Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- Part III Multivariate Enumeration
- 7 Overview of analytic methods for multivariate GFs
- 8 Effective computations and ACSV
- 9 Smooth point asymptotics
- 10 Multiple point asymptotics
- 11 Cone point asymptotics
- 12 Combinatorial applications
- 13 Challenges and extensions
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
8 - Effective computations and ACSV
from Part III - Multivariate Enumeration
Published online by Cambridge University Press: 08 February 2024
Book contents
- Frontmatter
- Dedication
- Contents
- Preface to the second edition
- Preface to the first edition
- List of Symbols
- Part I Combinatorial Enumeration
- Part II Mathematical Background
- Part III Multivariate Enumeration
- 7 Overview of analytic methods for multivariate GFs
- 8 Effective computations and ACSV
- 9 Smooth point asymptotics
- 10 Multiple point asymptotics
- 11 Cone point asymptotics
- 12 Combinatorial applications
- 13 Challenges and extensions
- Appendix A Integration on manifolds
- Appendix B Algebraic topology
- Appendix C Residue forms and classical Morse theory
- Appendix D Stratification and stratified Morse theory
- References
- Author Index
- Subject Index
Summary
This chapter discusses computer algebra techniques used to apply the theorems of analytic combinatorics in several variables. We describe basic algebraic primitives, including Gröbner basis techniques, and then apply them to create algorithms certifying critical points, minimal points, Whitney stratifications, and more.
- Type
- Chapter
- Information
- Analytic Combinatorics in Several Variables , pp. 221 - 244Publisher: Cambridge University PressPrint publication year: 2024