code stringlengths 17 6.64M |
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class Latte_count(Executable):
'\n Feature for the executable ``count`` from :ref:`LattE integrale <spkg_latte_int>`.\n '
def __init__(self):
'\n TESTS::\n\n sage: from sage.features.latte import Latte_count\n sage: isinstance(Latte_count(), Latte_count)\n ... |
class Latte_integrate(Executable):
'\n Feature for the executable ``integrate`` from :ref:`LattE integrale <spkg_latte_int>`.\n '
def __init__(self):
'\n TESTS::\n\n sage: from sage.features.latte import Latte_integrate\n sage: isinstance(Latte_integrate(), Latte_in... |
class Latte(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of excecutables\n from :ref:`LattE integrale <spkg_latte_int>`.\n\n EXAMPLES::\n\n sage: from sage.features.latte import Latte\n sage: Latte().is_present() # optional - latte_int\n FeatureTestRes... |
def all_features():
return [Latte()]
|
class Lrs(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of the ``lrs``\n binary which comes as a part of ``lrslib``.\n\n EXAMPLES::\n\n sage: from sage.features.lrs import Lrs\n sage: Lrs().is_present() # optional - lrslib\n FeatureTestResult('lrs', True... |
class LrsNash(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of the ``lrsnash``\n binary which comes as a part of ``lrslib``.\n\n EXAMPLES::\n\n sage: from sage.features.lrs import LrsNash\n sage: LrsNash().is_present() # optional - lrslib\n FeatureTestRe... |
class Lrslib(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the executables\n :class:`lrs <Lrs>` and :class:`lrsnash <LrsNash>` provided by the :ref:`lrslib <spkg_lrslib>` package.\n\n EXAMPLES::\n\n sage: from sage.features.lrs import Lrslib\n sage: Lrslib()... |
def all_features():
return [Lrslib()]
|
class Mcqd(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the :mod:`~sage.graphs.mcqd` module,\n which is the SageMath interface to the :ref:`mcqd <spkg_mcqd>` library\n\n EXAMPLES::\n\n sage: from sage.features.mcqd import Mcqd\n sage: Mcqd().is_present() #... |
def all_features():
return [Mcqd()]
|
class Meataxe(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the Sage modules\n that depend on the :ref:`meataxe <spkg_meataxe>` library.\n\n EXAMPLES::\n\n sage: from sage.features.meataxe import Meataxe\n sage: Meataxe().is_present() # optional - meataxe\n... |
def all_features():
return [Meataxe()]
|
class MIPBackend(Feature):
'\n A :class:`~sage.features.Feature` describing whether a :class:`MixedIntegerLinearProgram` backend is available.\n '
def _is_present(self):
"\n Test for the presence of a :class:`MixedIntegerLinearProgram` backend.\n\n EXAMPLES::\n\n sage: ... |
class CPLEX(MIPBackend):
'\n A :class:`~sage.features.Feature` describing whether the :class:`MixedIntegerLinearProgram` backend ``CPLEX`` is available.\n '
def __init__(self):
"\n TESTS::\n\n sage: from sage.features.mip_backends import CPLEX\n sage: CPLEX()._is_pr... |
class Gurobi(MIPBackend):
'\n A :class:`~sage.features.Feature` describing whether the :class:`MixedIntegerLinearProgram` backend ``Gurobi`` is available.\n '
def __init__(self):
"\n TESTS::\n\n sage: from sage.features.mip_backends import Gurobi\n sage: Gurobi()._i... |
class COIN(JoinFeature):
'\n A :class:`~sage.features.Feature` describing whether the :class:`MixedIntegerLinearProgram` backend ``COIN`` is available.\n '
def __init__(self):
"\n TESTS::\n\n sage: from sage.features.mip_backends import COIN\n sage: COIN()._is_prese... |
class CVXOPT(JoinFeature):
'\n A :class:`~sage.features.Feature` describing whether the :class:`MixedIntegerLinearProgram` backend ``CVXOPT`` is available.\n '
def __init__(self):
"\n TESTS::\n\n sage: from sage.features.mip_backends import CVXOPT\n sage: CVXOPT()._... |
def all_features():
return [CPLEX(), Gurobi(), COIN(), CVXOPT()]
|
class msolve(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of :ref:`msolve <spkg_msolve>`.\n\n EXAMPLES::\n\n sage: from sage.features.msolve import msolve\n sage: msolve().is_present() # optional - msolve\n FeatureTestResult('msolve', True)\n "
def... |
def all_features():
return [msolve()]
|
class NautyExecutable(Executable):
"\n A :class:`~sage.features.Feature` which checks for executables from the :ref:`nauty <spkg_nauty>` package.\n\n EXAMPLES::\n\n sage: from sage.features.nauty import NautyExecutable\n sage: NautyExecutable('converseg').is_present() ... |
