The SAGE Manual
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Front Matter
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The SAGE Manual
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1. Introduction
Contents
1. Introduction
2. Miscellaneous Functionality
2.1 Miscellaneous
2.1.1 misc.misc - Miscellaneous functions
2.2 Functional Notation
2.2.1 misc.functional - Functional notation
3. Functions and Algebraic Structures
3.1 Functions
3.1.1 structure.function - Classes that define maps and homomorphisms
4. Rings
4.1 Infinity
4.1.1 rings.infinity -
4.2 The Integer Ring
4.2.1 rings.integer_ring - The Integer Ring
4.2.2 rings.integer - Integers
4.3 The Rational Field
4.3.1 rings.rational_field - The field of rational numbers.
4.3.2 rings.rational -
4.4 The Real and Complex Numbers
4.4.1 rings.real_field - The field of real numbers.
4.4.2 rings.real_number - Real number
4.4.3 rings.complex_field - Complex numbers
4.4.4 rings.complex_number - A complex number
4.5 Quaternion Algebras
4.5.1 rings.quatalg - Quaternion algebras
4.5.2 rings.quaternion - Quaternions
4.6 Univariate Polynomials
4.6.1 rings.polynomial_ring - Univariate Polynomial Rings
4.6.2 rings.polynomial - Univariate Polynomial
4.7 Quotients of Univariate Polynomial Rings
4.7.1 rings.polyquo - Quotients of univariate polynomial rings
4.8 Multivariate Polynomials
4.8.1 rings.multi_polynomial_ring - Multivariate Polynomials
4.8.2 rings.multi_polynomial - Multivariate polynomial element.
4.9 Finite Fields
4.9.1 rings.finite_field - A finite field
4.9.2 rings.finite_field_element - Element of finite field.
4.10 The Integers Modulo
4.10.1 rings.integer_mod_ring - Ring of integers modulo n.
4.10.2 rings.integer_mod - Element of integers modulo n.
4.11 Power Series
4.11.1 rings.power_series_ring - Univariate Power Series Rings
4.11.2 rings.power_series - Power series ring
4.12 Laurent Series
4.12.1 rings.laurent_series_ring - Laurent series ring
4.12.2 rings.laurent_series - A Laurent series
4.13 Number Fields
4.13.1 rings.number_field - Number fields
4.13.2 rings.number_field_element - Number field element
4.14
-Adic Numbers
4.14.1 rings.padic_field - Field Q_p of p-adic numbers.
4.14.2 rings.padic - p-adic numbers
5. Linear Algebra
5.1 Vector Spaces
5.1.1 linalg.vector_space - Vector space
5.2 Vectors
5.2.1 linalg.vector - Vectors
5.3 Matrix Spaces
5.3.1 linalg.matrix_space - Space of matrices over a ring.
5.4 Matrices
5.4.1 linalg.matrix - Matrices
6. Curves
6.1 Elliptic Curves
6.1.1 ellcurve.constructor - Elliptic curve constructor
6.1.2 ellcurve.ell_generic - Elliptic curves over a general ring
6.1.3 ellcurve.ell_rational_field - Elliptic curves over the rational numbers
6.1.4 ellcurve.ell_finite_field - Elliptic curves over finite fields
7. Modular Forms
7.1 Congruence Subgroups
7.1.1 modular.congroup - Congruence subgroups of SL_2(Z)
7.2 Dirichlet Characters
7.2.1 modular.dirichlet - Dirichlet characters
7.3 Cusps
7.3.1
modular.cusps
- The set
of cusps
7.4 Dimension and Other Formulas
7.4.1 modular.dims - Dimensions of spaces of modular forms
7.5 Modular Forms
7.5.1 modular.modform.modform - Modular Forms
8. Modular Symbols
8.1 Creation of Modular Symbols Spaces
8.1.1 Examples
8.2 Creation
8.2.1 modular.modsym.modsym - Create modular symbols spaces
8.3 Generic Spaces
8.3.1 modular.modsym.space - Generic spaces of modular symbols.
8.4 Ambient Spaces
8.4.1 modular.modsym.ambient - Ambient spaces of modular symbols.
8.5 Subspaces of Ambient Spaces
8.5.1 modular.modsym.subspace - Subspace of ambient spaces of modular symbols
8.6 Elements of Modular Symbols Spaces
8.6.1 modular.modsym.element - A single element of an ambient space of modular symbols.
8.6.2 modular.modsym.manin_symbols - Manin symbols
8.7 Boundary Modular Symbols
8.7.1 modular.modsym.boundary - Space of boundary modular symbols.
8.8 Cremona-Heilbronn-Merel Matrices
8.8.1 modular.modsym.heilbronn -
8.9 The Projective Line
8.9.1 modular.modsym.p1list -
8.10 Relation Matrices
8.10.1 modular.modsym.relation_matrix - Relation matrices for ambient modular symbols spaces.
9. Tables
9.1 Elliptic Curves: John Cremona's Tables
9.1.1 tables.cremona - Cremona's tables of elliptic curves.
9.2 Number Fields: John Jones's Tables
9.2.1 tables.jones - John Jones's tables of number fields
9.3 Conway Polynomials: Frank Luebeck's Tables
9.3.1 tables.conway - Frank Luebeck's tables of Conway polynomials over finite fields.
10. C/C++ Libraries
10.1 The MWRANK C++ Library
10.1.1 libs.mwrank -
10.2 The NTL C++ Library
10.2.1 libs.ntl -
10.3 The PARI C Library
10.3.1 libs.pari - Interface to PARI C library
11. Interfaces
11.1 The GAP Interface
11.1.1 interfaces.gap - Interface to GAP
11.2 The Singular Interface
11.2.1 interfaces.singular - Interface to Singular
A. History and License
A.1 License
A.1.1 The GNU General Public License
Module Index
Index
The SAGE Manual
Previous:
Front Matter
Up:
The SAGE Manual
Next:
1. Introduction
Release 0.6.beta1, documentation updated on September 7, 2005.
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