Recent research towards integrating symbolic mathematical reasoning and computation has led to prototypes of interfaces and environments. This paper introduces computation theories and structures to represent mathematical objects and applications of algorithms occuring in algorithmic services. The composition of reasoning and computation theories and structures provide a formal framework for th...

Conjectures involving infinite families of restricted partition congruences can be difficult to verify for a number individual cases, even with computer. We demonstrate how the machinery Radu's algorithm may modified and employed efficiently check very large cases such conjectures. This allows substantial evidence collected given conjecture, before complete proof is attempted.

In the paper which inspired the SC project, [E. Ábráham, Building Bridges between Symbolic Computation and Satisfiability Checking, Proc. ISSAC ’15, pp. 1–6, ACM, 2015] the author identified the use of sophisticated heuristics as a technique that the Satisfiability Checking community excels in and from which it is likely the Symbolic Computation community could learn and prosper. To start this ...

Content 1. Computational turn seen from different perspectives 2. Models of computation 2.1 Turing machine model of computation and its scope 2.2 Computation as information processing 3. Computation and information 4. The difference between mathematical and computational (executable) models 5. Computation in the wild 5.1 Physical computation – computing nature 5.2 New computationalism. Non-symb...