The SAGE Manual
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Front Matter
The SAGE Manual
William A. Stein
wstein@ucsd.edu
Date:
October 22, 2005
Front Matter
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
7.1.3 Design
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 MAGMA Interface
15.2.1
interfaces.magma
- Interface to MAGMA
15.3 The Octave Interface
15.3.1
interfaces.octave
- Interface to the Octave interpreter
15.4 The GP/PARI Interface
15.4.1
interfaces.gp
- Interface to the gp interpreter
15.5 The SAGE Interface
15.5.1
interfaces.sage0
- Interface to the SAGE interpreter (!)
15.6 The Singular Interface
15.6.1
interfaces.singular
- Interface to Singular
A. History and License
A.1 License
A.1.1 The GNU General Public License
Module Index
Index
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The SAGE Manual
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