{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:21:22Z","timestamp":1775053282284,"version":"3.50.1"},"publisher-location":"New York, NY, USA","reference-count":17,"publisher":"ACM","license":[{"start":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T00:00:00Z","timestamp":1248739200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2009,7,28]]},"DOI":"10.1145\/1576702.1576725","type":"proceedings-article","created":{"date-parts":[[2009,7,28]],"date-time":"2009-07-28T12:45:28Z","timestamp":1248785128000},"page":"151-158","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":17,"title":["Solving systems of polynomial equations with symmetries using SAGBI-Gr\u00f6bner bases"],"prefix":"10.1145","author":[{"given":"Jean-Charles","family":"Faug\u00e8re","sequence":"first","affiliation":[{"name":"INRIA, Paris, France"}]},{"given":"Sajjad","family":"Rahmany","sequence":"additional","affiliation":[{"name":"UPMC, Univ Paris 06, LIP6, Paris, France"}]}],"member":"320","published-online":{"date-parts":[[2009,7,28]]},"reference":[{"key":"e_1_3_2_1_1_1","volume-title":"Solving a system of algebraic equations with symmetries. Pure and applied algebra, 117--118:195--215","author":"Colin A.","year":"1997","unstructured":"A. Colin . Solving a system of algebraic equations with symmetries. Pure and applied algebra, 117--118:195--215 , 1997 . A. Colin. Solving a system of algebraic equations with symmetries. Pure and applied algebra, 117--118:195--215, 1997."},{"key":"e_1_3_2_1_2_1","first-page":"113","volume-title":"Reine Angew.Math","author":"Conca G. A.","year":"1996","unstructured":"G. A. Conca , J. Herzog . Sagbi bases and application to blow-up algebras . Reine Angew.Math , pages 113 -- 138 , 1996 . G. A. Conca, J. Herzog. Sagbi bases and application to blow-up algebras. Reine Angew.Math, pages 113--138, 1996."},{"key":"e_1_3_2_1_3_1","series-title":"Ser","first-page":"131","volume-title":"Recent Advances in Fourier Analysis and its Applications","author":"Bj G.","year":"1989","unstructured":"G. Bj ¨ork. Functions of modulus 1 on Zn, whose Fourier transforms have constant modulus, and \"cyclic n-roots \". In J.S. Byrnes and J.F. Byrnes, editor, Recent Advances in Fourier Analysis and its Applications , volume 315 of Ser . C : Math. Phys. Sci., Kluwer , pages 131 -- 140 . NATO Adv. Sci. Inst., 1989 . G. Bj¨ork. Functions of modulus 1 on Zn, whose Fourier transforms have constant modulus, and \"cyclic n-roots\". In J.S. Byrnes and J.F. Byrnes, editor, Recent Advances in Fourier Analysis and its Applications, volume 315 of Ser. C: Math. Phys. Sci., Kluwer, pages 131--140. NATO Adv. Sci. Inst., 1989."},{"key":"e_1_3_2_1_4_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-7091-4368-1","volume-title":"Algorithms in Invariant Theory","author":"Sturmfels B.","year":"1993","unstructured":"B. Sturmfels . Algorithms in Invariant Theory . Springer-Verlag , Wien ,New York, 1993 . B. Sturmfels. Algorithms in Invariant Theory. Springer-Verlag, Wien,New York, 1993."},{"key":"e_1_3_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01844169"},{"key":"e_1_3_2_1_7_1","series-title":"Lect","first-page":"3","volume-title":"Proc. EUROSAM 79","author":"B.","year":"1979","unstructured":"Buchberger B. A Criterion for Detecting Unnecessary Reductions in the Construction of Gr¨obner Basis . In Proc. EUROSAM 79 , volume 72 of Lect . Notes in Comp. Sci., pages 3 -- 21 . Springer Verlag , 1979 . Buchberger B. A Criterion for Detecting Unnecessary Reductions in the Construction of Gr¨obner Basis. In Proc. EUROSAM 79, volume 72 of Lect. Notes in Comp. Sci., pages 3--21. Springer Verlag, 1979."},{"key":"e_1_3_2_1_8_1","volume-title":"Varieties and Algorithms. Undergraduate Texts in Mathematics","author":"Cox D.","year":"2007","unstructured":"D. Cox , J. Little , and D. O'Shea . Ideals , Varieties and Algorithms. Undergraduate Texts in Mathematics . Springer Verlag , New York , 3 rd ed. 2007 . corr. 2nd printing, 2008, xvi edition, 2007. 560 p. D. Cox, J. Little, and D. O'Shea. Ideals, Varieties and Algorithms. Undergraduate Texts in Mathematics. Springer Verlag, New York, 3rd ed. 2007. corr. 2nd printing, 2008, xvi edition, 2007. 