consumptive preferences of rural communities influence the flow of goods at a regional and interregional level? This is examined by cataloguing the finds from Carolingian sites in the Netherlands and comparing their distributions between regions. It can be demonstrated that rural dwellers indeed played a part in developments in the production and distribution of goods. At the same time the conducted analyses do not allow the establishment of a single model of how rural dwellers participated in exchange networks of the period. In fact, this study contends that there is little meaning in determining the relative importance of different groups in society for the establishment and maintenance of exchange networks at any one time. Show less
Why should we look at art when we talk about nuclear power? Nuclear power, military and civilian, has been framed as a solution many times: a solution to end war and sustain global peace, a... Show moreWhy should we look at art when we talk about nuclear power? Nuclear power, military and civilian, has been framed as a solution many times: a solution to end war and sustain global peace, a solution for growing energy demands in rich countries, and more recently, a solution to climate change. All of these solutions soon produced a number of new problems, or turned into problems themselves, contributing to the wicked complexity of the techno-human condition. Yet, it is a mistake to turn away from complexity and seek answers in the form of certainties. After all, the ‘solutions’ listed above are a product of creating certainties where there are none, of trying to overcome complexity and ambiguity.In this study, I argue that art is relevant to the nuclear debate not despite, but because the answers it offers to the societal questions raised by nuclear technologies suggest other problems. Drawing on Braden R. Allenby and Daniel Sarewitz’s notion of ‘intelligent muddling’ as a strategy to navigate the techno-human condition, I show through a series of close readings of recent artistic responses to nuclear energy production and its ‘by-products’ that art points towards ways of muddling through nuclear complexity. Show less
