Algorithms for checking rational roots of b-functions and their applications
The Bernstein–Sato polynomial of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called checkRoot for optimized checking whether a given rational num...
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| Vydáno v: | Journal of algebra Ročník 352; číslo 1; s. 408 - 429 |
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15.02.2012
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| Abstract | The Bernstein–Sato polynomial of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called
checkRoot for optimized checking whether a given rational number is a root of Bernstein–Sato polynomial and in the affirmative case, computing its multiplicity. These algorithms are used in the new approach to compute the global or local Bernstein–Sato polynomial and
b-function of a holonomic ideal with respect to a weight vector. They can be applied in numerous situations, where a multiple of the Bernstein–Sato polynomial can be established. Namely, a multiple can be obtained by means of embedded resolution, for topologically equivalent singularities or using the formula of AʼCampo and spectral numbers. We also present approaches to the logarithmic comparison problem and the intersection homology D-module. Several applications are presented as well as solutions to some challenges which were intractable with the classical methods. One of the main applications is the computation of a stratification of affine space with the local
b-function being constant on each stratum. Notably, the algorithm we propose does not employ primary decomposition. Our results can be also applied for the computation of Bernstein–Sato polynomials for varieties. The examples in the paper have been computed with our implementation of the methods described in
Singular:Plural. |
|---|---|
| AbstractList | The Bernstein–Sato polynomial of a hypersurface is an important object with many applications. However, its computation is hard, as a number of open questions and challenges indicate. In this paper we propose a family of algorithms called
checkRoot for optimized checking whether a given rational number is a root of Bernstein–Sato polynomial and in the affirmative case, computing its multiplicity. These algorithms are used in the new approach to compute the global or local Bernstein–Sato polynomial and
b-function of a holonomic ideal with respect to a weight vector. They can be applied in numerous situations, where a multiple of the Bernstein–Sato polynomial can be established. Namely, a multiple can be obtained by means of embedded resolution, for topologically equivalent singularities or using the formula of AʼCampo and spectral numbers. We also present approaches to the logarithmic comparison problem and the intersection homology D-module. Several applications are presented as well as solutions to some challenges which were intractable with the classical methods. One of the main applications is the computation of a stratification of affine space with the local
b-function being constant on each stratum. Notably, the algorithm we propose does not employ primary decomposition. Our results can be also applied for the computation of Bernstein–Sato polynomials for varieties. The examples in the paper have been computed with our implementation of the methods described in
Singular:Plural. |
| Author | Martín-Morales, J. Levandovskyy, V. |
| Author_xml | – sequence: 1 givenname: V. surname: Levandovskyy fullname: Levandovskyy, V. email: viktor.levandovskyy@rwth-aachen.de organization: Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, D-52062 Aachen, Germany – sequence: 2 givenname: J. surname: Martín-Morales fullname: Martín-Morales, J. email: jorge@unizar.es organization: Centro Universitario de la Defensa de Zaragoza, Academia General Militar, Ctra. de Huesca s/n. 50090 Zaragoza, Spain |
