sage.libs.ntl.ntl_ZZ_pE.ntl_ZZ_pE:
File: sage/libs/ntl/ntl_ZZ_pE.pyx (starting at line 63)
The \class{ZZ_pE} class is used to model $\Z / p\Z [x] / (f(x))$.
sage.rings.number_field.totallyreal_data.tr_data:
File: sage/rings/number_field/totallyreal_data.pyx (starting at line 406)
This class encodes the data used in the enumeration of totally real
fields.
sage.libs.ntl.ntl_lzz_p.ntl_zz_p:
File: sage/libs/ntl/ntl_lzz_p.pyx (starting at line 57)
The class \class{zz_p} implements arithmetic modulo $p$,
for p smaller than a machine word.
sage.graphs.base.sparse_graph.SparseGraph:
File: sage/graphs/base/sparse_graph.pyx (starting at line 30)
Implements compiled sparse graphs via an array of hash tables.
sage.graphs.base.dense_graph.DenseGraph:
File: sage/graphs/base/dense_graph.pyx (starting at line 11)
Implements compiled dense graphs, as an array of packed bits.
sage.rings.polynomial.real_roots.context:
File: sage/rings/polynomial/real_roots.pyx (starting at line 4138)
A simple context class, which is passed through parts of the
real root isolation algorithm to avoid global variables.
sage.rings.polynomial.real_roots.island:
File: sage/rings/polynomial/real_roots.pyx (starting at line 3112)
This implements the island portion of my ocean-island root isolation
algorithm.
sage.combinat.dyck_word.DyckWordBacktracker:
DyckWordBacktracker: this class is an iterator for all Dyck words
with n opening parentheses and n - endht closing parentheses using
the backtracker class.
sage.libs.ntl.ntl_ZZ.ntl_ZZ:
File: sage/libs/ntl/ntl_ZZ.pyx (starting at line 43)
The \class{ZZ} class is used to represent signed, arbitrary length integers.
sage.libs.ntl.ntl_ZZ_pX.ntl_ZZ_pX:
File: sage/libs/ntl/ntl_ZZ_pX.pyx (starting at line 53)
The class \class{ZZ_pX} implements polynomial arithmetic modulo $p$.
sage.ext.multi_modular.MultiModularBasis_base:
File: sage/ext/multi_modular.pyx (starting at line 38)
This class stores a list of machine-sized prime numbers,
and can do reduction and Chinese Remainder Theorem lifting
modulo these primes.
sage.ext.multi_modular.MultiModularBasis:
File: sage/ext/multi_modular.pyx (starting at line 468)
Class used for storing a MultiModular bases of a fixed length.
sage.ext.multi_modular.MutableMultiModularBasis:
File: sage/ext/multi_modular.pyx (starting at line 533)
Class used for performing multi-modular methods,
with the possiblity of removing bad primes.
sage.gsl.ode.ode_solver:
File: sage/gsl/ode.pyx (starting at line 105)
ode_solver is a class that wraps the GSL libraries ode solver routines
To use it instantiate a class,
sage: T=ode_solver()
To solve a system of the form dy_i/dt=f_i(t,y), you must supply a
vector or tuple/list valued function f representing f_i.
exceptions.BaseException:
Common base class for all exceptions
exceptions.Exception:
Common base class for all non-exit exceptions.
exceptions.StandardError:
Base class for all standard Python exceptions that do not represent
interpreter exiting.
sage.libs.ntl.ntl_ZZ_pEX.ntl_ZZ_pEX:
File: sage/libs/ntl/ntl_ZZ_pEX.pyx (starting at line 45)
The class \class{ZZ_pEX} implements polynomials over finite ring extensions of $\Z / p\Z$.
sage.structure.parent.Parent:
File: sage/structure/parent.pyx (starting at line 61)
Parents are the SAGE/mathematical analogues of container objects
in computer science.
sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic:
EXAMPLES:
sage: FF = FiniteField(2003)
sage: R.<x> = PolynomialRing(FF)
sage: f = x**5 + 1184*x**3 + 1846*x**2 + 956*x + 560
sage: C = HyperellipticCurve(f)
sage: J = C.jacobian()
sage: a = x**2 + 376*x + 245; b = 1015*x + 1368
sage: X = J(FF)
sage: D = X([a,b])
sage: D
(x^2 + 376*x + 245, y + 988*x + 635)
sage: J(0)
(1)
sage: D == J([a,b])
True
sage: D == D + J(0)
True
An more extended example, demonstrating arithmetic in J(QQ) and J(K)
for a number field K/QQ.
sage.schemes.generic.glue.GluedScheme:
INPUT:
f -- open immersion from a scheme U to a scheme X
g -- open immersion from U to a scheme Y
OUTPUT:
The scheme obtained by gluing X and Y along the open set U.
