A note on geometric involutive bases for positive dimensional polynomial ideals and SDP methods

Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14 ◽

10.1145/2631948.2631958 ◽

2014 ◽

Author(s):

Greg Reid ◽

Fei Wang ◽

Wenyuan Wu

Keyword(s):

Polynomial Ideals ◽

Involutive Bases

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Involutive bases of polynomial ideals

Mathematics and Computers in Simulation ◽

10.1016/s0378-4754(97)00127-4 ◽

1998 ◽

Vol 45 (5-6) ◽

pp. 519-541 ◽

Cited By ~ 101

Author(s):

Vladimir P. Gerdt ◽

Yuri A. Blinkov

Keyword(s):

Polynomial Ideals ◽

Involutive Bases

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Computation of the radical of polynomial ideals over fields of arbitrary characteristic

Proceedings of the 2001 international symposium on Symbolic and algebraic computation - ISSAC '01 ◽

10.1145/384101.384118 ◽

2001 ◽

Cited By ~ 1

Author(s):

Elisabetta Fortuna ◽

Patrizia Gianni ◽

Barry Trager

Keyword(s):

Arbitrary Characteristic ◽

Polynomial Ideals

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Computation of inverses in residue class rings of parametric polynomial ideals

Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09 ◽

10.1145/1576702.1576745 ◽

2009 ◽

Cited By ~ 3

Author(s):

Yosuke Sato ◽

Akira Suzuki

Keyword(s):

Residue Class ◽

Polynomial Ideals

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Cellular reductions of the Pommaret-Seiler resolution for Quasi-stable ideals

ACM Communications in Computer Algebra ◽

10.1145/3511528.3511537 ◽

2021 ◽

Vol 55 (3) ◽

pp. 102-106

Author(s):

Rodrigo Iglesias ◽

Eduardo Sáenz de Cabezón

Keyword(s):

Algebraic Geometry ◽

Commutative Algebra ◽

Gröbner Bases ◽

Grobner Bases ◽

Combinatorial Properties ◽

Pommaret Bases ◽

Involutive Bases

Involutive bases were introduced in [6] as a type of Gröbner bases with additional combinatorial properties. Pommaret bases are a particular kind of involutive bases with strong relations to commutative algebra and algebraic geometry[11, 12].

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On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility

Monatshefte für Mathematik ◽

10.1007/s00605-013-0534-x ◽

2013 ◽

Vol 173 (3) ◽

pp. 379-415 ◽

Cited By ~ 14

Author(s):

Daniel Pellegrino ◽

Joilson Ribeiro

Keyword(s):

Banach Spaces ◽

New Approach ◽

Polynomial Ideals

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Dimension-dependent bounds for Gröbner bases of polynomial ideals

Journal of Symbolic Computation ◽

10.1016/j.jsc.2011.12.018 ◽

2013 ◽

Vol 49 ◽

pp. 78-94 ◽

Cited By ~ 11

Author(s):

Ernst W. Mayr ◽

Stephan Ritscher

Keyword(s):

Gröbner Bases ◽

Grobner Bases ◽

Polynomial Ideals

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Universal Gröbner Basis for Parametric Polynomial Ideals

Mathematical Software – ICMS 2018 - Lecture Notes in Computer Science ◽

10.1007/978-3-319-96418-8_23 ◽

2018 ◽

pp. 191-199

Author(s):

Amir Hashemi ◽

Mahdi Dehghani Darmian ◽

Marzieh Barkhordar

Keyword(s):

Gröbner Basis ◽

Grobner Basis ◽

Polynomial Ideals ◽

Universal Gröbner Basis

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Geometric Involutive Bases and Applications to Approximate Commutative Algebra

Texts and Monographs in Symbolic Computation - Approximate Commutative Algebra ◽

10.1007/978-3-211-99314-9_4 ◽

2009 ◽

pp. 99-124 ◽

Cited By ~ 1

Author(s):

Robin Scott ◽

Greg Reid ◽

Wenyuan Wu ◽

Lihong Zhi

Keyword(s):

Commutative Algebra ◽

Involutive Bases

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The range of all regularities for polynomial ideals with a given Hilbert function

Journal of Algebra ◽

10.1016/j.jalgebra.2020.10.003 ◽

2021 ◽

Vol 566 ◽

pp. 435-442

Author(s):

Francesca Cioffi

Keyword(s):

Hilbert Function ◽

Polynomial Ideals

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Modular Algorithms for Computing Minimal Associated Primes and Radicals of Polynomial Ideals

Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '18 ◽

10.1145/3208976.3209014 ◽

2018 ◽

Cited By ~ 1

Author(s):

Toru Aoyama ◽

Masayuki Noro

Keyword(s):

Associated Primes ◽

Polynomial Ideals

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