An extension of Buchberger's algorithm and calculationsin enveloping fields of lie algebras
Journal of Symbolic Computation
Non-commutative Gröbner bases in algebras of solvable type
Journal of Symbolic Computation
Finite Gröbner bases in non-Noetherian skew polynomial rings
ISSAC '92 Papers from the international symposium on Symbolic and algebraic computation
An algorithm for constructing Gro¨bner and free Schreier bases in free group algebras
Journal of Symbolic Computation
An introduction to commutative and noncommutative Gro¨bner bases
Selected papers of the second international colloquium on Words, languages and combinatorics
The ideal membership problem in non-commutative polynomial rings
Journal of Symbolic Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Non-commmutative elimination in ore algebras proves multivariate identities
Journal of Symbolic Computation
Algorithms and orders for finding noncommutative Grobner bases
Algorithms and orders for finding noncommutative Grobner bases
Multiplicative bases, Gröbner bases, and right Gröbner bases
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Computational ideal theory in finitely generated extension rings
Theoretical Computer Science
Groebner Bases for Non-Commutative Polynomial Rings
AAECC-3 Proceedings of the 3rd International Conference on Algebraic Algorithms and Error-Correcting Codes
Groebner Bases in Non-Commutative Algebras
ISAAC '88 Proceedings of the International Symposium ISSAC'88 on Symbolic and Algebraic Computation
Opal: A System for Computing Noncommutative Gröbner Bases
RTA '97 Proceedings of the 8th International Conference on Rewriting Techniques and Applications
Complete involutive rewriting systems
Journal of Symbolic Computation
A Singular Introduction to Commutative Algebra
A Singular Introduction to Commutative Algebra
Looking for Gröbner basis theory for (almost) skew 2-nomial algebras
Journal of Symbolic Computation
Non-commutative subsystems of singular
ACM Communications in Computer Algebra
Skew polynomial rings, Gröbner bases and the letterplace embedding of the free associative algebra
Journal of Symbolic Computation
Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals
Journal of Symbolic Computation
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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In this paper we propose a 1-to-1 correspondence between graded two-sided ideals of the free associative algebra and some class of ideals of the algebra of polynomials, whose variables are double-indexed commuting ones. We call these ideals the ''letterplace analogues'' of graded two-sided ideals. We study the behaviour of the generating sets of the ideals under this correspondence, and in particular that of the Grobner bases. In this way, we obtain a new method for computing non-commutative homogeneous Grobner bases via polynomials in commuting variables. Since the letterplace ideals are stable under the action of a monoid of endomorphisms of the polynomial algebra, the proposed algorithm results in an example of a Buchberger procedure ''reduced by symmetry''. Owing to the portability of our algorithm to any computer algebra system able to compute commutative Grobner bases, we present an experimental implementation of our method in Singular. By means of a representative set of examples, we show finally that our implementation is competitive with computer algebra systems that provide non-commutative Grobner bases from classical algorithms.