In many fields of modern mathematics specialised scientific software becomes increasingly important. Therefore, tremendous effort is taken by numerous groups all over the world to develop appropriate solutions. Topics include commutative algebra, group and number theory, as well as algebraic, computational, discrete, and differential geometry.

With growing complexity of these software systems, the designers more than ever feel compelled to include functionality which might require techniques other than the roots of the respective system. Those techniques can often be found in other branches of mathematics. Instead of implementing new software individually it is preferable to make use of already existing stable software written by experts in their field. This raises the question for interfaces between software components. Several frameworks have been suggested and are still being discussed.

Topics of the seminar include, but are not restricted to, the following.

• algorithms which require components from both geometry and algebra
• abilities and limitations of existing software systems from algebra and geometry
• general purpose interfaces for mathematical software
• visualisation components
• XML based techniques for the presentation and the exchange of mathematical objects

This seminar shall serve as a forum for authors of mathematical software where they can formulate their needs and display the expertise they can contribute to other systems. Presently programmers in algebra and geometry seldom have the opportunity to meet and exchange their ideas. The goal is to combine a great variety of features of well-established systems in order to build yet more powerful tools. We want to discuss and explore ways to build and apply hybrid math software systems.