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Afternotes on Differential Algebra
This note covers the following topics: Conventions and Preliminaries, Ideals Defined by Triangular Sets are Unmixed, Regular Chains, Lazard’s Lemma, Rosenfeld’s Lemma, The Differential Nullstellensatz, Regular Differential Chains, Normal Forms, The RosenfeldGroebner Algorithm, The Henri-Michaelis-Menten Formula, Parameter Estimation.
Author(s): Francois Boulier
88 Pages 
Notes on Differential Algebra by Reid Dale
This PDF book covers the following topics related to Differential Algebra : Basic Differential Algebra, Derivations and Dual Numbers, Differential Ideals and Ritt Noetherianity, Characteristic Sets and the Partial Ritt-Raudenbush, Basic Differential Algebraic Geometry: Properties of the Kolchin Topology, Differentially Closed Fields, Differential Dimension Polynomials, Differential Galois Theory, Binding Groups and Internality, Pillay’s X-strongly-normal theory, Galois Theory of Linear Differential Equations, Algebraic D-Groups and Logarithmic Derivatives, Constrained Cohomology, The Galois Groupoid, Differential Algebraic Groups, Preliminaries from Model Theory.
Author(s): Reid Dale
47 Pages
This PDF book covers the following topics related to Differential Algebra : Foundations of Differential Algebra, the Ring of Differential Polynomials and Its Ideals, Differential Algebraic Extensions, Differential Galois Theory, Linear Algebraic Groups, Liouvillian Extensions.
Author(s): Alexey Ovchinnikov, Maxwell Shapiro, Peter Thompson
41 Pages
Differential algebra on lattice Green functions and Calabi Yau operators
This note explains miscellaneous linear differential operators mostly associated with lattice Green functions in arbitrary dimensions, but also Calabi-Yau operators and order-seven operators corresponding to exceptional differential Galois groups.
Author(s): Salah Boukraa, Saoud Hassani, Jean-Marie Maillard, Jacques-Arthur Weil
62 Pages
Asymptotic Differential Algebra
This note introduces both, state some of their basic properties, and explain connections to o-minimal structures. Also describe a common algebraic framework for these examples: the category of H-fields. This unified setting leads to a better understanding of Hardy fields and transseries from an algebraic and model-theoretic perspective.
Author(s): Matthias Aschenbrenner
38 PagesAdvertisement
