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sage
algebras
algebras
: Algebras
old
algebras
: Algebras
quatalg
: nodoctest...
quaternion
: nodoctest Quaternions
quatalg
: Quaternion algebras:...
quaternion
: Quaternions
all
: nodoctest
all.py -- much of sage is imported into this module, so you don't
have to import everything individually.
ellcurve
ext
functions
transcendental
: Computation of transcendental functions.
groups
abelian
: Abelian groups
interface
linalg
: Classes for matrix algebra.
dense_matrix
dense_matrix_pyx
install
: Script to create shared library associated to pyrex file.
linalg
matrix
: Matrix generic
matrix_setup
matrix_space
: Space of matrices over a ring.
sparse_matrix
: Sparse matrices
To create an m x n sparse matrix over a ring R, use the command
SparseMatrix(base_ring, nrows, ncols, entries=[])
where entries is a list of 3-tuples (i,j,x).
sparse_matrix_pyx
vector
: Vectors
vector_space
: Vector space
misc
mode
modular
abvar
modabvar
: Modular abelian varieties
congroup
: Congruence subgroups of SL_2(Z)
cusps
dims
: Dimensions of spaces of modular forms
dirichlet
: Dirichlet characters
hecke
: Hecke algebras and modules
modform
modform
: Modular Forms
DESIGN NOTES:
Our implementation depends heavily on the fact that we have good
dimension formulas (see dims.py) for spaces of modular forms with
character, and new subspaces, so that we don't have to compute
q-expansions for the whole space in order to compute q-expansions /
elements / and dimensions of certain subspaces.
modsym
ambient
: Ambient spaces of modular symbols.
boundary_symbol
: Boundary modular symbols.
element
: A single element of an ambient space of modular symbols.
g1list
: List of coset represenatives for Gamma_1(N) in SL_2(Z).
heilbronn
manin_symbols
: Manin symbols
modsym
: Creating modular symbols spaces
p1list
relation_matrix
: Relations matrices for modular symbols.
space
: nodoctest Generic spaces of modular symbols.
subspace
: Ambient spaces of modular symbols with a nontrivial Dirichlet
character.
ssmod
ssmod
: The module of supersingular points
pari
buhler_gross
expect
: A pexpect interface to gp interpreter.
func
py_pari
py_pari_py
wrap
: Interface to gp interpreter
plot
graph
: Package for drawing graphs related to elliptic curves, etc.
profile
rings
arith
: Basic arithmetic functions
arith_c
arith_gmp
big_oh
: Big O for various types (power series, p-adics, etc.)
coerce
: Coercion helper functions
complex_field
: Complex numbers
complex_number
: A complex number
element
element2
: Abstract base class for ring elements.
element_py
finite_field
: A finite field
finite_field_element
: Element of finite field.
infinity
integer
integer_mod
: Element of integers modulo n.
integer_mod_ring
: Ring of integers modulo n.
integer_py
: Tests of examples in integer.
integer_ring
: The ring of rational integers
interval
: Basic interval arithmetic class
intmod_pyx
laurent_series
: A Laurent series
laurent_series_ring
: Laurent series ring
multi_polynomial
: Multivariate polynomial.
multi_polynomial_ring
: Multivariate Polynomials
number_field
: Number field
number_field_element
: Number field element
padic
: p-adic Ring
padic_field
: Field Q_p of p-adic numbers.
pari_ring
: Ring of pari objects.
polylist_fcns
: Polylist functionality.
polynomial
: Univariate Polynomial
polynomial_pyx
polynomial_ring
: Univariate Polynomial Rings
power_series
: Power series ring
power_series_ring
: Univariate Power Series Rings
rational
rational_field
: The field of rational numbers.
real_field
: The field of real numbers.
real_number
: Real number
ring
: Abstract base class for rings
rings
: Rings
sparse_poly
structure
tables
all
: Tables.
compressed_storage
: Compression for ZODB.
conv
db
: Generic database that uses ZODB.
elliptic_curves
: Table of elliptic curves of conductor <= 30000.
gamma0wt2
: Table of arithmetic information about modular forms of weight 2 on
Gamma_0(N) for N <= 10000.
jones
: nodoctest
odlyzko
: Tables of zeros of the Riemann-Zeta function.
tables
: Access to external tables of modular forms and elliptic curves
version
__builtin__.object
:
The most base type
sage.ellcurve.ellcurve.EllipticCurve
:
Elliptic curve.
sage.ellcurve.ellcurve.EllipticCurve_generic
:
Elliptic curve over a generic base ring.
