The paper deals with defining abstract algebraic structures in symbolic computation systems. By adopting a parameterized and object oriented approach, the categories defined for the algebraic structures will be particularized in specific domains. This approach has a good deal of efficiency, conceptual and practical advantages. The paper introduces constructive and algorithmic definitions for th...

We derive a combinatorial formula for quantized Donaldson-Thomas invariants of the m-loop quiver. Our main tools are the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver. 2010 Mathematics Subject Classification: Primary 16G20, secondary 05E05, 14N35

Fifteen years ago, I reviewed Mathematica 2 [1]. I thought that the system then had many very positive and a few very negative aspects. In 1999, I compared Mathematica 3 with six other general purpose computer algebra systems (CASs) [2]. All the systems were quirky (they still are!), but Mathematica performed reasonably well overall and could do some interesting examples, although it still lack...