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| Cites_doi | 10.24033/asens.1627 10.1007/BF01444876 10.5802/aif.2322 10.1090/S0002-9939-04-07678-6 10.1006/aama.1997.0527 10.1016/j.jsc.2004.11.011 10.1016/j.jsc.2009.06.004 10.2977/prims/1241553132 10.24033/bsmf.2227 10.1016/j.jsc.2003.08.005 10.1112/S0010437X06002193 10.4171/RMI/425 10.1016/S0022-4049(97)00024-8 10.1016/j.jsc.2007.06.008 10.1007/BF01390168 10.1215/S0012-7094-97-08705-6 10.1112/S0010437X04001149 10.1016/j.jsc.2010.01.003 |
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| Keywords | 16S32 68W30 Singularity 32S40 D-module Non-commutative Gröbner basis Bernstein–Sato polynomial |
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| References | Budur, Mustaţǎ, Saito (br0070) 2006; 142 J. Briançon, Ph. Maisonobe, Remarques sur lʼidéal de Bernstein associé à des polynômes, Preprint no. 650, Univ. Nice Sophia-Antipolis, 2002. Artal-Bartolo (br0020) 1994; 109 Oaku (br0320) 1997; 117/118 Jorge Martín-Morales, Embedded Mathias Schulze, A Narváez-Macarro (br0270) 2008; vol. 474 Saito (br0350) 1994; 122 Kashiwara (br0170) 1976/1977; 38 Goodearl, Warfield (br0130) 2004; vol. 61 Bernstein (br0040) 1972; 6 3.0 library for resolution of singularities (desingularization) with the algorithm of Villamayor Schulze (br0360) 2004; 38 Walther (br0420) 2005; 141 Granger, Oaku, Takayama (br0140) 2005; 39 3.0 library for topological zeta-function and some other applications of desingularization Saito (br0340) 1993; 295 Greuel, Levandovskyy, Motsak, Schönemann (br0150) 2006 Lipman (br0200) 1988; 74 Oaku (br0310) 1997; 19 Frühbis-Krüger (br0120) 2007 Saito, Sturmfels, Takayama (br0330) 2000; vol. 6 Bravo, Encinas, Orlando Villamayor (br0050) 2005; 21 resolutions and Yomdin–Lê surface singularities, PhD dissertation, IUMA-University of Zaragoza, December 2011, URL Noro (br0290) 2002 Nishiyama, Noro (br0280) 2010; 45 Castro-Jiménez, Ucha-Enríquez (br0080) 2005; 133 2005. Levandovskyy (br0180) 2005 Oaku (br0300) 1997; 87 Frühbis-Krüger (br0110) 2007 Guimarães, Hefez (br0160) 2007; 57 3.0 library to compute invariants related to the Gauss–Manin system of an isolated hypersurface singularity Malgrange (br0210) 1975 Malgrange (br0220) 1983; vol. 101 McConnell, Robson (br0240) 2001; vol. 30 Nakayama (br0260) 2009; 44 . Torrelli (br0400) 2009; 45 Levandovskyy, Martín-Morales (br0190) 2008 Andres, Levandovskyy, Martín-Morales (br0010) 2009 Bahloul, Oaku (br0030) 2010; 45 Steenbrink (br0380) 1977 Mebkhout, Narváez-Macarro (br0250) 1991; 24 Varchenko (br0410) 1981; 45 2004. Torrelli (br0390) 2007 A. Frühbis-Krüger, G. Pfister, A Andres (10.1016/j.jalgebra.2011.12.002_br0010) 2009 Bravo (10.1016/j.jalgebra.2011.12.002_br0050) 2005; 21 Nakayama (10.1016/j.jalgebra.2011.12.002_br0260) 2009; 44 Noro (10.1016/j.jalgebra.2011.12.002_br0290) 2002 Kashiwara (10.1016/j.jalgebra.2011.12.002_br0170) 1976; 38 Narváez-Macarro (10.1016/j.jalgebra.2011.12.002_br0270) 2008; vol. 474 Torrelli (10.1016/j.jalgebra.2011.12.002_br0390) 2007 Guimarães (10.1016/j.jalgebra.2011.12.002_br0160) 2007; 57 10.1016/j.jalgebra.2011.12.002_br0060 Saito (10.1016/j.jalgebra.2011.12.002_br0330) 2000; vol. 6 Schulze (10.1016/j.jalgebra.2011.12.002_br0360) 2004; 38 Steenbrink (10.1016/j.jalgebra.2011.12.002_br0380) 1977 Mebkhout (10.1016/j.jalgebra.2011.12.002_br0250) 1991; 24 Nishiyama (10.1016/j.jalgebra.2011.12.002_br0280) 2010; 45 Walther (10.1016/j.jalgebra.2011.12.002_br0420) 2005; 141 Budur (10.1016/j.jalgebra.2011.12.002_br0070) 2006; 142 10.1016/j.jalgebra.2011.12.002_br0100 Varchenko (10.1016/j.jalgebra.2011.12.002_br0410) 1981; 45 Malgrange (10.1016/j.jalgebra.2011.12.002_br0210) 1975 Malgrange (10.1016/j.jalgebra.2011.12.002_br0220) 1983; vol. 101 Bernstein (10.1016/j.jalgebra.2011.12.002_br0040) 1972; 6 Oaku (10.1016/j.jalgebra.2011.12.002_br0320) 1997; 117/118 Castro-Jiménez (10.1016/j.jalgebra.2011.12.002_br0080) 2005; 133 Frühbis-Krüger (10.1016/j.jalgebra.2011.12.002_br0120) 2007 Saito (10.1016/j.jalgebra.2011.12.002_br0340) 