sage.ellcurve.ellcurve.EllipticCurve_RationalField
:
Elliptic curve over the Rational Field.
sage.misc.misc.lazy_prop
sage.rings.multi_polynomial_ring.MPolynomialRing
:
Multivariate polynomial ring.
sage.pari.wrap.PariObject
sage.rings.real_field.RealField
:
The field of real numbers.
sage.rings.real_field.RealField_decimal
:
EXAMPLES:
sage.rings.real_field.RealField_mpf
:
EXAMPLES:
sage.linalg.sparse_matrix.SparseMatrix
sage.linalg.sparse_matrix.Sparse_matrix_generic
:
A generic sparse matrix.
sage.linalg.sparse_matrix.Sparse_matrix_rational
:
A sparse matrix over the rational numbers.
sage.linalg.sparse_matrix.SparseVectorSpace
sage.linalg.sparse_matrix.Sparse_vector_space_generic
:
Sparse vector space.
__builtin__.type
:
type(object) -> the object's type type(name, bases, dict) -> a
new type
sage.linalg.vector_space.VectorSpace
:
Create a Vector Space.
sage.linalg.vector_space.VectorSpace_generic
sage.linalg.vector_space.VectorSpace_ambient
:
Ambient vector space:
base_field -- a field
degree -- int >= 0, the degree of the vector space
(number of components of vectors).
sage.linalg.vector_space.VectorSpace_subspace
sage.algebras.old.quatalg.Lattice
sage.algebras.quatalg.Lattice
sage.ellcurve.ellcurve.Point
:
Point on an elliptic curve.
sage.groups.abelian.AbelianGroup
sage.linalg.matrix.Matrix
sage.linalg.matrix.Matrix_generic_dense
sage.linalg.matrix.Matrix_generic_sparse
:
A generic sparse matrix is a dictionary with keys pairs (i,j)
and entries in the base ring.
sage.linalg.matrix.Matrix_rational_dense
sage.linalg.sparse_matrix.SparseVector
:
A generic sparse vector.
sage.linalg.vector.Vector
sage.linalg.vector.Vector_generic_dense
sage.linalg.vector.Vector_generic_sparse
:
A generic sparse vector is a dictionary with keys ints i
and entries in the base ring.
sage.misc.errors.UsageError
sage.modular.abvar.modabvar.HomSpace
sage.modular.abvar.modabvar.Homology
sage.modular.abvar.modabvar.LSeries
sage.modular.abvar.modabvar.TorsionPoint
sage.modular.congroup.CongruenceSubgroup
sage.modular.cusps.Cusp
:
The set of cusps.
sage.modular.dirichlet.DirichletCharacter
:
A DirichletCharacter is the extension of a homomorphism
(Z/NZ)^* --> R^*, for some ring R, to a map Z/NZ --> R,
got by sending those x with (N,x)>1 to 0.
sage.modular.hecke.HeckeModule
sage.modular.abvar.modabvar.ModularAbelianVariety
sage.modular.modform.modform.ModularFormsSpace
:
A generic space of modular forms.
sage.modular.modform.modform.ModularForms
:
An ambient space of modular forms.
sage.modular.modform.modform.ModularFormsWithCharacter
:
A space of modular forms with character.
sage.modular.modform.modform.ModularFormsSubspace
:
A subspace of an ambient space of modular forms.
sage.modular.modsym.space.ModularSymbolsSpace
sage.modular.modsym.ambient.ModularSymbolsAmbient
:
An ambient space of modular symbols for a congruence subgroup of SL_2(Z).
sage.modular.modsym.subspace.ModularSymbolsSubspace
sage.modular.ssmod.ssmod.SupersingularModule
sage.modular.hecke.UniversalHeckeAlgebra
sage.modular.hecke.UniversalHeckeOperator
sage.modular.modform.modform.ModularFormElement
:
A modular form.
sage.modular.modsym.boundary_symbol.BoundarySymbol
:
Specific boundary modular symbol.
sage.modular.modsym.element.ModularSymbolElement
:
ModularSymbolElement:
sage.modular.modsym.g1list.G1list
sage.modular.modsym.manin_symbols.ManinSymbol
:
A Manin symbol [X^i*Y^(k-2-i),(u,v)].
sage.modular.modsym.manin_symbols.ManinSymbolList
:
All sage symbols for a given group, weight, and character.
sage.modular.modsym.manin_symbols.ManinSymbolList_character
:
List of Manin Symbols with character.
sage.modular.modsym.manin_symbols.ManinSymbolList_gamma0
:
List of Manin symbols for Gamma0(N).