sage.groups.group_homset.GroupHomset_generic:
This class will not work since morphism.GroupHomomorphism_coercion
is undefined and morphism.GroupHomomorphism_im_gens is undefined.
sage.combinat.root_system.ambient_space.AmbientSpace:
Abstract class for ambient spaces
Any implementation of this class should implement a class method
smallest_base_ring as described below, and a method dimension
working on a partially initialized instance with just root_system
as attribute.
sage.rings.real_mpfr.RealField:
File: sage/rings/real_mpfr.pyx (starting at line 220)
An approximation to the field of real numbers using floating
point numbers with any specified precision.
sage.rings.real_mpfi.RealIntervalField:
File: sage/rings/real_mpfi.pyx (starting at line 156)
RealIntervalField(prec, sci_not, rnd):
INPUT:
prec -- (integer) precision; default = 53
prec is the number of bits used to represent the
mantissa of a floating-point number.
sage.rings.real_double.RealDoubleField_class:
File: sage/rings/real_double.pyx (starting at line 59)
An approximation to the field of real numbers using double
precision floating point numbers.
sage.rings.complex_double.ComplexDoubleField_class:
File: sage/rings/complex_double.pyx (starting at line 117)
An approximation to the field of complex numbers using double
precision floating point numbers.
sage.rings.real_rqdf.RealQuadDoubleField_class:
File: sage/rings/real_rqdf.pyx (starting at line 149)
An approximation to a real number using quad double precision
floating point numbers.
sage.combinat.root_system.ambient_space.AmbientSpace:
Abstract class for ambient spaces
Any implementation of this class should implement a class method
smallest_base_ring as described below, and a method dimension
working on a partially initialized instance with just root_system
as attribute.
sage.structure.wrapper_parent.WrapperParent_model0:
File: sage/structure/wrapper_parent.pyx (starting at line 71)
This class is designed to wrap around unique parents to provide facility for different coercions, actions and embeddings.
sage.groups.group_homset.GroupHomset_generic:
This class will not work since morphism.GroupHomomorphism_coercion
is undefined and morphism.GroupHomomorphism_im_gens is undefined.
sage.crypto.cryptosystem.Cryptosystem:
A cryptosystem is a pair of maps
$$
E : {\mathcal K} \rightarrow {\rm Hom}({\mathcal M},{\mathcal C})
$$
$$
D : {\mathcal K} \rightarrow {\rm Hom}({\mathcal C},{\mathcal M})
$$
where ${\mathcal K}$ is the keyspace, ${\mathcal M}$ is the plaintext
or message space, and ${\mathcal C}$ is the ciphertext space.
sage.plot.plot3d.index_face_set.IndexFaceSet:
File: sage/plot/plot3d/index_face_set.pyx (starting at line 146)
Graphics3D object that consists of a list of polygons, also used for
triangulations of other objects.
sage.plot.plot3d.parametric_surface.ParametricSurface:
File: sage/plot/plot3d/parametric_surface.pyx (starting at line 71)
EXAMPLES:
sage: from sage.plot.plot3d.parametric_surface import ParametricSurface
sage: def f(x,y): return cos(x)*sin(y), sin(x)*sin(y), cos(y)+log(tan(y/2))+0.2*x
sage: S = ParametricSurface(f, (srange(0,12.4,0.1), srange(0.1,2,0.1)))
sage: show(S)
sage: len(S.face_list())
2214
The Hessenberg surface:
sage: def f(u,v):
...
sage.plot.plot3d.shapes.Box:
File: sage/plot/plot3d/shapes.pyx (starting at line 57)
EXAMPLES:
sage: from sage.plot.plot3d.shapes import Box
A square black box:
sage: show(Box([1,1,1]))
A red rectangular box.
sage.lfunctions.lcalc.LCalc:
Rubinstein's $L$-functions Calculator
Type \code{lcalc.[tab]} for a list of useful commands that are
implemented using the command line interface, but return objects
that make sense in SAGE.
sage.plot.plot.Graphics:
The Graphics object is an empty list of graphics objects
It is useful to use this object when intializing a
for loop where different graphics object will be added
to the empty object.
sage.rings.qqbar.ANDescr:
An AlgebraicNumber or AlgebraicReal is a wrapper around an ANDescr object.
sage.plot.plot3d.base.RenderParams:
File: sage/plot/plot3d/base.pyx (starting at line 777)
This class is a container for all parameters that may be
needed to render triangulate/render an object to a certain
format.
sage.modular.modform.numerical.NumericalEigenforms:
numerical_eigenforms(group, weight=2, eps=1e-20,
delta=1e-2, tp=[2,3,5])
INPUT:
group -- a congruence subgroup of a Dirichlet character of
order 1 or 2
weight -- an integer >= 2
eps -- a small float; abs( ) < eps is what "equal to zero" is
interpreted as for floating point numbers.
