Invariant G2V algorithm for computing SAGBI-Gröbner bases
Faugère and Rahmany have presented the invariant F 5 algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this alg...
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| Published in | Science China. Mathematics Vol. 56; no. 9; pp. 1781 - 1794 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2013
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1674-7283 1869-1862 |
| DOI | 10.1007/s11425-012-4506-8 |
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| Abstract | Faugère and Rahmany have presented the invariant F
5
algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely,
invariant G
2
V algorithm
, to compute SAGBI-Gröbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G
2
V algorithm; a variant of the F
5
algorithm to compute Gröbner bases. We have implemented our new algorithm in Maple, and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F
5
algorithm. |
|---|---|
| AbstractList | Faugère and Rahmany have presented the invariant F
5
algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely,
invariant G
2
V algorithm
, to compute SAGBI-Gröbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G
2
V algorithm; a variant of the F
5
algorithm to compute Gröbner bases. We have implemented our new algorithm in Maple, and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F
5
algorithm. |
| Author | M.-Alizadeh, Benyamin Riahi, Monireh Hashemi, Amir |
| Author_xml | – sequence: 1 givenname: Amir surname: Hashemi fullname: Hashemi, Amir email: Amir.Hashemi@cc.iut.ac.ir organization: Department of Mathematical Sciences, Isfahan University of Technology – sequence: 2 givenname: Benyamin surname: M.-Alizadeh fullname: M.-Alizadeh, Benyamin organization: Young Researchers Club, Science and Research Branch, Islamic Azad University – sequence: 3 givenname: Monireh surname: Riahi fullname: Riahi, Monireh organization: Department of Mathematics, Damghan University |
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| Cites_doi | 10.1016/S0747-7171(88)80048-8 10.1007/978-0-387-35651-8 10.1006/jsco.1996.0006 10.1016/S0022-4049(99)00005-5 10.1016/0001-8708(74)90067-X 10.1006/jsco.1996.0017 10.1112/plms/s1-35.1.3 10.1007/3-540-09519-5_52 10.1016/j.tcs.2011.04.040 10.1007/978-1-4613-9647-5_1 10.1016/j.jsc.2010.06.019 10.1006/jsco.1998.0247 10.1016/j.jsc.2010.06.013 10.1006/jsco.1998.0243 10.1007/s11424-011-0218-3 10.1006/jsco.1998.0210 10.1007/BFb0085537 10.1007/3-540-12868-9_99 10.1145/780506.780516 10.46298/dmtcs.2285 |
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| Keywords | invariant F invariant G 68W30 G V algorithm 13P10 SAGBI-Gröbner bases algorithm |
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| References | Faugère (CR8) 1994; 139 Lazard (CR24) 1983 Sun, Wang (CR32) 2011 Gao, Guan, Volny (CR11) 2010 Miller (CR26) 1996; 21 CR35 CR12 CR34 Thiéry, Thomassé (CR36) 2004 CR31 Göbel (CR14) 1999; 26 CR30 Hochster, Roberts (CR16) 1974; 13 Buchberger (CR5) 1979 Hashemi, M.-Alizadeh (CR15) 2011; 412 Kuroda (CR23) 2002; 39 Gebauer, Möller (CR13) 1988; 6 Becker, Weispfenning (CR3) 1993 Macaulay (CR25) 1902; 35 Adams, Hosten, Loustaunau (CR1) 1999; 27 Faugère, Rahmany (CR10) 2009 Eder, Perry (CR7) 2010; 45 CR4 Faugère (CR9) 2002 Ars, Hashemi (CR2) 2010; 45 Sun, Wang (CR33) 2011; 24 CR28 Kemper (CR19) 1996; 21 Ollivier (CR29) 1991 Kemper (CR20) 1998; XII Kemper (CR21) 2002 Miller, Miller (CR27) 1998 Kemper (CR18) 1999; 27 Kapur, Madlener, Kaltofen, Watt (CR17) 1989 Kemper, Steel (CR22) 1999; 173 Cox, Little, O’shea (CR6) 2007 D. Kapur (4506_CR17) 1989 M. Kuroda (4506_CR23) 2002; 39 F. Ollivier (4506_CR29) 1991 D. Lazard (4506_CR24) 1983 Y. Sun (4506_CR32) 2011 B. Buchberger (4506_CR5) 1979 J. C. Faugère (4506_CR9) 2002 T. Becker (4506_CR3) 1993 D. Cox (4506_CR6) 2007 J. C. Faugère (4506_CR10) 2009 4506_CR4 S. Gao (4506_CR11) 2010 A. Hashemi (4506_CR15) 2011; 412 4506_CR28 G. Ars (4506_CR2) 2010; 45 Y. Sun (4506_CR33) 2011; 24 J. C. Faugère (4506_CR8) 1994; 139 M. Göbel (4506_CR14) 1999; 26 R. Gebauer (4506_CR13) 1988; 6 G. Kemper (4506_CR21) 2002 N. M. Thiéry (4506_CR36) 2004 W. W. Adams (4506_CR1) 1999; 27 C. Eder (4506_CR7) 2010; 45 G. Kemper (4506_CR19) 1996; 21 F. S. Macaulay (4506_CR25) 1902; 35 J. L. Miller (4506_CR26) 1996; 21 G. Kemper (4506_CR22) 1999; 173 4506_CR30 4506_CR31 G. Kemper (4506_CR18) 1999; 27 J. L. Miller (4506_CR27) 1998 4506_CR12 4506_CR34 4506_CR35 M. Hochster (4506_CR16) 1974; 13 G. Kemper (4506_CR20) 1998; XII |