sage.modular.modsym.manin_symbols.ManinSymbolList_gamma1
:
List of Manin symbols for Gamma0(N).
sage.pari.wrap.PariCall
sage.plot.graph.Command
sage.plot.graph.Axes
sage.plot.graph.Circle
sage.plot.graph.Color
sage.plot.graph.Curve
sage.plot.graph.Disc
sage.plot.graph.EllipticCurve
sage.plot.graph.Function
:
Draw
sage.plot.graph.Grid
sage.plot.graph.Line
sage.plot.graph.Path
sage.plot.graph.Polygon
sage.plot.graph.Set
sage.plot.graph.Text
sage.plot.graph.Ticks
:
Put a vertical tick mark and label at each position on the x-axis
between xmin and xmax that when scaled is an integer multiple of
xmult.
sage.plot.graph.Graph
sage.plot.graph.Point
sage.rings.element2.Element
:
Generic ring element base class, so all this functionality must be
defined by any ring element.
sage.rings.number_field.FractionalIdeal
sage.rings.polylist_fcns.PolyList
sage.rings.ring.Ring
:
Generic ring class, so all the functions below must be defined by all
rings, since they derive from this class.
sage.algebras.old.quatalg.Algebra
sage.algebras.quatalg.Algebra
sage.rings.complex_field.ComplexField
:
The field of complex numbers.
sage.rings.finite_field.FiniteField
:
Finite field of order q, where q is a prime power.
sage.rings.integer_mod_ring.IntegerModRing
:
The ring of integers modulo N, e.g., when N is prime
this is a prime finite field.
sage.rings.integer_ring.IntegerRing
:
The ring of integers.
sage.rings.interval.IntervalRing
sage.rings.multi_polynomial_ring.MPolynomialRing_base
sage.rings.number_field.NumberField
sage.rings.number_field.CyclotomicField
:
Create a cyclotomic extension of the rational field.
sage.rings.number_field.QuadraticField
:
Create a quadratic extension of the rational field.
sage.rings.padic_field.pAdicField
:
Field Q_p of p-adic numbers.
sage.rings.pari_ring.PariRing
sage.rings.polynomial_ring.PolynomialRing
:
Univariate polynomial ring.
sage.rings.power_series_ring.PowerSeriesRing
sage.rings.laurent_series_ring.LaurentSeriesRing
:
Univariate Laurent Series Ring
sage.rings.rational_field.RationalField
:
The field of rational numbers.
sage.rings.real_field.RealField
:
The field of real numbers.
sage.rings.real_field.RealField_decimal
:
EXAMPLES:
sage.rings.real_field.RealField_mpf
:
EXAMPLES:
sage.structure.function.Function
sage.structure.gens.Gens
sage.algebras.old.quatalg.Algebra
sage.algebras.quatalg.Algebra
sage.modular.dirichlet.DirichletGroup
:
The group of Dirichlet character mod modulus with values in the
subgroup <zeta> of the multiplicative group of the base_ring.
sage.rings.finite_field.FiniteField
:
Finite field of order q, where q is a prime power.
sage.linalg.matrix_space.MatrixSpace
:
The space of all nrows x ncols matrices over base_ring.
sage.modular.modsym.space.ModularSymbolsSpace
sage.modular.modsym.ambient.ModularSymbolsAmbient
:
An ambient space of modular symbols for a congruence subgroup of SL_2(Z).
sage.modular.modsym.subspace.ModularSymbolsSubspace
sage.rings.multi_polynomial_ring.MPolynomialRing_base
sage.rings.number_field.NumberField
sage.rings.number_field.CyclotomicField
:
Create a cyclotomic extension of the rational field.
sage.rings.number_field.QuadraticField
:
Create a quadratic extension of the rational field.
sage.rings.polynomial_ring.PolynomialRing
:
Univariate polynomial ring.
sage.rings.power_series_ring.PowerSeriesRing
sage.rings.laurent_series_ring.LaurentSeriesRing
:
Univariate Laurent Series Ring
sage.linalg.vector_space.VectorSpace_generic
sage.linalg.vector_space.VectorSpace_ambient
:
Ambient vector space:
base_field -- a field
degree -- int >= 0, the degree of the vector space
(number of components of vectors).
sage.linalg.vector_space.VectorSpace_subspace
sage.tables.compressed_storage.CompressedStorage
sage.tables.compressed_storage.ZWrap
:
Wrap a function to produce a new one that can take a compressed string
as the first argument.
sage.tables.conv.ModularForm
sage.tables.elliptic_curves.EllipticCurve
:
Class that defines an elliptic curve in the database.
sage.tables.gamma0wt2.ModularForm
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