GVW algorithm over principal ideal domains

Li, Dongmei; Liu, Jinwang; Liu, Weijun; Zheng, Licui

doi:10.1007/s11424-013-2130-5

Cited by 5 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In such a case, we would stop the reductions steps. Still, this would mean that the proxy would involutively reduce to (0, 0) by the final G ∪ H. Now the next lemma 14 is the most important one to prove the termination of the semi-involutive case. Still, we will formulate the fully involutive variant.…”

Section: Proofmentioning

confidence: 97%

“…Moreover, there are various papers about adapting the GVW algorithm to different mathematical applications as well as to make it more efficient. For instance, in [14], the authors are interested in adapting the GVW algorithm to principal ideal domains. For efficiency, in [15], the authors use an approach from linear algebra to implement the GVW algorithm with the help of matrix operations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Involutive GVW Algorithm and the Computation of Pommaret Bases

et al. 2021

View full text Add to dashboard Cite

The GVW algorithm computes simultaneously Gröbner bases of a given ideal and of the syzygy module of the given generating set. In this work, we discuss an extension of it to involutive bases. Pommaret bases play here a special role in several respects. We distinguish between a fully involutive GVW algorithm which determines involutive bases for both the given ideal and the syzygy module and a semi-involutive version which computes for the syzygy module only an ordinary Gröbner basis. A prototype implementation of the developed algorithms in Maple is described.

show abstract

Section: Proofmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

An Involutive GVW Algorithm and the Computation of Pommaret Bases

et al. 2021

View full text Add to dashboard Cite

show abstract

“…We call the algorithm as VID − GVW. e main idea of VID − GVW is analogue to the GVW algorithm of principal ideal domain [23]. First, we form J pairs by the initial pairs(e 1 , g 1 ), .…”

Section: Algorithm and Examplementioning

confidence: 99%

“…Several algorithms have been widely investigated for Gröbner bases to rings, such as Euclidean domain, principle ideal domain, and valuation rings that may contain zero divisors [22][23][24].…”

Section: Introductionmentioning

confidence: 99%