| References_xml | – volume: 6 start-page: 275 year: 1988 end-page: 286 ident: CR13 article-title: On an installation of Buchberger’s algorithm publication-title: J Symb Comp doi: 10.1016/S0747-7171(88)80048-8 – volume: 39 start-page: 665 year: 2002 end-page: 680 ident: CR23 article-title: The finiteness of the SAGBI basis for certain invariant rings publication-title: Osaka J Math – start-page: 379 year: 1991 end-page: 400 ident: CR29 article-title: Canonical bases: relations with standard bases, finiteness conditions and application to tame automorphisms publication-title: MEGA0, Progress in Mathematics, 94 – volume: XII start-page: 5 year: 1998 end-page: 26 ident: CR20 article-title: Computational invariant theory publication-title: The Curves Seminar at Queen – year: 2007 ident: CR6 publication-title: Ideals, Varieties, and Algorithms doi: 10.1007/978-0-387-35651-8 – ident: CR4 – start-page: 151 year: 2009 end-page: 158 ident: CR10 article-title: Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases publication-title: ISSAC’09 – volume: 21 start-page: 139 year: 1996 end-page: 153 ident: CR26 article-title: Analogues of Gröbner bases in polynomial rings over a ring publication-title: J Symb Comp doi: 10.1006/jsco.1996.0006 – ident: CR12 – ident: CR30 – volume: 139 start-page: 61 year: 1994 end-page: 88 ident: CR8 article-title: A new efficient algorithm for computing Gröbner bases (F ) publication-title: J Pure Appl Algebra doi: 10.1016/S0022-4049(99)00005-5 – volume: 13 start-page: 115 year: 1974 end-page: 175 ident: CR16 article-title: Ring of invariants of reductive groups acting on regular rings are cohen-macaulay publication-title: Adv Math doi: 10.1016/0001-8708(74)90067-X – ident: CR35 – start-page: 259 year: 2004 end-page: 263 ident: CR36 article-title: Convex cones and SAGBI bases of permutation invariants in invariant theory in all characteristic publication-title: CRM Proceedings and Lecture Notes, vol. 35 – volume: 21 start-page: 351 year: 1996 end-page: 366 ident: CR19 article-title: Calculating invariant rings of finite groups over arbitrary field publication-title: J Symb Comp doi: 10.1006/jsco.1996.0017 – volume: 35 start-page: 3 year: 1902 end-page: 27 ident: CR25 article-title: Some formulae in elimination publication-title: Proc London Math Soc doi: 10.1112/plms/s1-35.1.3 – start-page: 3 year: 1979 end-page: 21 ident: CR5 article-title: A criterion for detecting unnecessary reductions in the construction of Gröbner bases publication-title: Symbolic and Algebraic Computation, EUROSAM’79, Intern Sympos, Marseille, 1979 doi: 10.1007/3-540-09519-5_52 – volume: 412 start-page: 4592 year: 2011 end-page: 4603 ident: CR15 article-title: Applying IsRewritten criterion on Buchberger algorithm publication-title: J Theor Comp Sci doi: 10.1016/j.tcs.2011.04.040 – start-page: 13 year: 2010 end-page: 19 ident: CR11 article-title: A new incremental algorithm for computing Gröbner bases publication-title: ISSAC’10 – start-page: 1 year: 1989 end-page: 11 ident: CR17 article-title: A completion procedure for computing a canonical basis for a K-subalgebra publication-title: Computers and Mathematics doi: 10.1007/978-1-4613-9647-5_1 – volume: 45 start-page: 1442 year: 2010 end-page: 1458 ident: CR7 article-title: F5C: a variant of Faugère’s F5 algorithm with reduced Gröbner bases publication-title: J Symb Comp doi: 10.1016/j.jsc.2010.06.019 – year: 2002 ident: CR21 publication-title: Computational Invariant Theory – volume: 27 start-page: 171 year: 1999 end-page: 184 ident: CR18 article-title: An algorithm to calculate optimal homogeneous systems of parameters publication-title: J Symb Comp doi: 10.1006/jsco.1998.0247 – volume: 173 start-page: 267 year: 1999 end-page: 285 ident: CR22 article-title: Some algorithms in invariant theory of finite groups publication-title: Computational Methods for Representations of Groups and Algebras, Euroconference in Essen, April 1–5, 1997, Progress in Mathematics – volume: 45 start-page: 1330 year: 2010 end-page: 1340 ident: CR2 article-title: Extended F5 criteria publication-title: J Symb Comp doi: 10.1016/j.jsc.2010.06.013 – start-page: 146 year: 1983 end-page: 156 ident: CR24 