The SAGE Manual
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Front Matter
The SAGE Manual
William A. Stein
wstein@ucsd.edu
Date:
September 7, 2005
Front Matter
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
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The SAGE Manual
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