bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
|---|---|---|
... def __repr__(self): | ... def __repr__(self): | 460,800 |
... def __repr__(self): | ... def __repr__(self): | 460,801 |
... def __repr__(self): | ... def __repr__(self): | 460,802 |
def __mod__(self, args): """ Binds the lazy format with its parameters | def __mod__(self, args): """ Binds the lazy format with its parameters | 460,803 |
def _ambient_space_point(self, data): r""" Try to convert ``data`` to a point of the ambient space of ``self``. | def _ambient_space_point(self, data): r""" Try to convert ``data`` to a point of the ambient space of ``self``. | 460,804 |
def contains(self, *args): r""" Check if a given point is contained in ``self``. | def contains(self, *args): r""" Check if a given point is contained in ``self``. | 460,805 |
def contains(self, *args): r""" Check if a given point is contained in ``self``. | def contains(self, *args): r""" Check if a given point is contained in ``self``. | 460,806 |
def dual(self): r""" Return the dual cone of ``self``. OUTPUT: - :class:`cone <ConvexRationalPolyhedralCone>`. EXAMPLES:: sage: cone = Cone([(1,0), (-1,3)]) sage: cone.dual().rays() (M(3, 1), M(0, 1)) Now let's look at a more complicated case:: sage: cone = Cone([(-2,-1,2), (4,1,0), (-4,-1,-5), (4,1,5)]) sage: co... | def dual(self): r""" Return the dual cone of ``self``. OUTPUT: - :class:`cone <ConvexRationalPolyhedralCone>`. EXAMPLES:: sage: cone = Cone([(1,0), (-1,3)]) sage: cone.dual().rays() (M(3, 1), M(0, 1)) Now let's look at a more complicated case:: sage: cone = Cone([(-2,-1,2), (4,1,0), (-4,-1,-5), (4,1,5)]) sage: co... | 460,807 |
def facet_normals(self): r""" Return normals to facets of ``self``. | def facet_normals(self): r""" Return normals to facets of ``self``. | 460,808 |
def facet_normals(self): r""" Return normals to facets of ``self``. | def facet_normals(self): r""" Return normals to facets of ``self``. | 460,809 |
def _split_ambient_lattice(self): r""" Compute a decomposition of the ``N``-lattice into `N_\sigma` and its complement `N(\sigma)`. | def _split_ambient_lattice(self): r""" Compute a decomposition of the ``N``-lattice into `N_\sigma` and its complement `N(\sigma)`. | 460,810 |
def _split_ambient_lattice(self): r""" Compute a decomposition of the ``N``-lattice into `N_\sigma` and its complement `N(\sigma)`. | def _split_ambient_lattice(self): r""" Compute a decomposition of the ``N``-lattice into `N_\sigma` and its complement `N(\sigma)`. | 460,811 |
def orthogonal_sublattice(self, *args, **kwds): r""" The sublattice (in the dual lattice) orthogonal to the sublattice spanned by the cone. Let `M=` ``self.lattice().dual()`` be the lattice dual to the ambient lattice of the given cone `\sigma`. Then, in the notation of [Fulton]_, this method returns the sublattice | def orthogonal_sublattice(self, *args, **kwds): r""" The sublattice (in the dual lattice) orthogonal to the sublattice spanned by the cone. Let `M=` ``self.dual_lattice()`` be the lattice dual to the ambient lattice of the given cone `\sigma`. Then, in the notation of [Fulton]_, this method returns the sublattice | 460,812 |
def transform(self, **kwds): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates sage: x, y, z = var('x y z') sage: T = _ArbitraryCoordinates((x + y, x - y, z), x,[y,z]) | def transform(self, **kwds): """ EXAMPLE:: sage: from sage.plot.plot3d.plot3d import _ArbitraryCoordinates sage: x, y, z = var('x y z') sage: T = _ArbitraryCoordinates((x + y, x - y, z), x,[y,z]) | 460,813 |
def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform. | def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform. | 460,814 |
def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | 460,815 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | 460,816 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | 460,817 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | 460,818 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def if prec == 1: return R2(O(t2)) elif prec == 2: return R2(t1+t2 - self.curve().a1()*t1*t2) group_law(self, if prec == 1: return R2(O(t2)) elif prec == 2: return R2(t1+t2 - self.curve().a1()*t1*t2) prec=10): if prec == 1: return R2(O(t2)) elif prec == 2: return R2(t1+t2 - self.curve().a1()*t1*t2) r""" if prec == 1... | 460,819 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | 460,820 |
def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | def group_law(self, prec=10): r""" The formal group law. INPUT: - ``prec`` - integer (default 10) OUTPUT: a power series with given precision in ZZ[[ ZZ[['t1']],'t2']] DETAILS: Return the formal power series .. math:: F(t_1, t_2) = t_1 + t_2 - a_1 t_1 t_2 - \cdots to precision `O(t^{prec})` of page 115 of [S... | 460,821 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,822 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,823 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,824 |
def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | def vectors_by_length(self, bound): """ Returns a list of short vectors together with their values. This is a naive algorithm which uses the Cholesky decomposition, but does not use the LLL-reduction algorithm. INPUT: bound -- an integer >= 0 OUTPUT: A list L of length (bound + 1) whose entry L[i] is a list of all v... | 460,825 |
