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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyofmathematics,and…tocoverboththetheoretical andpracticaladvancesinthe eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovided reportsonaverytightschedule. Refereeingofthesubmissionfromamemberof theMagmagroupwasorganizedbyJoeBuhler. Theprogramcommitteethanksthegenerousadvicefromorganizersofpre- ousANTSconferences,particularlyJoeBuhler,WiebBosma,HendrikLenstra, andBartdeSmit. TheconferencewasgenerouslysupportedbytheCollegeof ScienceandTechnology,theSchoolofMathematicsandStatistics(bothatthe UniversityofSydney),theAustralianDefenceScienceTechnologyOrganisation, andeSign. April2002 JohnCannon ClausFieker DavidKohel TableofContents InvitedTalks GaussCompositionandGeneralizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ManjulBhargava EllipticCurves TheCrossroadsofTheoryandComputation. . . . . . . . . . 9 JohnCoates TheWeilandTatePairingsasBuildingBlocks forPublicKeyCryptosystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 AntoineJoux UsingEllipticCurvesofRankOnetowardstheUndecidability ofHilbert sTenthProblemoverRingsofAlgebraicIntegers. . . . . . . . . . . . . 33 BjornPoonen Onp-adicPointCountingAlgorithmsforEllipticCurves overFiniteFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 TakakazuSatoh NumberTheory OnArithmeticallyEquivalentNumberFieldsofSmallDegree . . . . . . . . . . . 67 WiebBosma,BartdeSmit ASurveyofDiscriminantCounting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 HenriCohen,FranciscoDiazyDiaz,MichelOlivier AHigher-RankMersenneProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 GrahamEverest,PeterRogers,ThomasWard AnApplicationofSiegelModularFunctions toKronecker sLimitFormula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 TakashiFukuda,KeiichiKomatsu ComputationalAspectsofNUCOMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 MichaelJ. Jacobson,Jr. ,AlfredJ. vanderPoorten E cientComputationofClassNumbersofRealAbelianNumberFields. . 134 St ephaneR. Louboutin AnAcceleratedBuchmannAlgorithmforRegulatorComputation inRealQuadraticFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 UlrichVollmer VIII TableofContents ArithmeticGeometry SomeGenus3CurveswithManyPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 RolandAuer,JaapTop 7 8 Trinomialsax +bx+candax +bx+c withGaloisGroupsofOrder168and8 168. . . . . . . . . . . . . . . . . . . . . . . . . . . 172 NilsBruin,NoamD. Elkies ComputationsonModularJacobianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 189 EnriqueGonz alez-Jim enez,JosepGonz alez,JordiGu`ardia IntegralPointsonPuncturedAbelianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . 198 AndrewKresch,YuriTschinkel Genus2Curveswith(3,3)-SplitJacobian andLargeAutomorphismGroup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 TonyShaska.
Lingua: Inglese
Editore: Springer, Berlin|Springer Nature Switzerland|Springer, 2024
Serie: Algorithms and Computation in Mathematics, Libro 24 di 24. Libro 24 di 24 - Algorithms and Computation in Mathematics
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Taschenbuch. Condizione: Neu. The Computer Algebra System OSCAR | Algorithms and Examples | Wolfram Decker (u. a.) | Taschenbuch | Algorithms and Computation in Mathematics | xviii | Englisch | 2026 | Springer | EAN 9783031621291 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juer…gen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical g…eometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software.The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tro…pical geometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software.The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -TheAlgorithmicNumberTheorySymposiabeganin1994atCornellUniversity inIthaca,NewYorktorecognizethegrowingimportanceofalgorithmicwork in the theory of numbers. The subject of the conference is broadly construed toencompassadiversebodyo…fmathematics,andtocoverboththetheoretical andpracticaladvancesinthe eld. Theyhavebeenheldeverytwoyearssince: inBordeaux(Universit eBordeauxI)in1996,Portland(ReedCollege)in1998, Leiden(UniversiteitLeiden)in2000,andthepresentconferencehostedbythe MagmaComputationalAlgebraGroupattheUniversityofSydney. TheconferenceprogramincludedinvitedtalksbyManjulBhargava(Prin- ton),JohnCoates(Cambridge),AntoineJoux(DCSSICryptoLab),BjornP- nen(Berkeley),andTakakazuSatoh(Saitama),aswellas34contributedtalks invariousareasofnumbertheory. Inadditiontothemathematicalprogram,the conferenceincludedaspecialdinnertohonourAlfvanderPoortenofMacquarie University,ontheoccasionofhis60thbirthday. Eachpaperwasreviewedbyatleasttwoexpertsexternaltotheprogram committeeandtheselectionofpaperswasmadeonthebasisoftheserec- mendations. Weexpressourappreciationtothe66expertrefereeswhoprovided reportsonaverytightschedule. Refereeingofthesubmissionfromamemberof theMagmagroupwasorganizedbyJoeBuhler. Theprogramcommitteethanksthegenerousadvicefromorganizersofpre- ousANTSconferences,particularlyJoeBuhler,WiebBosma,HendrikLenstra, andBartdeSmit. TheconferencewasgenerouslysupportedbytheCollegeof ScienceandTechnology,theSchoolofMathematicsandStatistics(bothatthe UniversityofSydney),theAustralianDefenceScienceTechnologyOrganisation, andeSign. April2002 JohnCannon ClausFieker DavidKohel TableofContents InvitedTalks GaussCompositionandGeneralizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 ManjulBhargava EllipticCurves TheCrossroadsofTheoryandComputation. . . . . . . . . . 9 JohnCoates TheWeilandTatePairingsasBuildingBlocks forPublicKeyCryptosystems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 AntoineJoux UsingEllipticCurvesofRankOnetowardstheUndecidability ofHilbert sTenthProblemoverRingsofAlgebraicIntegers. . . . . . . . . . . . . 