560 p.","edition":"3"},{"key":"e_1_3_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(99)00005-5"},{"key":"e_1_3_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/780506.780516"},{"key":"e_1_3_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1993.1051"},{"key":"e_1_3_2_1_12_1","first-page":"1","volume-title":"A completion procedure for computing a canonical basis for a k-subalgebra. Computers and mathematics","author":"Kapur G.","year":"1989","unstructured":"G. Kapur and K. Madlener . A completion procedure for computing a canonical basis for a k-subalgebra. Computers and mathematics , pages 1 -- 11 , June 1989 . G. Kapur and K. Madlener. A completion procedure for computing a canonical basis for a k-subalgebra. Computers and mathematics, pages 1--11, June 1989."},{"key":"e_1_3_2_1_13_1","volume-title":"Computational Invariant Theory","author":"Kemper G.","year":"2002","unstructured":"G. Kemper . Computational Invariant Theory . Springer-Verlag , New York , 2002 . G. Kemper. Computational Invariant Theory. Springer-Verlag, New York, 2002."},{"key":"e_1_3_2_1_14_1","first-page":"267","volume-title":"ANTS III","author":"Hoffstein J.","year":"1998","unstructured":"J. Hoffstein , J. Pipher , and J. Silverman . Ntru: a ring-based public key cryptosystem . In ANTS III , volume 1423 , pages 267 -- 288 . Springer Verlag , 1998 . J. Hoffstein, J. Pipher, and J. Silverman. Ntru: a ring-based public key cryptosystem. In ANTS III, volume 1423, pages 267--288. Springer Verlag, 1998."},{"key":"e_1_3_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0006"},{"key":"e_1_3_2_1_16_1","first-page":"421","volume-title":"Effective algorithms for intrinsically computing SAGBI-Gr¨obner bases in a polynomial ring over a filed. Groebner bases and application (Linz)","author":"Miller J.L.","year":"1998","unstructured":"J.L. Miller . Effective algorithms for intrinsically computing SAGBI-Gr¨obner bases in a polynomial ring over a filed. Groebner bases and application (Linz) , pages 421 -- 433 , February 1998 . J.L. Miller. Effective algorithms for intrinsically computing SAGBI-Gr¨obner bases in a polynomial ring over a filed. Groebner bases and application (Linz), pages 421--433, February 1998."},{"key":"e_1_3_2_1_17_1","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1007\/BFb0085537","volume-title":"Subalgebra bases. Commutative algebra","author":"Robbiano L.","year":"1990","unstructured":"L. Robbiano and M. Sweedler . Subalgebra bases. Commutative algebra , pages 61 -- 87 , 1990 . L. Robbiano and M. Sweedler. Subalgebra bases. Commutative algebra, pages 61--87, 1990."},{"key":"e_1_3_2_1_18_1","first-page":"84","volume-title":"International Conference DM-CCG, Discrete Model-Combinatorics, Computation and Geometry","author":"Thiery N.M.","year":"2002","unstructured":"N.M. Thiery . Computing minimal generating sets of invariant rings of permutation groups with SAGBI-Gr¨obner basis . International Conference DM-CCG, Discrete Model-Combinatorics, Computation and Geometry , pages 84 -- 89 , July 2002 . N.M. Thiery. Computing minimal generating sets of invariant rings of permutation groups with SAGBI-Gr¨obner basis. International Conference DM-CCG, Discrete Model-Combinatorics, Computation and Geometry, pages 84--89, July 2002."}],"event":{"name":"ISSAC '09: International Symposium on Symbolic and Algebraic Computation","location":"Seoul Republic of Korea","acronym":"ISSAC '09","sponsor":["ACM Association for Computing Machinery","SIGSAM ACM Special Interest Group on Symbolic and Algebraic Manipulation"]},"container-title":["Proceedings of the 2009 international symposium on Symbolic and algebraic computation"],"original-title":[],"link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1576702.1576725","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1576702.1576725","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T12:23:09Z","timestamp":1750249389000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1576702.1576725"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,28]]},"references-count":17,"alternative-id":["10.1145\/1576702.1576725","10.1145\/1576702"],"URL":"https:\/\/doi.org\/10.1145\/1576702.1576725","relation":{},"subject":[],"published":{"date-parts":[[2009,7,28]]},"assertion":[{"value":"2009-07-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}