Constructions in
SAGE
(How to)
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Constructions in SAGE (How
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Constructions in SAGE (How
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1. Tabular layout
Contents
1. Tabular layout
2. Calculus
2.1 Using maxima
2.2 Ordinary differential equations
2.3 Euler's method for numerically solving an ODE
3. Plotting
3.1 gnuplot
3.2 Plotting functions using matplotlib
4. Groups
4.1 Permutation groups
4.2 Conjugacy classes
4.3 Normal subgroups
4.4 Centers
5. Linear algebra
5.1 Vector spaces
5.2 Kernels
5.3 Eigenvectors and eigenvalues
5.4 Row reduction
5.5 Characteristic polynomial
5.6 Solving systems of linear equations
6. Linear codes and ciphers
6.1 Codes
6.2 Ciphers (LFSRs)
7. Graph theory
7.1 Cayley graphs
7.2 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. Taking powers
10.1 Integers
10.2 Matrices
10.3 Polynomials
11. Polynomial
11.1 Factorization
11.2 Polynomial GCD's
11.3 Roots of polynomials
11.4 Evaluation of multivariate functions
11.5 Gröbner bases
12. Elementary number theory
12.1 Discrete logs
12.2 Prime numbers
12.3 Divisors
12.4 Quadratic residues
13. Modular forms
13.1 Cusp forms
13.2 Coset representatives
13.3 Modular form associated to an elliptic curve over
13.4 Modular symbols and Hecke operators
13.5 Genus formulas
14. Elliptic curves
14.1 conductor
14.2
-invariant
14.3 The
-rational points on E
15. Number fields
15.1 Ramification
15.2 Class numbers
15.3 Integral basis
16. Algebraic geometry
16.1 Plotting curves
16.1.1 matplotlib
16.1.2 surf
16.2 Plotting surfaces
16.3 Point counting on curves
16.4 Riemann-Roch spaces
16.4.1 AG codes
17. Interface issues
17.1 Background jobs
17.2 Referencing SAGE
17.3 Logging your SAGE session
17.4 LaTeX conversion
17.5 SAGE and other computer algebra systems
17.6 Command-line SAGE help
17.7 Reading and importing files into SAGE
17.8 Installation for the impatient
17.9 Python language program code for SAGE commands
17.10 ``Special functions'' in SAGE
17.11 What is SAGE?
17.11.1 History of SAGE
18. Contributions to this document
Bibliography
Index
Constructions in
SAGE
(How to)
Previous:
Constructions in SAGE (How
Up:
Constructions in SAGE (How
Next:
1. Tabular layout
Release 2006.05.25, documentation updated on May 25, 2006.
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