The SAGE Manual
Previous:
Front Matter
Up:
The SAGE Manual
Next:
1. Introduction
Contents
1. Introduction
2. Miscellaneous
2.1 Miscellaneous
2.1.1 misc.misc - Miscellaneous functions
2.2 Functional Notation
2.2.1 misc.functional - Functional notation
2.3 Latex Notation
2.3.1 misc.latex - Latex printing support
3. Structures
3.1 Generators
3.1.1 structure.gens - Base class for objects with generators
3.2 Formal Sums
3.2.1 structure.formal_sum - Formal sum
3.3 Factorizations
3.3.1 structure.factorization - Type that holds the factorization of an object
3.4 Elements
3.4.1 structure.element -
4. Category, Morphisms, and Functors
4.1 Categories
4.1.1 categories.categories - Categories
4.2 Homspaces
4.2.1 categories.homspaces - Hom spaces between objects of a category
4.3 Morphisms
4.3.1 categories.morphisms - Classes that defines morphisms
4.3.2 categories.matrix_morphisms - Morphisms defined by a matrix
4.4 Functors
4.4.1 categories.functors - Functors
5. Monoids
5.1 Free Monoids
5.1.1 monoids.free_monoid - Free monoids
5.1.2 monoids.free_monoid_element - Monoid elements
5.2 Free Abelian Monoids
5.2.1 monoids.free_abelian_monoid - Free abelian monoids
5.2.2 monoids.free_abelian_monoid_element - Abelain monoid elements
6. Rings and Fields
6.1 Infinity
6.1.1 rings.infinity -
6.2 The Integer Ring
6.2.1 rings.integer_ring - The Integer Ring
6.2.2 rings.integer - Integers
6.3 The Integers Modulo
6.3.1 rings.integer_mod_ring - Ring of integers modulo n.
6.3.2 rings.integer_mod - Element of integers modulo n.
6.4 The Rational Field
6.4.1 rings.rational_field - The field of rational numbers.
6.4.2 rings.rational -
6.5 The Real Numbers
6.5.1 rings.real_field -
6.5.2 rings.real_field_element -
6.6 The Complex Numbers
6.6.1 rings.complex_field - Complex numbers
6.6.2 rings.complex_number - A complex number
6.7 Finite Fields
6.7.1 rings.finite_field - A finite field
6.7.2 rings.finite_field_element - Element of finite field.
6.8 Number Fields
6.8.1 rings.number_field - Number fields
6.8.2 rings.number_field_element - Number field element
6.9 Local Fields
6.9.1 rings.padic_field - Field Q_p of p-adic numbers.
6.9.2 rings.padic - p-adic numbers
6.10 Fraction Fields
6.10.1 rings.fraction_field - Fraction field of any integral domain.
6.10.2 rings.fraction_field_element - Fraction field element.
6.11 Univariate Polynomial Rings
6.11.1 rings.polynomial_ring - Univariate Polynomial Rings
6.11.2 rings.polynomial_element - Univariate Polynomial
6.12 Quotients of Univariate Polynomial Rings
6.12.1 rings.polynomial_quotient_ring - Quotients of univariate polynomial rings
6.12.2 rings.polynomial_quotient_ring_element - Elements of quotients of univariate polynomial rings
6.13 Multivariate Polynomial Rings
6.13.1 rings.multi_polynomial_ring - Multivariate Polynomials
6.13.2 rings.multi_polynomial - Multivariate polynomial element
6.14 Power Series Rings
6.14.1 rings.power_series_ring - Univariate Power Series Rings
6.14.2 rings.power_series - Element of a power series
6.15 Laurent Series Rings
6.15.1 rings.laurent_series_ring - Laurent series ring
6.15.2 rings.laurent_series - Element of Laurent series ring
6.16 Ideals of Rings
6.16.1 rings.ideal - Ideals
7. Matrices
7.1 Matrix Spaces
7.1.1 matrix.matrix_space - Space of matrices over a ring.
7.1.2 matrix.matrix - Matrices
8. Modules
8.1 Free Modules
8.1.1 modules.free_module - Free modules
8.1.2 modules.free_module_element -
8.2 Homspaces
8.2.1 modules.free_module_homspace - Hom spaces between objects of a category of free modules.
