Singular

7.7.3 References and history of LETTERPLACE

LETTERPLACE has undergone several stages of development.

The first one, the pure Letterplace implementation for homogeneous ideals, was created by V. Levandovskyy and H. Schoenemann in 2007-2009.

Later in 2010-2014, experiments with advanced (among other, with shift-invariant) data structures were performed by V. Levandovskyy, B. Schnitzler and G. Studzinski, and new libraries for -dimension, -bases, and Ufnarovskij graph were written.

The next stage started in 2017, when K. Abou Zeid joined the team of H. Schoenemann and V. Levandovskyy. Those recent activities led to the change of interface to the one, usual in the free algebra. The Letterplace data structure is still at heart of the implementation, though not explicitly visible by default.

References:

[LL09]: Roberto La Scala and Viktor Levandovskyy, "Letterplace ideals and non-commutative Groebner bases", Journal of Symbolic Computation, Volume 44, Issue 10, October 2009, Pages 1374-1393, see http://dx.doi.org/10.1016/j.jsc.2009.03.002.

[LL13]: Roberto La Scala and Viktor Levandovskyy, "Skew polynomial rings, Groebner bases and the letterplace embedding of the free associative algebra", Journal of Symbolic Computation, Volume 48, Issue 1, January 2013, Pages 1374-1393, see http://dx.doi.org/10.1016/j.jsc.2012.05.003 and also http://arxiv.org/abs/1009.4152.

[LSS13]: Viktor Levandovskyy, Grischa Studzinski and Benjamin Schnitzler , "Enhanced Computations of Groebner Bases in Free Algebras as a New Application of the Letterplace Paradigm", Proc. ISSAC 2013, ACM Press, 259-266, see https://doi.org/10.1145/2465506.2465948.

[L14]: Roberto La Scala, "Extended letterplace correspondence for nongraded noncommutative ideals and related algorithms", International Journal of Algebra and Computation, Volume 24, Number 08, Pages 1157-1182, 2014, see also https://doi.org/10.1142/S0218196714500519.