COmputational COmmutative Algebra
Villa Gualino, Torino, Italy
May 31 - June 5, 1999
Theorema: A New Kind of Mathematical Software System
Research Institute for Symbolic Computation
Johannes Kepler University, Linz, Austria
In the Theorema system, the user can
The emphasis of the system is on providing various automated provers. The
proofs generated by these provers read like proofs generated by human
mathematicians, i.e. they are sequences of formulae with intermediate
"explanations" in natural language. The proofs are presented in
hierarchical text cells that can be opened and closed so that proof details
can be shown or not according to the taste of the reader.
- enter definitions, axioms, propositions, algorithms and other formal math
text in a syntax, which is as close as possible to the "usual" syntax of
- group these formal texts in hierarchies of "knowledge bases"
- evaluate, solve, and prove formulae using knowledge bases
The system is implemented in Mathematica 3.0 and uses, in particular, the
advanced front-end facility of this system.
In the talk we will give various examples that will
Theorema reflects the personal view and experience of the speaker on
mathematical research and education and is currently under development by a
working group at RISC directed by the speaker.
- demonstrate the touch and feel of the system
- explain the logical proof techniques and the implementation techniques used
- and give an impression of how a system of this type will change they way
we can do mathematical research and teach mathematics.