The report "Elementary Analysis" and "Algorithmic Linear Algebra" (Pdf file, 140 KB) was written for the ICMI (International Commission on Mathematical Instruction) Study "On the Teaching and Learning of Mathematics at University Level" in November 1998. For reasons which we do not know the editors did not publish the text. It contains short descriptions of the most important projects carried out in the "Heinrich-Behnke-Seminar für Didaktik der Mathematik".
The 'Sums of Powers Algorithm' (SPA) is the last one of six new central algorithms published in the book "Algorithmische Lineare Algebra" (Algorithmic Linear Algebra, Editors: Vieweg Verlag Wiesbaden, 1997, written in German). Here you find a paper entitled "An Efficient Reliable Algorithm for the Approximation of All Polynomial Roots Based on the Method of D. BERNOULLI " (Pdf file, 224 KB).
Many of the facts which let the corresponding rootfinding program SPA (Maple-V5 text file, 32 KB) fulfill the well-known criteria of reliability and efficiency have been developed and tested by D. GUNSTHÖVEL who planned to write a dissertation in this field.
"GaPFilL" (Graphics as PostScript Filtered for LaTeX) is a new method for the generation of LaTeX picture environments in a four step way:
i) Construction of the desired figure with a drawing program;
ii) Export as a PostScript file;
iii) Application of a Perl filter program to the PostScript text;
iv) Transfer of the resulting code into a LaTeX document.
The following two prototypes of filter programs are written with MacPerl 5.6 for the Macintosh version of Cabri GéomètreTMII and for the PostScript driver "Virtual Printer". The first program requires the package ebezier. The second filter in addition supplies the package pict2e :
CABebez.pl (text file, 28 KB),
CABpict.pl (text file, 32 KB).
Since April 2006 these two Perl programs and an English documentation entitled "How to Generate LaTeX Picture Environments Using the GaPFilL Method" (Pdf-Programm, 607 KB) are available in the Internet archive "Comprehensive TeX Archive Network" (CTAN, http://dante.ctan.org/CTAN).
A new Perl filter program OOopict.pl (Text-File, 28 KB) is added for the powerful free drawing software OpenOffice.org 3 Draw which has its own PostScript generator not depending on the operating systems supplied by OpenOffice.org, namely Linux, Mac OS, Unix and Windows. The English documentation contained in the CTAN is entitled "How to Generate LaTeX Picture Environments Using OpenOffice.org 3 Draw" (Pdf-Programm, 366 KB).
The complete actual folder of the CTAN can be downloaded as zip archive:
gapfill.zip (zip archive, 774 KB):
Siegfried Kurz who was enthusiastic about the above-mentioned book "Algorithmische Lineare Algebra" has voluntarily translated 180 of its 405 pages. Here is a scanned version of his script "Algorithmic Linear Algebra" (Pdf file, 1.5 MB).