publication-title: Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations – start-page: 421 year: 1998 end-page: 433 ident: CR27 article-title: Effective algorithms for intrinsically computing SAGBI-Grbner bases in a polynomial ring over a field publication-title: London Math Soc Lecture Note Ser, 251 – ident: CR31 – volume: 27 start-page: 31 year: 1999 end-page: 47 ident: CR1 article-title: Sagbi and sagbi Gröbner bases over principal ideal domains publication-title: J Symb Comp doi: 10.1006/jsco.1998.0243 – ident: CR34 – volume: 24 start-page: 1218 year: 2011 end-page: 1231 ident: CR33 article-title: The F5 algorithm in Buchberger’s style publication-title: J Syst Sci Comp doi: 10.1007/s11424-011-0218-3 – ident: CR28 – year: 1993 ident: CR3 publication-title: Gröbner Bases, A Computational Approach to Commutative Algebra – start-page: 75 year: 2002 end-page: 83 ident: CR9 article-title: A new efficient algorithm for computing Gröbner bases without reduction to zero (F ) publication-title: ISSAC’02 – start-page: 337 year: 2011 end-page: 344 ident: CR32 article-title: A generalized criterion for signature related Gröbner basis algorithms publication-title: ISSAC’11 – volume: 26 start-page: 261 year: 1999 end-page: 272 ident: CR14 article-title: A constructive description of SAGBI bases for polynomial invariants of permutation groups publication-title: J Symb Comp doi: 10.1006/jsco.1998.0210 – ident: 4506_CR31 doi: 10.1007/BFb0085537 – volume-title: Gröbner Bases, A Computational Approach to Commutative Algebra year: 1993 ident: 4506_CR3 – start-page: 1 volume-title: Computers and Mathematics year: 1989 ident: 4506_CR17 doi: 10.1007/978-1-4613-9647-5_1 – ident: 4506_CR4 – volume: 39 start-page: 665 year: 2002 ident: 4506_CR23 publication-title: Osaka J Math – start-page: 379 volume-title: MEGA0, Progress in Mathematics, 94 year: 1991 ident: 4506_CR29 – start-page: 13 volume-title: ISSAC’10 year: 2010 ident: 4506_CR11 – volume-title: Computational Invariant Theory year: 2002 ident: 4506_CR21 – volume: 35 start-page: 3 year: 1902 ident: 4506_CR25 publication-title: Proc London Math Soc doi: 10.1112/plms/s1-35.1.3 – volume: 173 start-page: 267 year: 1999 ident: 4506_CR22 publication-title: Computational Methods for Representations of Groups and Algebras, Euroconference in Essen, April 1–5, 1997, Progress in Mathematics – volume: 26 start-page: 261 year: 1999 ident: 4506_CR14 publication-title: J Symb Comp doi: 10.1006/jsco.1998.0210 – volume: 412 start-page: 4592 year: 2011 ident: 4506_CR15 publication-title: J Theor Comp Sci doi: 10.1016/j.tcs.2011.04.040 – volume: 45 start-page: 1330 year: 2010 ident: 4506_CR2 publication-title: J Symb Comp doi: 10.1016/j.jsc.2010.06.013 – volume: 27 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volume-title: ISSAC’11 year: 2011 ident: 4506_CR32 – volume: 139 start-page: 61 year: 1994 ident: 4506_CR8 publication-title: J Pure Appl Algebra doi: 10.1016/S0022-4049(99)00005-5 – volume: 24 start-page: 1218 year: 2011 ident: 4506_CR33 publication-title: J Syst Sci Comp doi: 10.1007/s11424-011-0218-3 – ident: 4506_CR35 doi: 10.46298/dmtcs.2285 – volume: 21 start-page: 139 year: 1996 ident: 4506_CR26 publication-title: J Symb Comp doi: 10.1006/jsco.1996.0006 – volume: 13 start-page: 115 year: 1974 ident: 4506_CR16 publication-title: Adv Math doi: 10.1016/0001-8708(74)90067-X – volume: 6 start-page: 275 year: 1988 ident: 4506_CR13 publication-title: J Symb Comp doi: 10.1016/S0747-7171(88)80048-8 – ident: 4506_CR30 – start-page: 259 volume-title: CRM Proceedings and Lecture Notes, vol. 35 year: 2004 ident: 4506_CR36 – volume-title: Ideals, Varieties, and Algorithms year: 2007 ident: 4506_CR6 doi: 10.1007/978-0-387-35651-8 – start-page: 3 volume-title: Symbolic and Algebraic Computation, EUROSAM’79, Intern Sympos, Marseille, 1979 year: 1979 ident: 4506_CR5 doi: 10.1007/3-540-09519-5_52 – start-page: 151 volume-title: ISSAC’09 year: 2009 ident: 4506_CR10 |
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| Snippet | Faugère and Rahmany have presented the invariant F
5
algorithm to compute SAGBI-Gröbner bases of ideals of invariant rings. This algorithm has an incremental... |
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| Title | Invariant G2V algorithm for computing SAGBI-Gröbner bases |
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