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1 Introduction
Notes on Symbolic Computation
Larry A. Lambe
School of Computer Science
1 Introduction
2 Symbolic Computation and the Finite Difference Method
2.1 The Finite Difference Method in
D
2.2 Higher Dimensions
2.3 The Helmholtz Equation
2.3.1 One dimension
2.3.2 Dimension two
2.3.3 Dimension three
2.4 Needed Functionality
2.4.1 ExprLib
2.4.2 Input and Output
2.4.3 Elementary Operations
2.4.4 More Advanced Operations
2.4.5 The integrals revisited
2.4.6 An example
2.5 Interpolation
2.5.1 Linear Algebra in Function Spaces
2.5.2 The geometry of sub-meshing
2.5.3 Deriving Interpolation Formulas Using Symbolic Computation
3 The Free Lie Algebra
3.1 Data Structures and Algorithms for the Free Lie Algebra
4 Non Abelian Rewriting and Non Abelian G-basis Techniques
4.1 The mod
Steenrod algebra
5 The Baker-Cambell-Hausdoff Formula
5.1 Associated Lie Algebra
5.2 Bialgebras, Primitives
5.3 The Free Algebra as a Bialgebra
6 Homological Algebra
6.1 Chain Complexes and Homology
6.2 Computing Homology
6.3 Resolutions Over Algebras
6.4 Special Homotopy Equivalences
6.5 Splitting Homotopies and SDR Data
6.6 The SDR Given by a Homology Decomposition
6.7 The Perturbation Lemma
Bibliography
Dr. Larry A. Lambe 2007-05-15
D
Steenrod algebra 