1993; 295 Torrelli (10.1016/j.jalgebra.2011.12.002_br0400) 2009; 45 Granger (10.1016/j.jalgebra.2011.12.002_br0140) 2005; 39 Frühbis-Krüger (10.1016/j.jalgebra.2011.12.002_br0110) 2007 Goodearl (10.1016/j.jalgebra.2011.12.002_br0130) 2004; vol. 61 Saito (10.1016/j.jalgebra.2011.12.002_br0350) 1994; 122 Bahloul (10.1016/j.jalgebra.2011.12.002_br0030) 2010; 45 McConnell (10.1016/j.jalgebra.2011.12.002_br0240) 2001; vol. 30 10.1016/j.jalgebra.2011.12.002_br0370 Levandovskyy (10.1016/j.jalgebra.2011.12.002_br0190) 2008 Artal-Bartolo (10.1016/j.jalgebra.2011.12.002_br0020) 1994; 109 10.1016/j.jalgebra.2011.12.002_br0090 Levandovskyy (10.1016/j.jalgebra.2011.12.002_br0180) 2005 Oaku (10.1016/j.jalgebra.2011.12.002_br0310) 1997; 19 Greuel (10.1016/j.jalgebra.2011.12.002_br0150) 2006 Lipman (10.1016/j.jalgebra.2011.12.002_br0200) 1988; 74 10.1016/j.jalgebra.2011.12.002_br0230 Oaku (10.1016/j.jalgebra.2011.12.002_br0300) 1997; 87 |
| References_xml | – year: 2009 ident: br0010 article-title: Principal intersection and Bernstein–Sato polynomial of an affine variety publication-title: Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSACʼ09) – year: 2005 ident: br0180 article-title: On preimages of ideals in certain non-commutative algebras publication-title: Computational Commutative and Non-Commutative Algebraic Geometry – volume: 24 start-page: 227 year: 1991 end-page: 256 ident: br0250 article-title: La théorie du polynôme de Bernstein–Sato pour les algèbres de Tate et de Dwork–Monsky–Washnitzer publication-title: Ann. Sci. École Norm. Sup. (4) – volume: 122 start-page: 163 year: 1994 end-page: 184 ident: br0350 article-title: On microlocal publication-title: Bull. Soc. Math. France – start-page: 525 year: 1977 end-page: 563 ident: br0380 article-title: Mixed Hodge structure on the vanishing cohomology publication-title: Real and Complex Singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) – volume: 45 start-page: 645 year: 2009 end-page: 660 ident: br0400 article-title: Intersection homology publication-title: Publ. Res. Inst. Math. Sci. – volume: 109 year: 1994 ident: br0020 article-title: Forme de Jordan de la monodromie des singularités superisolées de surfaces publication-title: Mem. Amer. Math. Soc. – volume: 295 start-page: 51 year: 1993 end-page: 74 ident: br0340 article-title: On publication-title: Math. Ann. – reference: , 3.0 library to compute invariants related to the Gauss–Manin system of an isolated hypersurface singularity – reference: 3.0 library for resolution of singularities (desingularization) with the algorithm of Villamayor – volume: vol. 101 start-page: 243 year: 1983 end-page: 267 ident: br0220 article-title: Polynômes de Bernstein–Sato et cohomologie évanescente publication-title: Analysis and Topology on Singular Spaces, II, III – volume: 142 start-page: 779 year: 2006 end-page: 797 ident: br0070 article-title: Bernstein–Sato polynomials of arbitrary varieties publication-title: Compos. Math. – reference: , 3.0 library for topological zeta-function and some other applications of desingularization – volume: vol. 474 start-page: 245 year: 2008 end-page: 269 ident: br0270 article-title: Linearity conditions on the Jacobian ideal and logarithmic-meromorphic comparison for free divisors publication-title: Singularities I – volume: 38 start-page: 1207 year: 2004 end-page: 1225 ident: br0360 article-title: A normal form algorithm for the Brieskorn lattice publication-title: J. Symbolic Comput. – reference: -resolutions and Yomdin–Lê surface singularities, PhD dissertation, IUMA-University of Zaragoza, December 2011, URL: – volume: 45 start-page: 46 year: 2010 end-page: 59 ident: br0030 article-title: Local Bernstein–Sato ideals: algorithm and examples publication-title: J. Symbolic Comput. – reference: , 2005. – volume: 38 start-page: 33 year: 1976/1977 end-page: 53 ident: br0170 publication-title: Invent. Math. – volume: 19 start-page: 61 year: 