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7.6 LETTERPLACE

This section describes mathematical notions and definitions used in the experimental LETTERPLACE extension of SINGULAR.

For further details, please, refer to the papers

[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.

All algebras are assumed to be associative $K$-algebras for some field $K$.

7.6.1 Free associative algebras  
7.6.2 Groebner bases for two-sided ideals in free associative algebras  
7.6.3 Letterplace correspondence  
7.6.4 Example of use of LETTERPLACE  
7.6.5 Release notes of LETTERPLACE  


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