Implicit rule formation in symbolic computation

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

Supporting Creativity in Symbolic Computation

For many people, creativity and computers are contradictory concepts: how can novel concepts arise in a machine which is designed to only do what it is programmed to do? In this paper, I give a computational model of at least one form of creativity and describe how the processes underlying it can be implemented in symbolic computation. Finally, I discuss the lessons that can be learned from the...

Merging Sub-symbolic and Symbolic Computation

In a recent short paper and a report (see [Neto et al. 98] and [Neto and Costa 99]) it was shown that programming languages can be translated efficiently on recurrent (analog, rational weighted) neural nets, using bounded resources. This fact was achieved by creating a neural programming language called NETDEF, such that each program corresponds to a modular neural net that computes it. This fr...

Hot Topics in Symbolic Computation

Challenges of Symbolic Computation

The success of the symbolic mathematical computation discipline is striking. The theoretical advances have been continuous and significant: Gröbner bases, the Risch integration algorithm, integer lattice basis reduction, hypergeometric summation algorithms, etc. From the beginning in the early 1960s, it has been the tradition of our discipline to create software that makes our ideas readily ava...