Enhanced computations of gröbner bases in free algebras as a new application of the letterplace paradigm
Viktor Levandovskyy, Grischa Studzinski, Benjamin Schnitzler · 2013
Recently, the notion of "letterplace correspondence" between ideals in the free associative algebra KX and certain ideals in the so-called letterplace ring KXP has evolved. We continue this research direction, started by La Scala and Levandovskyy, and present novel ideas, supported by the implementation, for effective computations with ideals in the free algebra by utilizing the generalized letterplace correspondance. In particular, we provide a direct algorithm to compute Gröbner bases of non-graded ideals. Surprizingly we realize its behavior as "homogenizing without a homogenization variable". Moreover, we develop new shift-invariant data structures for this family of algorithms and discuss about them.