def _sympy_(self): """ Converts pi to sympy pi. EXAMPLES:: sage: import sympy sage: sympy.pi == pi # indirect doctest True """ import sympy return sympy.pi | def _sympy_(self): """ Converts pi to sympy pi. EXAMPLES:: sage: import sympy sage: sympy.pi == pi # indirect doctest True """ import sympy return sympy.pi | 460,826 |
def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): r""" Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependen... | def desolve(de, dvar, ics=None, ivar=None, show_method=False, contrib_ode=False): r""" Solves a 1st or 2nd order linear ODE via maxima. Including IVP and BVP. *Use* ``desolve? <tab>`` *if the output in truncated in notebook.* INPUT: - ``de`` - an expression or equation representing the ODE - ``dvar`` - the dependen... | 460,827 |
def get_fake_div(self, ex): """ EXAMPLES:: | def get_fake_div(self, ex): """ EXAMPLES:: | 460,828 |
def get_fake_div(self, ex): """ EXAMPLES:: | def get_fake_div(self, ex): """ EXAMPLES:: | 460,829 |
def arithmetic(self, ex, operator): r""" EXAMPLES:: | def arithmetic(self, ex, operator): r""" EXAMPLES:: | 460,830 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,831 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,832 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 460,833 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 460,834 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 460,835 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 460,836 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,837 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,838 |
def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | def sturm_bound(self, M=None): r""" For a space M of modular forms, this function returns an integer B such that two modular forms in either self or M are equal if and only if their q-expansions are equal to precision B (note that this is 1+ the usual Sturm bound, since `O(q^\mathrm{prec})` has precision prec). If M is... | 460,839 |
def __call__(self, x, check=True): """ Convert ``x`` to an element of this multivariate polynomial ring, possibly non-canonically. EXAMPLES: | def __call__(self, x, check=True): """ Convert ``x`` to an element of this multivariate polynomial ring, possibly non-canonically. EXAMPLES: | 460,840 |
def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field. | def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field. | 460,841 |
def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field. | def hasse_invariant(self): r""" Returns the Hasse invariant of an elliptic curve over a field of positive characteristic, which is an element of the field. | 460,842 |
def __init__(self, point, r, angle, options): """ Initializes base class Disk. | def __init__(self, point, r, angle, options): """ Initializes base class Disk. | 460,843 |
def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | def get_minmax_data(self): """ Returns a dictionary with the bounding box data. | 460,844 |
def _allowed_options(self): """ Return the allowed options for the Disk class. | def _allowed_options(self): """ Return the allowed options for the Disk class. | 460,845 |
def _repr_(self): """ String representation of Disk primitive. | def _repr_(self): """ String representation of Disk primitive. | 460,846 |
def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | def plot3d(self, z=0, **kwds): """ Plots a 2D disk (actually a 52-gon) in 3D, with default height zero. | 460,847 |
def deprecation(message, version=None): r""" Issue a deprecation warning. INPUT: - ``message`` - an explanation why things are deprecated and by what it should be replaced. - ``version`` - (optional) on which version and when the deprecation occured. Please put there the version of sageq at the time of deprecation. ... | def deprecation(message, version=None): r""" Issue a deprecation warning. INPUT: - ``message`` - an explanation why things are deprecated and by what it should be replaced. - ``version`` - (optional) on which version and when the deprecation occurred. Please put there the version of sage at the time of deprecation. ... | 460,848 |
sage: def bar(): | sage: def bar(): | 460,849 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 460,850 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 460,851 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=None): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in t... | 460,852 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | 460,853 |
def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | def lagrange_polynomial(self, points, algorithm="divided_difference", previous_row=[]): """ Return the Lagrange interpolation polynomial in ``self`` associated to the given list of points. Given a list of points, i.e. tuples of elements of ``self``'s base ring, this function returns the interpolation polynomial in the... | 460,854 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 460,855 |
def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | def plot(self, *args, **kwds): """ The R plot function. Type r.help('plot') for much more extensive documentation about this function. See also below for a brief introduction to more plotting with R. | 460,856 |
def library_interact(f): """ This is a decorator for using interacts in the Sage library. EXAMPLES:: sage: @interacts.decorator.library_interact ... def f(n=5): print n ... sage: f() # an interact appears <html>...</html> """ @sage_wraps(f) def library_wrapper(): # Maybe program around bug (?) in the notebook: html(... | def library_interact(f): """ This is a decorator for using interacts in the Sage library. EXAMPLES:: sage: @interacts.library.library_interact ... def f(n=5): print n ... sage: f() # an interact appears <html>...</html> """ @sage_wraps(f) def library_wrapper(): # Maybe program around bug (?) in the notebook: html("<... | 460,857 |