1997 end-page: 105 ident: br0310 article-title: Algorithms for publication-title: Adv. in Appl. Math. – volume: 117/118 start-page: 495 year: 1997 end-page: 518 ident: br0320 article-title: Algorithms for the publication-title: Algorithms for Algebra – reference: , 2004. – volume: 74 start-page: 1 year: 1988 end-page: 107 ident: br0200 article-title: Topological invariants of quasi-ordinary singularities publication-title: Mem. Amer. Math. Soc. – volume: vol. 6 year: 2000 ident: br0330 article-title: Gröbner Deformations of Hypergeometric Differential Equations publication-title: Algorithms Comput. Math. – volume: vol. 61 year: 2004 ident: br0130 article-title: An Introduction to Noncommutative Noetherian Rings publication-title: London Math. Soc. Stud. Texts – reference: Mathias Schulze, A – volume: 39 start-page: 417 year: 2005 end-page: 431 ident: br0140 article-title: Tangent cone algorithm for homogenized differential operators publication-title: J. Symbolic Comput. – year: 2008 ident: br0190 article-title: Computational publication-title: Proc. of the International Symposium on Symbolic and Algebraic Computation (ISSACʼ08) – year: 2007 ident: br0110 article-title: An application of resolution of singularities: Computing the topological publication-title: Singularity Theory – start-page: 147 year: 2002 end-page: 157 ident: br0290 article-title: An efficient modular algorithm for computing the global publication-title: Mathematical Software – volume: vol. 30 year: 2001 ident: br0240 article-title: Noncommutative Noetherian Rings publication-title: Grad. Stud. Math. – volume: 6 start-page: 26 year: 1972 end-page: 40 ident: br0040 article-title: Analytic continuation of generalized functions with respect to a parameter publication-title: Funktsional. Anal. i Prilozhen. – reference: Jorge Martín-Morales, Embedded – reference: J. Briançon, Ph. Maisonobe, Remarques sur lʼidéal de Bernstein associé à des polynômes, Preprint no. 650, Univ. Nice Sophia-Antipolis, 2002. – start-page: 98 year: 1975 end-page: 119 ident: br0210 article-title: Le polynôme de Bernstein dʼune singularité isolée publication-title: Fourier Integral Operators and Partial Differential Equations (Colloq. Internat., Univ. Nice, Nice, 1974) – start-page: 995 year: 2007 end-page: 1009 ident: br0390 article-title: Logarithmic comparison theorem and publication-title: Singularity Theory – start-page: 253 year: 2007 end-page: 327 ident: br0120 article-title: Computational aspects of singularities publication-title: Singularities in Geometry and Topology – volume: 141 start-page: 121 year: 2005 end-page: 145 ident: br0420 article-title: Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements publication-title: Compos. Math. – volume: 45 start-page: 462 year: 2010 end-page: 480 ident: br0280 article-title: Stratification associated with local b-functions publication-title: J. Symbolic Comput. – volume: 44 start-page: 449 year: 2009 end-page: 462 ident: br0260 article-title: Algorithm computing the local publication-title: J. Symbolic Comput. – reference: A. Frühbis-Krüger, G. Pfister, A – year: 2006 ident: br0150 – volume: 133 start-page: 1417 year: 2005 end-page: 1422 ident: br0080 article-title: Logarithmic comparison theorem and some Euler homogeneous free divisors publication-title: Proc. Amer. Math. Soc. – volume: 87 start-page: 115 year: 1997 end-page: 132 ident: br0300 article-title: An algorithm of computing publication-title: Duke Math. J. – volume: 21 start-page: 349 year: 2005 end-page: 458 ident: br0050 article-title: A simplified proof of desingularization and applications publication-title: Rev. Mat. Iberoam. – volume: 57 start-page: 2031 year: 2007 end-page: 2040 ident: br0160 article-title: Bernstein–Sato polynomials and spectral numbers publication-title: Ann. Inst. Fourier (Grenoble) – reference: . – volume: 45 start-page: 540 year: 1981 end-page: 591 ident: br0410 article-title: Asymptotic Hodge