class Nauty(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the executables\n which comes as a part of :ref:`nauty <spkg_nauty>`.\n\n EXAMPLES::\n\n sage: from sage.features.nauty import Nauty\n sage: Nauty().is_present() ... |
def all_features():
return [Nauty()]
|
class PyNormaliz(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the\n Python package :ref:`PyNormaliz <spkg_pynormaliz>`.\n\n EXAMPLES::\n\n sage: from sage.features.normaliz import PyNormaliz\n sage: PyNormaliz().is_present() # optional - ... |
def all_features():
return [PyNormaliz()]
|
class PalpExecutable(Executable):
'\n A :class:`~sage.features.Feature` describing the presence of a :ref:`PALP <spkg_palp>` executable.\n\n INPUT:\n\n - ``palpprog`` -- string, one of ``"poly"``, ``"class"``, ``"nef"``, ``"cws"``.\n\n - ``suff`` -- string or ``None``.\n '
def __init__(self, p... |
class Palp(JoinFeature):
'\n A :class:`~sage.features.Feature` describing the presence of :ref:`PALP <spkg_palp>`.\n '
def __init__(self):
'\n TESTS::\n\n sage: from sage.features.palp import Palp\n sage: isinstance(Palp(), Palp)\n True\n '
... |
def all_features():
return [Palp()]
|
class Pandoc(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of :ref:`pandoc <spkg_pandoc>`.\n\n EXAMPLES::\n\n sage: from sage.features.pandoc import Pandoc\n sage: Pandoc().is_present() # optional - pandoc\n FeatureTestResult('pandoc', True)\n "
def... |
def all_features():
return [Pandoc()]
|
class pdf2svg(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of :ref:`pdf2svg <spkg_pdf2svg>`.\n\n EXAMPLES::\n\n sage: from sage.features.pdf2svg import pdf2svg\n sage: pdf2svg().is_present() # optional - pdf2svg\n FeatureTestResult('pdf2svg', Tr... |
def all_features():
return [pdf2svg()]
|
class Phitigra(PythonModule):
"\n A :class:`sage.features.Feature` describing the presence of :ref:`phitigra <spkg_phitigra>`.\n\n Phitigra is provided by an optional package in the Sage distribution.\n\n EXAMPLES::\n\n sage: from sage.features.phitigra import Phitigra\n sage: Phitigra().is... |
def all_features():
return [Phitigra()]
|
class PackageSystem(Feature):
"\n A :class:`Feature` describing a system package manager.\n\n EXAMPLES::\n\n sage: from sage.features.pkg_systems import PackageSystem\n sage: PackageSystem('conda')\n Feature('conda')\n "
def _is_present(self):
"\n Test whether ``s... |
class SagePackageSystem(PackageSystem):
"\n A :class:`Feature` describing the package manager of the SageMath distribution.\n\n EXAMPLES::\n\n sage: from sage.features.pkg_systems import SagePackageSystem\n sage: SagePackageSystem()\n Feature('sage_spkg')\n "
@staticmethod
d... |
class PipPackageSystem(PackageSystem):
"\n A :class:`Feature` describing the Pip package manager.\n\n EXAMPLES::\n\n sage: from sage.features.pkg_systems import PipPackageSystem\n sage: PipPackageSystem()\n Feature('pip')\n "
@staticmethod
def __classcall__(cls):
'\n... |
class JuPyMake(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the :ref:`JuPyMake <spkg_jupymake>`\n module, a Python interface to the :ref:`polymake <spkg_polymake>` library.\n\n EXAMPLES::\n\n sage: from sage.features.polymake import JuPyMake\n sage: JuPyMak... |
def all_features():
return [JuPyMake()]
|
class pdftocairo(Executable):
"\n A :class:`sage.features.Feature` describing the presence of\n ``pdftocairo``\n\n EXAMPLES::\n\n sage: from sage.features.poppler import pdftocairo\n sage: pdftocairo().is_present() # optional: pdftocairo\n FeatureTestResult('pdftocairo', ... |
def all_features():
return [pdftocairo()]
|
class cu2(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``cu2``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import cu2\n sage: cu2().is_present() # optional - rubiks\n FeatureTestResult('cu2', True)\n "
def __init__(self):
'\n ... |
class size222(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``size222``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import size222\n sage: size222().is_present() # optional - rubiks\n FeatureTestResult('size222', True)\n "
def __init__(se... |
class optimal(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``optimal``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import optimal\n sage: optimal().is_present() # optional - rubiks\n FeatureTestResult('optimal', True)\n "
def __init__(se... |
class mcube(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``mcube``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import mcube\n sage: mcube().is_present() # optional - rubiks\n FeatureTestResult('mcube', True)\n "
def __init__(self):
... |
