Constructions in
Sage
: A
Sage
cookbook
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Constructions in Sage: A
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1. Tabular layout
Contents
1. Tabular layout
2. Calculus
2.1 Differentiation
2.1.1 Critical points
2.1.2 Power series
2.2 Integration
2.2.1 Convolution
2.2.2 Riemann and trapezoid sums for integrals
2.2.3 Laplace transforms
2.3 Ordinary differential equations
2.4 Fourier series of periodic functions
3. Plotting
3.1 Plotting functions in 2D
3.2 Plotting curves
3.2.1 matplotlib
3.2.2 surf
3.3 openmath
3.4 Tachyon 3D plotting
3.5 gnuplot
3.6 Plotting surfaces
4. Groups
4.1 Permutation groups
4.2 Conjugacy classes
4.3 Normal subgroups
4.4 Centers
4.5 The group id database
5. Linear algebra
5.1 Vector spaces
5.2 Matrix powers
5.3 Kernels
5.4 Eigenvectors and eigenvalues
5.5 Row reduction
5.6 Characteristic polynomial
5.7 Solving systems of linear equations
6. Linear codes and ciphers
6.1 Codes
6.2 Ciphers
6.2.1 LFSRs
6.2.2 Classical ciphers
7. Graph theory
7.1 Networkx
7.2 Cayley graphs
7.3 Graphs from adjacency matrices
8. Representation theory
8.1 Ordinary characters
8.2 Brauer characters
9. Rings
9.1 Matrix rings
9.2 Polynomial rings
9.3
-adic numbers
9.4 Quotient rings of polynomials
10. Polynomials
10.1 Polynomial powers
10.2 Factorization
10.3 Polynomial GCD's
10.4 Roots of polynomials
10.5 Evaluation of multivariate functions
10.6 Roots of multivariate polynomials
10.7 Gröbner bases
11. Elementary number theory
11.1 Taking modular powers
11.2 Discrete logs
11.3 Prime numbers
11.4 Divisors
11.5 Quadratic residues
12. Modular forms
12.1 Cusp forms
12.2 Coset representatives
12.3 Modular symbols and Hecke operators
12.4 Genus formulas
13. Elliptic curves
13.1 Conductor
13.2
-invariant
13.3 The
-rational points on E
13.4 Modular form associated to an elliptic curve over
14. Number fields
14.1 Ramification
14.2 Class numbers
14.3 Integral basis
15. Algebraic geometry
15.1 Point counting on curves
15.1.1 Other methods
15.2 Riemann-Roch spaces using Singular
15.2.1 AG codes
16. Interface issues
16.1 Background jobs
16.2 Referencing Sage
16.3 Logging your Sage session
16.4 LaTeX conversion
16.5 Sage and other computer algebra systems
16.6 Command-line Sage help
16.7 Reading and importing files into Sage
16.8 Installation for the impatient
16.9 Python language program code for Sage commands
16.10 ``Special functions'' in Sage
16.11 What is Sage?
16.11.1 History of Sage
17. Contributions to this document
Bibliography
Index
Constructions in
Sage
: A
Sage
cookbook
Previous:
Constructions in Sage: A
Up:
Constructions in Sage: A
Next:
1. Tabular layout
Release 2008.07.11, documentation updated on July 11, 2008.
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