structure on vanishing cohomology publication-title: Izv. Akad. Nauk SSSR Ser. Mat. – volume: 24 start-page: 227 issue: 2 year: 1991 ident: 10.1016/j.jalgebra.2011.12.002_br0250 article-title: La théorie du polynôme de Bernstein–Sato pour les algèbres de Tate et de Dwork–Monsky–Washnitzer publication-title: Ann. Sci. École Norm. Sup. (4) doi: 10.24033/asens.1627 – year: 2008 ident: 10.1016/j.jalgebra.2011.12.002_br0190 article-title: Computational D-module theory with singular, comparison with other systems and two new algorithms – volume: vol. 61 year: 2004 ident: 10.1016/j.jalgebra.2011.12.002_br0130 article-title: An Introduction to Noncommutative Noetherian Rings – volume: 295 start-page: 51 issue: 1 year: 1993 ident: 10.1016/j.jalgebra.2011.12.002_br0340 article-title: On b-function, spectrum and rational singularity publication-title: Math. Ann. doi: 10.1007/BF01444876 – ident: 10.1016/j.jalgebra.2011.12.002_br0230 – volume: vol. 30 year: 2001 ident: 10.1016/j.jalgebra.2011.12.002_br0240 article-title: Noncommutative Noetherian Rings – start-page: 525 year: 1977 ident: 10.1016/j.jalgebra.2011.12.002_br0380 article-title: Mixed Hodge structure on the vanishing cohomology – volume: 57 start-page: 2031 issue: 6 year: 2007 ident: 10.1016/j.jalgebra.2011.12.002_br0160 article-title: Bernstein–Sato polynomials and spectral numbers publication-title: Ann. Inst. Fourier (Grenoble) doi: 10.5802/aif.2322 – volume: 133 start-page: 1417 issue: 5 year: 2005 ident: 10.1016/j.jalgebra.2011.12.002_br0080 article-title: Logarithmic comparison theorem and some Euler homogeneous free divisors publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-04-07678-6 – start-page: 98 year: 1975 ident: 10.1016/j.jalgebra.2011.12.002_br0210 article-title: Le polynôme de Bernstein dʼune singularité isolée – volume: 19 start-page: 61 issue: 1 year: 1997 ident: 10.1016/j.jalgebra.2011.12.002_br0310 article-title: Algorithms for b-functions, restrictions, and algebraic local cohomology groups of D-modules publication-title: Adv. in Appl. Math. doi: 10.1006/aama.1997.0527 – start-page: 995 year: 2007 ident: 10.1016/j.jalgebra.2011.12.002_br0390 article-title: Logarithmic comparison theorem and D-modules: an overview – volume: 45 start-page: 540 issue: 3 year: 1981 ident: 10.1016/j.jalgebra.2011.12.002_br0410 article-title: Asymptotic Hodge structure on vanishing cohomology publication-title: Izv. Akad. Nauk SSSR Ser. Mat. – ident: 10.1016/j.jalgebra.2011.12.002_br0100 – volume: 109 issue: 525 year: 1994 ident: 10.1016/j.jalgebra.2011.12.002_br0020 article-title: Forme de Jordan de la monodromie des singularités superisolées de surfaces publication-title: Mem. Amer. Math. Soc. – ident: 10.1016/j.jalgebra.2011.12.002_br0060 – volume: 39 start-page: 417 issue: 3–4 year: 2005 ident: 10.1016/j.jalgebra.2011.12.002_br0140 article-title: Tangent cone algorithm for homogenized differential operators publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2004.11.011 – year: 2005 ident: 10.1016/j.jalgebra.2011.12.002_br0180 article-title: On preimages of ideals in certain non-commutative algebras – volume: 45 start-page: 46 issue: 1 year: 2010 ident: 10.1016/j.jalgebra.2011.12.002_br0030 article-title: Local Bernstein–Sato ideals: algorithm and examples publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2009.06.004 – year: 2007 ident: 10.1016/j.jalgebra.2011.12.002_br0110 article-title: An application of resolution of singularities: Computing the topological ζ-function of isolated surface singularities in (C3,0) – volume: 74 start-page: 1 issue: 388 year: 1988 ident: 10.1016/j.jalgebra.2011.12.002_br0200 article-title: Topological invariants of quasi-ordinary singularities publication-title: Mem. Amer. Math. Soc. – volume: 6 start-page: 26 issue: 4 year: 1972 ident: 10.1016/j.jalgebra.2011.12.002_br0040 article-title: Analytic continuation of generalized functions with respect to a parameter publication-title: