The Classification of Real Singularities Using SINGULAR. Part I: Splitting Lemma and Simple Singularities

We present algorithms to classify isolated hypersurface singularities over the real numbers according to the classification by V.I. Arnold (Arnold et al., 1985). This first part covers the splitting lemma and the simple singularities; a second and a third part will be devoted to the unimodal singularities up to corank 2. All algorithms are implemented in the SINGULAR library realclassify.lib (Marais and Steenpass, 2012).Comment: 12 pages, 1 tabl

Differentiated speed limits that will work

Paper presented at the 31st Annual Southern African Transport Conference 9-12 July 2012 "Getting Southern Africa to Work", CSIR International Convention Centre, Pretoria, South Africa.Following a research report (Van As and Joubert, 1998) and a fatal bus accident involving British tourists in 1999 the then Minister of Transport reduced the maximum speed limit for public transport vehicles (buses and minibus taxis) to 100km/h. This meant that light vehicles and public transport vehicles could have different speed limits on the same road – something that already applied to heavy vehicles. The purpose of this paper is to determine the effectiveness of the different speed limits for different vehicle classes on the same road. The effectiveness is defined as the extent to which the drivers of the different types of vehicle keep to these limits. The paper describes a project in which the free-flow speeds of different types of vehicle were measured on roads where the geometry was such that it did not affect the speeds. The speeds of nearly 9 000 vehicles were determined on 12 sections of two, four and six-lane roads in the Western and Eastern Cape Provinces where the general speed limit (ie for light vehicles) is 120 km/h. It was found that 85% of the drivers of light vehicles and buses do keep to their respective limits, but that the drivers of heavy vehicles and minibus taxis to a large extent exceed their limits.This paper was transferred from the original CD ROM created for this conference. The material was published using Adobe Acrobat 10.1.0 Technology. The original CD ROM was produced by Document Transformation Technologies Postal Address: PO Box 560 Irene 0062 South Africa. Tel.: +27 12 667 2074 Fax: +27 12 667 2766 E-mail: nigel@doctech URL: http://www.doctech.co.zadm201

Mora’s holy graal: Algorithms for computing in localizations at prime ideals

This article discusses a computational treatment of the localization AL of an affine coordinate ring A at a prime ideal L and its associated graded ring Gra(AL) with the means of standard basis techniques. Building on Mora’s work, we present alternative proofs on two of the central statements and expand on the applications mentioned by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of AL. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.The African Institute for Mathematical Sciences, the Department of Mathematics and Applied Mathematics of the University of Pretoria and a grant awarded by Wolfram Decker.http://www.worldscientific.com/worldscinet/ijachb2017Mathematics and Applied Mathematic

Mora’s holy graal: Algorithms for computing in localizations at prime ideals

This article discusses a computational treatment of the localization AL of an affine coordinate ring A at a prime ideal L and its associated graded ring Gra(AL) with the means of standard basis techniques. Building on Mora’s work, we present alternative proofs on two of the central statements and expand on the applications mentioned by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of AL. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.The African Institute for Mathematical Sciences, the Department of Mathematics and Applied Mathematics of the University of Pretoria and a grant awarded by Wolfram Decker.http://www.worldscientific.com/worldscinet/ijachb2017Mathematics and Applied Mathematic