class dikcube(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``dikcube``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import dikcube\n sage: dikcube().is_present() # optional - rubiks\n FeatureTestResult('dikcube', True)\n "
def __init__(se... |
class cubex(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of ``cubex``.\n\n EXAMPLES::\n\n sage: from sage.features.rubiks import cubex\n sage: cubex().is_present() # optional - rubiks\n FeatureTestResult('cubex', True)\n "
def __init__(self):
... |
class Rubiks(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of the\n :class:`cu2`, :class:`cubex`, :class:`dikcube`, :class:`mcube`, :class:`optimal`, and\n :class:`size222` programs from the :ref:`rubiks <spkg_rubiks>` package.\n\n EXAMPLES::\n\n sage: from sage.fe... |
def all_features():
return [Rubiks()]
|
class sagemath_doc_html(StaticFile):
"\n A :class:`~sage.features.Feature` which describes the presence of the documentation\n of the Sage library in HTML format.\n\n Developers often use ``make build`` instead of ``make`` to avoid the\n long time it takes to compile the documentation. Although comman... |
class sage__combinat(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.combinat`.\n\n EXAMPLES:\n\n Python modules that provide elementary combinatorial objects such as :mod:`sage.combinat.subset`,\n :mod:`sage.combinat.composition`, :mod:`sage.combinat.permutat... |
class sage__geometry__polyhedron(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.geometry.polyhedron`.\n\n EXAMPLES:\n\n Doctests that use polyhedra, cones, geometric complexes, triangulations, etc. should use\n the tag ``# needs sage.geometry.polyhedron``::\n... |
class sage__graphs(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.graphs`.\n\n EXAMPLES:\n\n Doctests that use anything from :mod:`sage.graphs` (:class:`Graph`, :class:`DiGraph`, ...)\n should be marked ``# needs sage.graphs``. The same applies to any doctest... |
class sage__groups(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of ``sage.groups``.\n\n EXAMPLES:\n\n Permutations and sets of permutations are always available, but permutation groups are\n implemented in Sage using the :ref:`GAP <spkg_gap>` system and require the tag\n... |
class sage__libs__braiding(PythonModule):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.libs.braiding`.\n\n EXAMPLES::\n\n sage: from sage.features.sagemath import sage__libs__braiding\n sage: sage__libs__braiding().is_present() ... |
class sage__libs__ecl(PythonModule):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.libs.ecl`.\n\n EXAMPLES::\n\n sage: from sage.features.sagemath import sage__libs__ecl\n sage: sage__libs__ecl().is_present() # optional - sage.libs.ecl\n ... |
class sage__libs__flint(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.flint`\n and other modules depending on FLINT and arb.\n\n In addition to the modularization purposes that this tag serves, it also provides attribution\n to the upstream project.\n\n ... |
class sage__libs__gap(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.gap`\n (the library interface to :ref:`GAP <spkg_gap>`) and :mod:`sage.interfaces.gap` (the pexpect\n interface to GAP). By design, we do not distinguish between these two, in order\n to... |
class sage__libs__linbox(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.linbox`\n and other modules depending on Givaro, FFLAS-FFPACK, LinBox.\n\n In addition to the modularization purposes that this tag serves, it also provides attribution\n to the upstr... |
class sage__libs__m4ri(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of Cython modules\n depending on the M4RI and/or M4RIe libraries.\n\n In addition to the modularization purposes that this tag serves,\n it also provides attribution to the upstream project.\n\n TESTS:... |
class sage__libs__ntl(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.ntl`\n and other modules depending on NTL.\n\n In addition to the modularization purposes that this tag serves,\n it also provides attribution to the upstream project.\n\n TESTS::\n\n... |
class sage__libs__pari(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.libs.pari`.\n\n SageMath uses the :ref:`PARI <spkg_pari>` library (via :ref:`cypari2\n <spkg_cypari>`) for numerous purposes. Doctests that involves such features\n should be marked ``# ne... |
class sage__libs__singular(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.libs.singular`\n (the library interface to Singular) and :mod:`sage.interfaces.singular` (the pexpect\n interface to Singular). By design, we do not distinguish between these two, in order\... |