33 BjornPoonen Onp-adicPointCountingAlgorithmsforEllipticCurves overFiniteFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 TakakazuSatoh NumberTheory OnArithmeticallyEquivalentNumberFieldsofSmallDegree . . . . . . . . . . . 67 WiebBosma,BartdeSmit ASurveyofDiscriminantCounting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 HenriCohen,FranciscoDiazyDiaz,MichelOlivier AHigher-RankMersenneProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 GrahamEverest,PeterRogers,ThomasWard AnApplicationofSiegelModularFunctions toKronecker sLimitFormula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 TakashiFukuda,KeiichiKomatsu ComputationalAspectsofNUCOMP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 MichaelJ. Jacobson,Jr. ,AlfredJ. vanderPoorten E cientComputationofClassNumbersofRealAbelianNumberFields. . 134 St ephaneR. Louboutin AnAcceleratedBuchmannAlgorithmforRegulatorComputation inRealQuadraticFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 UlrichVollmer VIII TableofContents ArithmeticGeometry SomeGenus3CurveswithManyPoints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 RolandAuer,JaapTop 7 8 Trinomialsax +bx+candax +bx+c withGaloisGroupsofOrder168and8 168. . . . . . . . . . . . . . . . . . . . . . . . . . . 172 NilsBruin,NoamD. Elkies ComputationsonModularJacobianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 189 EnriqueGonz alez-Jim enez,JosepGonz alez,JordiGu`ardia IntegralPointsonPuncturedAbelianSurfaces. . . . . . . . . . . . . . . . . . . . . . . . . 198 AndrewKresch,YuriTschinkel Genus2Curveswith(3,3)-SplitJacobian andLargeAutomorphismGroup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 TonyShaska 532 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Invited Talks.- Gauss Composition and Generalizations.- Elliptic Curves - The Crossroads of Theory and Computation.- The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems.- Using Elliptic Curves of Rank One towards… the Undecidability of Hilbert's Tenth Problem over Rings of Algebraic Integers.- On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields.- Number Theory.- On Arithmetically Equivalent Number Fields of Small Degree.- A Survey of Discriminant Counting.- A Higher-Rank Mersenne Problem.- An Application of Siegel Modular Functions to Kronecker's Limit Formula.- Computational Aspects of NUCOMP.- Efficient Computation of Class Numbers of Real Abelian Number Fields.- An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic Fields.- Arithmetic Geometry.- Some Genus 3 Curves with Many Points.- Trinomials ax 7 + bx + c and ax 8 + bx + c with Galois Groups of Order 168 and 8 168.- Computations on Modular Jacobian Surfaces.- Integral Points on Punctured Abelian Surfaces.- Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group.- Transportable Modular Symbols and the Intersection Pairing.- Elliptic Curves and CM.- Action of Modular Correspondences around CM Points.- Curves Dy 2 = x 3 - x of Odd Analytic Rank.- Comparing Invariants for Class Fields of Imaginary Quadratic Fields.- A Database of Elliptic Curves - First Report.- Point Counting.- Isogeny Volcanoes and the SEA Algorithm.- Fast Elliptic Curve Point Counting Using Gaussian Normal Basis.- An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2.- Cryptography.- Implementing the Tate Pairing.- Smooth Orders and Cryptographic Applications.- Chinese Remaindering for Algebraic Numbers in a Hidden Field.-Function Fields.- An Algorithm for Computing Weierstrass Points.- New Optimal Tame Towers of Function Fields over Small Finite Fields.- Periodic Continued Fractions in Elliptic Function Fields.- Discrete Logarithms and Factoring.- Fixed Points and Two-Cycles of the Discrete Logarithm.- Random Cayley Digraphs and the Discrete Logarithm.- The Function Field Sieve Is Quite Special.- MPQS with Three Large Primes.- An Improved Baby Step Giant Step Algorithm for Point Counting of Hyperelliptic Curves over Finite Fields.- Factoring N = pq 2 with the Elliptic Curve Method.- Gröbner Bases.- A New Scheme for Computing with Algebraically Closed Fields.- Complexity.- Additive Complexity and Roots of Polynomials over Number Fields and -adic Fields.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 532 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for po…lyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software.The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts. 512 pp. Englisch.
Lingua: Inglese
Editore: Springer, Springer Jan 2025, 2025
Serie: Algorithms and Computation in Mathematics, Libro 24 di 24. Libro 24 di 24 - Algorithms and Computation in Mathematics
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for polyhedra…l and tropical geometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software.The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts. 512 pp. Englisch.
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for polyhe…dral and tropical geometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software. The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts. 512 pp. Englisch.
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Serie: Algorithms and Computation in Mathematics, Libro 24 di 24. Libro 24 di 24 - Algorithms and Computation in Mathematics
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Buch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -This book presents version 1.0 of the new Computer Algebra System OSCAR.Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral an…d tropical geometry, and Singular for commutative algebra and algebraic geometry.It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.It is freely available, open source software.The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 512 pp. Englisch.
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