Funktsional. Anal. i Prilozhen. – volume: 45 start-page: 645 issue: 2 year: 2009 ident: 10.1016/j.jalgebra.2011.12.002_br0400 article-title: Intersection homology D-module and Bernstein polynomials associated with a complete intersection publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1241553132 – volume: 122 start-page: 163 issue: 2 year: 1994 ident: 10.1016/j.jalgebra.2011.12.002_br0350 article-title: On microlocal b-function publication-title: Bull. Soc. Math. France doi: 10.24033/bsmf.2227 – volume: 38 start-page: 1207 issue: 4 year: 2004 ident: 10.1016/j.jalgebra.2011.12.002_br0360 article-title: A normal form algorithm for the Brieskorn lattice publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2003.08.005 – ident: 10.1016/j.jalgebra.2011.12.002_br0370 – start-page: 147 year: 2002 ident: 10.1016/j.jalgebra.2011.12.002_br0290 article-title: An efficient modular algorithm for computing the global b-function – volume: vol. 474 start-page: 245 year: 2008 ident: 10.1016/j.jalgebra.2011.12.002_br0270 article-title: Linearity conditions on the Jacobian ideal and logarithmic-meromorphic comparison for free divisors – year: 2009 ident: 10.1016/j.jalgebra.2011.12.002_br0010 article-title: Principal intersection and Bernstein–Sato polynomial of an affine variety – volume: 142 start-page: 779 issue: 3 year: 2006 ident: 10.1016/j.jalgebra.2011.12.002_br0070 article-title: Bernstein–Sato polynomials of arbitrary varieties publication-title: Compos. Math. doi: 10.1112/S0010437X06002193 – start-page: 253 year: 2007 ident: 10.1016/j.jalgebra.2011.12.002_br0120 article-title: Computational aspects of singularities – volume: 21 start-page: 349 issue: 2 year: 2005 ident: 10.1016/j.jalgebra.2011.12.002_br0050 article-title: A simplified proof of desingularization and applications publication-title: Rev. Mat. Iberoam. doi: 10.4171/RMI/425 – volume: vol. 101 start-page: 243 year: 1983 ident: 10.1016/j.jalgebra.2011.12.002_br0220 article-title: Polynômes de Bernstein–Sato et cohomologie évanescente – volume: 117/118 start-page: 495 year: 1997 ident: 10.1016/j.jalgebra.2011.12.002_br0320 article-title: Algorithms for the b-function and D-modules associated with a polynomial publication-title: J. Pure Appl. Algebra doi: 10.1016/S0022-4049(97)00024-8 – volume: 44 start-page: 449 issue: 5 year: 2009 ident: 10.1016/j.jalgebra.2011.12.002_br0260 article-title: Algorithm computing the local b-function by an approximate division algorithm in Dˆ publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2007.06.008 – year: 2006 ident: 10.1016/j.jalgebra.2011.12.002_br0150 – volume: 38 start-page: 33 issue: 1 year: 1976 ident: 10.1016/j.jalgebra.2011.12.002_br0170 article-title: B-functions and holonomic systems. Rationality of roots of B-functions publication-title: Invent. Math. doi: 10.1007/BF01390168 – volume: 87 start-page: 115 issue: 1 year: 1997 ident: 10.1016/j.jalgebra.2011.12.002_br0300 article-title: An algorithm of computing b-functions publication-title: Duke Math. J. doi: 10.1215/S0012-7094-97-08705-6 – volume: vol. 6 year: 2000 ident: 10.1016/j.jalgebra.2011.12.002_br0330 article-title: Gröbner Deformations of Hypergeometric Differential Equations – volume: 141 start-page: 121 issue: 1 year: 2005 ident: 10.1016/j.jalgebra.2011.12.002_br0420 article-title: Bernstein–Sato polynomial versus cohomology of the Milnor fiber for generic hyperplane arrangements publication-title: Compos. Math. doi: 10.1112/S0010437X04001149 – ident: 10.1016/j.jalgebra.2011.12.002_br0090 – volume: 45 start-page: 462 issue: 4 year: 2010 ident: 10.1016/j.jalgebra.2011.12.002_br0280 article-title: Stratification associated with local b-functions publication-title: J. Symbolic Comput. doi: 10.1016/j.jsc.2010.01.003 |
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| Title | Algorithms for checking rational roots of b-functions and their applications |
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