Algebra, Geometry and Computer Algebra Group

Software in mathematical research

Mathematical research is currently showing two significant trends: Research is becoming more and more interdisciplinary, and at the same time, research questions are increasingly requiring computational methods to cope with the emerging complexity. Many researchers use modern computer algebra systems and collections of mathematical data.

In the working group the systems SINGULAR, ANTIC, Hecke and Nemo as well as the comprehensive system of the next generation OSCAR are developed.

SINGULAR

Singular is a computer algebra system for polynomial calculations with a special focus on commutative and noncommutative algebra, algebraic geometry, and singularity theory. With Singular, the long-standing tradition in the development of world-leading computer algebra systems at the University of Kaiserslautern has been established.

ANTIC, Hecke und Nemo

ANTIC, Hecke and Nemo are new software projects of number theory, which focus on calculations in and with number fields and certain finite rings. They are written in the programming languages C and Julia.

OSCAR

All existing systems together with the external systems GAP and Polymake are to be integrated into the new comprehensive computer algebra system OSCAR developed within the framework of the SFB-TRR 195. This will achieve a next-generation system. The goal is to sustainably enrich worldwide mathematical research through this tool.

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