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We describe an algorithm to compute Grobner bases which combines F4-style reduction with the F5 criteria. Both F4 and F5 originate in the work of Jean-Charles Faug`ere, who has successfully computed many Grobner bases that were previously considered intractable. Another description of a similar algorithm already exists in Gwenole Ars dissertation; unfortunately, this is only available in French, and although an implementation exists, it is not made available for study. We not only describe the algorithm, we also direct the reader to a study implementation for the free and open source Sage computer algebra system. We conclude with a short discussion of how the approach described here compares and contrasts with that of Ars dissertation.
We present an algebra related to the Coxeter group of type F4 which can be viewed as the Brauer algebra of type F4 and is obtained as a subalgebra of the Brauer algebra of type E6. We also describe some properties of this algebra.
We present a survey on the developments related to Groebner bases, and show explicit examples in CoCoA. The CoCoA project dates back to 1987: its aim was to create a mathematician-friendly computational laboratory for studying Commutative Algebra, mo
The characters of irreducible finite dimensional representations of compact simple Lie group G are invariant with respect to the action of the Weyl group W(G) of G. The defining property of the new character-like functions (hybrid characters) is the
In this paper, we solve the equation of the title under the assumption that $gcd(x,d)=1$ and $ngeq 2$. This generalizes earlier work of the first author, Patel and Siksek [BPS16]. Our main tools include Frey-Hellegouarch curves and associated modular
The population of comets hosted by the Oort cloud is heterogeneous. Most studies in this area focused on highly active objects, those with small perihelion distances or examples of objects with peculiar physical properties and/or unusual chemical com