A Completion Procedure for Computing a Canonical Basis for a k-Subalgebra

Kapur, Deepak; Madlener, Klaus

doi:10.1007/978-1-4613-9647-5_1

Cited by 62 publications

(57 citation statements)

References 6 publications

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“…The concept of SAGBI basis was first considered by Robbiano and Sweedler (1990) and by Kapur and Madlener (1989), separately. The acronym SAGBI stands for "Subalgebra Analogs to Gröbner Bases for Ideals".…”

Section: Sagbi Basesmentioning

confidence: 99%

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Ferreira

Fleischmann

2017

Journal of Symbolic Computation

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Let G be a Sylow p-subgroup of the unitary groups GU (3, q 2 ), GU (4, q 2 ), the sympletic group Sp(4, q) and, for q odd, the orthogonal group O + (4, q). In this paper we construct a presentation for the invariant ring of G acting on the natural module. In particular we prove that these rings are generated by orbit products of variables and certain invariant polynomials which are images under Steenrod operations, applied to the respective invariant form defining the corresponding classical group. We also show that these generators form a SAGBI basis and the invariant ring for G is a complete intersection.

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Section: Sagbi Basesmentioning

confidence: 99%

The invariant rings of the Sylow groups of GU(3,q2), GU(4,q2), Sp(4,q) and O+(4,q) in the natural characteristic

Ferreira

Fleischmann

2017

Journal of Symbolic Computation

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“…, x n ], denote the polynomial ring over the field K and R[t] be the polynomial ring in the variable "t" over R. The concept of Gröbner bases for ideals of a polynomial ring over a field K can be adapted in a natural way to K-subalgebras of a polynomial ring. In [11] Sagbi (Subalgebra Analog to Gröbner Basis for Ideals) basis for the K-subalgebra of R are defined, this concept was independently developed in [5]. It is shown in [5,11] that Sagbi bases play the same computational role for subalgebras as Gröbner bases play for ideals.…”

Section: Introductionmentioning

confidence: 99%

“…In [11] Sagbi (Subalgebra Analog to Gröbner Basis for Ideals) basis for the K-subalgebra of R are defined, this concept was independently developed in [5]. It is shown in [5,11] that Sagbi bases play the same computational role for subalgebras as Gröbner bases play for ideals. Miller extended Sagbi basis theory to polynomial rings over a commutative Noetherian domain in [8].…”

Section: Introductionmentioning

confidence: 99%

On the (De)homogenization of Sagbi Bases

Khan

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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“…The notion was introduced by Kapur and Madlener [1989] and independently by Robbiano and Sweedler [1990]. SAGBI bases are used to test subalgebra membership.…”

Section: Introductionmentioning

confidence: 99%

“…SAGBI bases are used to test subalgebra membership. Algorithms for computing canonical subalgebra bases are presented in both [Kapur and Madlener 1989] and [Robbiano and Sweedler 1990].…”

Section: Introductionmentioning

confidence: 99%