sage.rings.padics.pow_computer_ext.PowComputer_ZZ_pX_big:
File: sage/rings/padics/pow_computer_ext.pyx (starting at line 1637)
This class caches all contexts and moduli between 1 and cache_limit, and also caches for prec_cap.
sage.graphs.bruhat_sn.BruhatIntervalSn:
File: sage/graphs/bruhat_sn.pyx (starting at line 98)
The subinterval [start, end] = {v : start <= v <= end} of Sn under Bruhat
ordering.
sage.graphs.bruhat_sn.BruhatSn:
File: sage/graphs/bruhat_sn.pyx (starting at line 25)
Returns the Hasse diagram of the symmetric group Sn, with respect to
Bruhat ordering.
sage.lfunctions.dokchitser.Dokchitser:
Dokchitser's $L$-functions Calculator
Create a Dokchitser $L$-series with
Dokchitser(conductor, gammaV, weight, eps,
poles, residues, init, prec)
where
conductor -- integer, the conductor
gammaV -- list of Gamma-factor parameters,
e.g.
sage.combinat.root_system.type_dual.CartanType:
A class for dual Cartan types
The dual of a cartan type is a cartan type with the same index
set, but all arrows reversed in the Dynkin diagram (otherwise
said, the Cartan matrix is transposed).
sage.lfunctions.sympow.Sympow:
Watkins Symmetric Power $L$-function Calculator
Type \code{sympow.[tab]} for a list of useful commands that are
implemented using the command line interface, but return objects
that make sense in SAGE.
sage.quadratic_forms.binary_qf.BinaryQF:
BinaryQF([a,b,c])
INPUT:
v -- a list of 3 entries: [a,b,c]
OUTPUT:
the binary quadratic form a*x^2 + b*x*y + c*y^2.
sage.schemes.elliptic_curves.ell_modular_symbols.ModularSymbol:
A modular symbol attached to an elliptic curve, which is the map
from $\QQ\to \QQ$ obtained by sending $r$ to the normalized
symmetrized (or anti-symmetrized) integral from r to infinity.
sage.combinat.integer_vector.IntegerVectors_nnondescents:
The combinatorial class of integer vectors v graded by two parameters:
- n: the sum of the parts of v
- comp: the non descents composition of v
In other words: the length of v equals c[1]+...+c[k], and v is
descreasing in the consecutive blocs of length c[1], ..., c[k]
Those are the integer vectors of sum n which are lexicographically
maximal (for the natural left->right reading) in their orbit by the
young subgroup S_{c_1} x \dots x S_{c_k}.
sage.combinat.family.FiniteFamilyWithHiddenKeys:
A close variant of FiniteFamily where the family contains some
hidden keys whose corresponding values are computed lazily (and
remembered).
sage.combinat.family.LazyFamily:
A LazyFamily(I, f) is an associative container which models the
(possibly infinite) family (f(i))_{i in I}.
sage.rings.complex_number.ComplexNumber:
File: sage/rings/complex_number.pyx (starting at line 67)
A floating point approximation to a complex number using any specified
precision.
sage.rings.complex_double.ComplexDoubleElement:
File: sage/rings/complex_double.pyx (starting at line 478)
An approximation to a complex number using double precision
floating point numbers.
sage.rings.qqbar.AlgebraicNumber_base:
This is the common base class for algebraic numbers (complex
numbers which are the zero of a polynomial in ZZ[x]) and algebraic
reals (algebraic numbers which happen to be real).
sage.rings.qqbar.AlgebraicNumber:
The class for algebraic numbers (complex numbers which are the roots
of a polynomial with integer coefficients).
sage.rings.real_double.RealDoubleElement:
File: sage/rings/real_double.pyx (starting at line 394)
An approximation to a real number using double precision
floating point numbers.
sage.rings.real_rqdf.QuadDoubleElement:
File: sage/rings/real_rqdf.pyx (starting at line 423)
A floating point approximation to a real number using quad
double precision.
sage.rings.integer_mod.IntegerMod_gmp:
File: sage/rings/integer_mod.pyx (starting at line 976)
Elements of $\Z/n\Z$ for n not small enough to be operated on in word size.
sage.rings.integer.Integer:
File: sage/rings/integer.pyx (starting at line 253)
The \class{Integer} class represents arbitrary precision
integers.
sage.rings.integer.IntegerWrapper:
File: sage/rings/integer.pyx (starting at line 248)
Python classes have problems inheriting from Integer directly, but
they don't have issues with inheriting from IntegerWrapper.
sage.rings.real_mpfr.RealNumber:
File: sage/rings/real_mpfr.pyx (starting at line 673)
A floating point approximation to a real number using any specified
precision.