8.3 Morphisms of Free Modules
8.3.1 modules.free_module_morphism - Morphisms of free modules
9. Algebras
9.1 Free Algebras
9.1.1 algebras.free_algebra - Free algebras
9.1.2 algebras.free_algebra_element - Free algebra elements
9.2 Quotients of Free Algebras
9.2.1 algebras.free_algebra_quotient - Free algebra quotients
9.2.2 algebras.free_algebra_quotient_element - Free algebra quotient elements
9.3 Quaternion Algebras
9.3.1 algebras.quaternion_algebra - Quaternion algebras
9.3.2 algebras.quaternion_algebra_element - Quaternion algebra elements
9.3.3 algebras.quaternion_order - Quaternion orders
9.3.4 algebras.quaternion_order_element - Quaternion order elements
9.3.5 algebras.quaternion_order_ideal - Quaternion ideal
9.3.6 algebras.quaternion_order_ideal_element - Quaternion ideal elements
10. Curves
10.1 Elliptic Curves
10.1.1 schemes.hypersurfaces.plane_curves.elliptic.constructor - Elliptic curve constructor
10.1.2 schemes.hypersurfaces.plane_curves.elliptic.ell_generic - Elliptic curves over a general ring
10.1.3 schemes.hypersurfaces.plane_curves.elliptic.ell_rational_field - Elliptic curves over the rational numbers
10.1.4 schemes.hypersurfaces.plane_curves.elliptic.ell_finite_field - Elliptic curves over finite fields
11. General Hecke Algebras and Hecke Modules
11.1 Hecke Modules
11.1.1 modular.hecke.modules - Hecke modules
11.1.2 modular.hecke.submodules - Submodule of a Hecke module.
11.1.3 modular.hecke.ambient_modules - Ambient Hecke modules
11.1.4 modular.hecke.elements - Elements of Hecke modules
11.2 Morphisms of Hecke Modules
11.2.1 modular.hecke.homspaces - Hom spaces between objects of the category of hecke modules over a given base ring.
11.2.2 modular.hecke.morphisms - Morphism of Hecke modules
11.3 Hecke Algebras
11.3.1 modular.hecke.algebra - Hecke algebras and modules
11.3.2 modular.hecke.operators - Hecke algebras and modules
12. Modular Symbols
12.1 Creation
12.1.1 modular.modsym.modsym - Create modular symbols spaces
12.2 Spaces of Modular Symbols
12.2.1 modular.modsym.space - Generic spaces of modular symbols.
12.2.2 modular.modsym.ambient - Ambient spaces of modular symbols.
12.2.3 modular.modsym.subspace - Subspace of ambient spaces of modular symbols
12.3 Elements of Modular Symbols Spaces
12.3.1 modular.modsym.element - A single element of an ambient space of modular symbols.
12.3.2 modular.modsym.manin_symbols - Manin symbols
12.4 Boundary Modular Symbols
12.4.1 modular.modsym.boundary - Space of boundary modular symbols.
12.5 Cremona-Heilbronn-Merel Matrices
12.5.1 modular.modsym.heilbronn -
12.6 The Projective Line
12.6.1 modular.modsym.p1list -
12.7 Relation Matrices
12.7.1 modular.modsym.relation_matrix - Relation matrices for ambient modular symbols spaces.
13. Databases
13.1 Elliptic Curves: John Cremona's Databases
13.1.1 databases.cremona - Cremona's tables of elliptic curves.
13.2 Number Fields: John Jones's Databases
13.2.1 databases.jones - John Jones's tables of number fields
13.3 Conway Polynomials: Frank Luebeck's Databases
13.3.1 databases.conway - Frank Luebeck's tables of Conway polynomials over finite fields.
14. C/C++ Libraries
14.1 The MWRANK C++ Library
14.1.1 libs.mwrank -
14.2 The NTL C++ Library
14.2.1 libs.ntl - Interface to NTL
14.3 The PARI C Library
14.3.1 libs.pari - Interface to PARI C library
15. Interfaces
15.1 The GAP Interface
15.1.1 interfaces.gap - Interface to the GAP interpreter
15.2 The Singular Interface
15.2.1 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 0.7.7, documentation updated on October 4, 2005.
See
About this document...
for information on suggesting changes.