class sage__modular(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.modular`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__modular\n sage: sage__modular().is_present() # needs sage.modular\... |
class sage__modules(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.modules`.\n\n EXAMPLES:\n\n All uses of implementations of vector spaces / free modules in SageMath, whether\n :class:`sage.modules.free_module.FreeModule`,\n :class:`sage.combinat.free_mod... |
class sage__numerical__mip(PythonModule):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.numerical.mip`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__numerical__mip\n sage: sage__numerical__mip().is_present() ... |
class sage__plot(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.plot`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__plot\n sage: sage__plot().is_present() # needs sage.plot\n Fea... |
class sage__rings__complex_double(PythonModule):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.complex_double`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__rings__complex_double\n sage: sage__rings__complex_double().is_present() ... |
class sage__rings__finite_rings(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.finite_rings`;\n specifically, the element implementations using the :ref:`PARI <spkg_pari>` library.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__rings... |
class sage__rings__function_field(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.function_field`.\n\n EXAMPLES:\n\n Rational function fields are always available::\n\n sage: K.<x> = FunctionField(QQ)\n sage: K.maximal_order()\n Maximal... |
class sage__rings__number_field(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.number_field`.\n\n Number fields are implemented in Sage using a complicated mixture of various libraries,\n including :ref:`FLINT <spkg_flint>`, :ref:`GAP <spkg_gap>`,\n :re... |
class sage__rings__padics(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of ``sage.rings.padics``.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__rings__padics\n sage: sage__rings__padics().is_present() # needs... |
class sage__rings__polynomial__pbori(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of :mod:`sage.rings.polynomial.pbori`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__rings__polynomial__pbori\n sage: sage__rings__polynomial__pbori().is_present() ... |
class sage__rings__real_double(PythonModule):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.real_double`.\n\n EXAMPLES:\n\n The Real Double Field is basically always available, and no ``# optional/needs`` tag is needed::\n\n sage: RDF.characteristic()\n 0... |
class sage__rings__real_mpfr(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.rings.real_mpfr`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__rings__real_mpfr\n sage: sage__rings__real_mpfr().is_present() ... |
class sage__sat(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.sat`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__sat\n sage: sage__sat().is_present() # needs sage.sat\n Feature... |
class sage__schemes(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.schemes`.\n\n TESTS::\n\n sage: from sage.features.sagemath import sage__schemes\n sage: sage__schemes().is_present() # needs sage.schemes\... |
class sage__symbolic(JoinFeature):
"\n A :class:`~sage.features.Feature` describing the presence of :mod:`sage.symbolic`.\n\n EXAMPLES:\n\n The symbolics subsystem of Sage will be provided by the distribution\n sagemath-symbolics, in preparation at :issue:`35095`. If it is not installed,\n Sage wil... |
def all_features():
"\n Return features corresponding to parts of the Sage library.\n\n These features are named after Python packages/modules (e.g., :mod:`sage.symbolic`),\n not distribution packages (**sagemath-symbolics**).\n\n This design is motivated by a separation of concerns: The author of a m... |
class Singular(Executable):
"\n A :class:`~sage.features.Feature` describing the presence of the :ref:`singular <spkg_singular>` executable.\n\n .. SEEALSO::\n\n :class:`Feature sage.libs.singular <~sage.features.sagemath.sage__libs__singular>`\n\n EXAMPLES::\n\n sage: from sage.features.si... |
def all_features():
return [Singular()]
|
class Sphinx(PythonModule):
