A survey on signature-based Gr\"obner basis computations

This paper is a survey on the area of signature-based Gr\"obner basis algorithms that was initiated by Faug\`ere's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research.Comment: 53 pages, 8 figures, 11 table

The Deadlock of the EU Budget: An Economic Analysis of Ways In and Ways Out

Most of the EU budget is spent on redistribution. Large sums of money are transferred from the member state governments to Brussels and back to these governments. Some member states end up as net receivers and some as net payers. Most economists agree that the resources of the budget should be reallocated from redistribution towards the provision of more Union-wide public goods. While such appeals have been made for years, little change has been observed. We want to explain why. We propose to distinguish two periods. In the early years of the Community, some larger member states or coalitions of member states were able to credibly threaten to terminate membership if their claims on budgetary resources were not fulfilled. Their activity has created a redistributive status quo to which, in the second period, the budgetary rules of the Treaty were applied. It is shown that the combination of the Council’s qualified majority rule on the expenditure side and the unanimity rule on the revenue side and on the programs are largely responsible for creating a deadlock in the status quo with large redistribution and few Union-wide public goods. In order to break the deadlock, a complementary budget procedure is proposed on the basis of voting by veto.