sage.libs.pari.gen.gen:
File: sage/libs/pari/gen.pyx (starting at line 118)
Python extension class that models the PARI GEN type.
sage.matrix.matrix_generic_dense.Matrix_generic_dense:
File: sage/matrix/matrix_generic_dense.pyx (starting at line 25)
The \class{Matrix_generic_dense} class derives from \class{Matrix}, and
defines functionality for dense matrices over any base ring.
sage.matrix.matrix_symbolic_dense.Matrix_symbolic_dense:
File: sage/matrix/matrix_symbolic_dense.pyx (starting at line 20)
The \class{Matrix_generic_dense} class derives from \class{Matrix}, and
defines functionality for dense matrices over any base ring.
sage.matrix.matrix_integer_2x2.Matrix_integer_2x2:
File: sage/matrix/matrix_integer_2x2.pyx (starting at line 22)
The \class{Matrix_generic_dense} class derives from \class{Matrix}, and
defines fast functionality 2x2 matrices over the integers.
sage.matrix.matrix_generic_sparse.Matrix_generic_sparse:
File: sage/matrix/matrix_generic_sparse.pyx (starting at line 63)
The \class{Matrix_generic_sparse} class derives from \class{Matrix}, and
defines functionality for sparse matrices over any base ring.
sage.rings.complex_double.FloatToCDF:
File: sage/rings/complex_double.pyx (starting at line 1741)
Fast morphism from anything with a __float__ method to an RDF element.
sage.structure.wrapper_parent.StealMorphism:
File: sage/structure/wrapper_parent.pyx (starting at line 55)
Represents a morphism S -> R that just sets the parent of x to R.
sage.rings.morphism.RingMap:
File: sage/rings/morphism.pyx (starting at line 341)
Set-theoretic map between rings.
sage.rings.residue_field.NFResidueFieldHomomorphism:
File: sage/rings/residue_field.pyx (starting at line 513)
The class representing a homomorphism from the order of a number
field to the residue field at a given prime.
sage.rings.morphism.RingMap_lift:
File: sage/rings/morphism.pyx (starting at line 351)
Given rings $R$ and $S$ such that for any $x \in R$ the function
\code{x.lift()} is an element that naturally coerces to $S$, this
returns the set-theoretic ring map $R \to S$ sending $x$ to
\code{x.lift()}.
sage.libs.ntl.ntl_GF2X.ntl_GF2X:
File: sage/libs/ntl/ntl_GF2X.pyx (starting at line 76)
Univariate Polynomials over GF(2) via NTL.
sage.rings.integer_mod.NativeIntStruct:
File: sage/rings/integer_mod.pyx (starting at line 158)
We store the various forms of the modulus here rather than in the
parent for efficiency reasons.
sage.rings.sparse_poly.Polynomial_rational:
File: sage/rings/sparse_poly.pyx (starting at line 423)
Polynomial_rational():
Create the zero polynomial over the rational numbers.
sage.libs.fplll.fplll.FP_LLL:
File: sage/libs/fplll/fplll.pyx (starting at line 40)
A basic wrapper class to support conversion to/from SAGE integer
matrices and executing the LLL computation.
sage.gsl.probability_distribution.RealDistribution:
File: sage/gsl/probability_distribution.pyx (starting at line 119)
The RealDistribution provides a number of routines for sampling
from and analyzing and visualizing probability distributions.
sage.gsl.probability_distribution.SphericalDistribution:
File: sage/gsl/probability_distribution.pyx (starting at line 52)
This class is capable of producing random points uniformly distributed on the surface of an
n-1 sphere in n dimensional euclidean space.
sage.libs.ntl.ntl_mat_GF2E.ntl_mat_GF2E:
File: sage/libs/ntl/ntl_mat_GF2E.pyx (starting at line 38)
The \class{mat_GF2E} class implements arithmetic with matrices over $GF(2**x)$.
sage.libs.ntl.ntl_ZZ_p.ntl_ZZ_p:
File: sage/libs/ntl/ntl_ZZ_p.pyx (starting at line 62)
The \class{ZZ_p} class is used to represent integers modulo $p$.
sage.libs.ntl.ntl_lzz_pX.ntl_zz_pX:
File: sage/libs/ntl/ntl_lzz_pX.pyx (starting at line 52)
The class \class{zz_pX} implements polynomial arithmetic modulo $p$,
for p smaller than a machine word.
sage.rings.polynomial.real_roots.rr_gap:
File: sage/rings/polynomial/real_roots.pyx (starting at line 3617)
A simple class representing the gaps between islands, in my
ocean-island root isolation algorithm.
sage.libs.ntl.ntl_mat_ZZ.ntl_mat_ZZ:
File: sage/libs/ntl/ntl_mat_ZZ.pyx (starting at line 70)
The \class{mat_ZZ} class implements arithmetic with matrices over $\Z$.