"\n A :class:`sage.features.Feature` describing the presence of :ref:`Sphinx <spkg_sphinx>`.\n\n Sphinx is provided by a standard package in the Sage distribution,\n but it can be disabled by ``configure --disable-doc``.\n\n EXAMPLES::\n\n sage: from sage.features.sp... |
def all_features():
return [Sphinx()]
|
def all_features():
return [PythonModule('cvxopt', spkg='cvxopt', type='standard'), PythonModule('fpylll', spkg='fpylll', type='standard'), JoinFeature('ipython', (PythonModule('IPython'),), spkg='ipython', type='standard'), JoinFeature('lrcalc_python', (PythonModule('lrcalc'),), spkg='lrcalc_python', type='stand... |
class symengine_py(JoinFeature):
"\n A :class:`sage.features.Feature` describing the presence of the\n Python package :ref:`symengine_py <spkg_symengine_py>`.\n\n EXAMPLES::\n\n sage: from sage.features.symengine_py import symengine_py\n sage: symengine_py().is_present() ... |
def all_features():
return [symengine_py()]
|
class Tdlib(JoinFeature):
'\n A :class:`~sage.features.Feature` describing the presence of the SageMath interface to the :ref:`tdlib <spkg_tdlib>` library.\n '
def __init__(self):
'\n TESTS::\n\n sage: from sage.features.tdlib import Tdlib\n sage: isinstance(Tdlib()... |
def all_features():
return [Tdlib()]
|
class FunctionAiryAiGeneral(BuiltinFunction):
def __init__(self):
"\n The generalized derivative of the Airy Ai function\n\n INPUT:\n\n - ``alpha`` -- Return the `\\alpha`-th order fractional derivative with\n respect to `z`.\n For `\\alpha = n = 1,2,3,\\ldots` this... |
class FunctionAiryAiSimple(BuiltinFunction):
def __init__(self):
'\n The class for the Airy Ai function.\n\n EXAMPLES::\n\n sage: from sage.functions.airy import airy_ai_simple\n sage: f = airy_ai_simple(x); f # needs sage.s... |
class FunctionAiryAiPrime(BuiltinFunction):
def __init__(self):
"\n The derivative of the Airy Ai function; see :func:`airy_ai`\n for the full documentation.\n\n EXAMPLES::\n\n sage: # needs sage.symbolic\n sage: x, n = var('x n')\n sage: airy_ai_prim... |
def airy_ai(alpha, x=None, hold_derivative=True, **kwds):
'\n The Airy Ai function\n\n The Airy Ai function `\\operatorname{Ai}(x)` is (along with\n `\\operatorname{Bi}(x)`) one of the two linearly independent standard\n solutions to the Airy differential equation `f\'\'(x) - x f(x) = 0`. It is\n d... |
class FunctionAiryBiGeneral(BuiltinFunction):
def __init__(self):
"\n The generalized derivative of the Airy Bi function.\n\n INPUT:\n\n - ``alpha`` -- Return the `\\alpha`-th order fractional derivative with\n respect to `z`.\n For `\\alpha = n = 1,2,3,\\ldots` thi... |
class FunctionAiryBiSimple(BuiltinFunction):
def __init__(self):
'\n The class for the Airy Bi function.\n\n EXAMPLES::\n\n sage: from sage.functions.airy import airy_bi_simple\n sage: f = airy_bi_simple(x); f # needs sage.s... |
class FunctionAiryBiPrime(BuiltinFunction):
def __init__(self):
"\n The derivative of the Airy Bi function; see :func:`airy_bi`\n for the full documentation.\n\n EXAMPLES::\n\n sage: # needs sage.symbolic\n sage: x, n = var('x n')\n sage: airy_bi_prim... |
def airy_bi(alpha, x=None, hold_derivative=True, **kwds):
'\n The Airy Bi function\n\n The Airy Bi function `\\operatorname{Bi}(x)` is (along with\n `\\operatorname{Ai}(x)`) one of the two linearly independent standard\n solutions to the Airy differential equation `f\'\'(x) - x f(x) = 0`. It is\n d... |
class Function_Bessel_J(BuiltinFunction):
"\n The Bessel J Function, denoted by bessel_J(`\\nu`, x) or `J_\\nu(x)`.\n As a Taylor series about `x=0` it is equal to:\n\n .. MATH::\n\n J_\\nu(x) = \\sum_{k=0}^\\infty \\frac{(-1)^k}{k! \\Gamma(k+\\nu+1)}\n \\left(\\frac{x}{2}\\right)^{2k+\\nu}... |
class Function_Bessel_Y(BuiltinFunction):
"\n The Bessel Y functions, also known as the Bessel functions of the second\n kind, Weber functions, or Neumann functions.\n\n `Y_\\nu(z)` is a holomorphic function of `z` on the complex plane,\n cut along the negative real axis. It is singular at `z = 0`. Wh... |
class Function_Bessel_I(BuiltinFunction):
"\n The Bessel I function, or the Modified Bessel Function of the First Kind.\n\n DEFINITION:\n\n .. MATH::\n\n I_\\nu(x) = i^{-\\nu} J_\\nu(ix)\n\n EXAMPLES::\n\n sage: bessel_I(1.0, 1.0) # ... |
class Function_Bessel_K(BuiltinFunction):
"\n The Bessel K function, or the modified Bessel function of the second kind.\n\n DEFINITION:\n\n .. MATH::\n\n K_\\nu(x) = \\frac{\\pi}{2} \\frac{I_{-\\nu}(x)-I_\\nu(x)}{\\sin(\\nu \\pi)}\n\n EXAMPLES::\n\n sage: bessel_K(1.0, 1.0) ... |
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