def demo(n=tuple(range(10)), m=tuple(range(10))): """ This is a demo interact that sums two numbers. INPUT: - `n` -- integer slider - `m` -- integer slider EXAMPLES:: sage: interacts.decorator.demo() <html>...</html> """ print n+m | def demo(n=tuple(range(10)), m=tuple(range(10))): """ This is a demo interact that sums two numbers. INPUT: - `n` -- integer slider - `m` -- integer slider EXAMPLES:: sage: interacts.library.demo() <html>...</html> """ print n+m | 460,858 |
def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | 460,859 |
def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | def hom(self, im_gens, codomain=None, check=True): """ Homomorphism defined by giving the images of ``self.gens()`` in some fixed fg R-module. .. note :: We do not assume that the generators given by ``self.gens()`` are the same as the Smith form generators, since this may not be true for a general derived class. IN... | 460,860 |
def matrix(*args, **kwds): """ Create a matrix. INPUT: The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of the matrix, and returns a matrix. The entries of a matrix can be specified as a flat list of elements, a list of lists (i.e., a list of rows), a list of Sage vec... | def matrix(*args, **kwds): """ Create a matrix. INPUT: The matrix command takes the entries of a matrix, optionally preceded by a ring and the dimensions of the matrix, and returns a matrix. The entries of a matrix can be specified as a flat list of elements, a list of lists (i.e., a list of rows), a list of Sage vec... | 460,861 |
def height(self): r""" Returns the height of self. | def height(self): r""" Returns the height of self. | 460,862 |
def width(self): r""" Returns the width of self. | def width(self): r""" Returns the width of self. | 460,863 |
def tikz_trajectory(self): r""" Returns the trajectory of self as a tikz str. | def tikz_trajectory(self): r""" Returns the trajectory of self as a tikz str. | 460,864 |
def tikz_trajectory(self): r""" Returns the trajectory of self as a tikz str. | def tikz_trajectory(self): r""" Returns the trajectory of self as a tikz str. | 460,865 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 460,866 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 460,867 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 460,868 |
def derivative(self, ex, operator): """ EXAMPLES:: | def derivative(self, ex, operator): """ EXAMPLES:: | 460,869 |
def ModularForms(group = 1, weight = 2, base_ring = None, use_cache = True, prec = defaults.DEFAULT_PRECISION): r""" Create an ambient space of modular forms. INPUT: - ``group`` - A congruence subgroup or a Dirichlet character eps. - ``weight`` - int, the weight, which must be an integer = 1. - ``base_ring`` -... | def ModularForms(group = 1, weight = 2, base_ring = None, use_cache = True, prec = defaults.DEFAULT_PRECISION): r""" Create an ambient space of modular forms. INPUT: - ``group`` - A congruence subgroup or a Dirichlet character eps. - ``weight`` - int, the weight, which must be an integer = 1. - ``base_ring`` -... | 460,870 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax), (ymin, ym... | 460,871 |
def __call__(cls, *args, **options): """ This method implements ``cls(<some arguments>)``. | def __call__(cls, *args, **options): """ This method implements ``cls(<some arguments>)``. | 460,872 |
... def __classcall__(cls): | ... def __classcall__(cls): | 460,873 |
... def __init__(self): | ... def __init__(self): | 460,874 |
... def __init__(self): | ... def __init__(self): | 460,875 |
... def __init__(self): | ... def __init__(self): | 460,876 |
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | def quotient(self, sub, check=True, positive_point=None, positive_dual_point=None): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | 460,877 |
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | 460,878 |
def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | def quotient(self, sub, check=True): """ Return the quotient of ``self`` by the given sublattice ``sub``. INPUT: | 460,879 |
def span(self, *args, **kwds): """ Return the span of the given generators. | def span(self, *args, **kwds): """ Return the span of the given generators. | 460,880 |
def span(self, *args, **kwds): """ Return the span of the given generators. | def span(self, *args, **kwds): """ Return the span of the given generators. | 460,881 |
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``. | def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``. | 460,882 |
def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``. | def span_of_basis(self, *args, **kwds): r""" Return the submodule with the given ``basis``. | 460,883 |
def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT: | def _latex_(self): r""" Return a LaTeX representation of ``self``. OUTPUT: | 460,884 |
def _repr_(self): r""" Return a string representation of ``self``. | def _repr_(self): r""" Return a string representation of ``self``. | 460,885 |
def _repr_(self): r""" Return a string representation of ``self``. | def _repr_(self): r""" Return a string representation of ``self``. | 460,886 |
def rank(self): r""" Return the rank of ``self``. OUTPUT: - integer. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V().rank() - self.W().rank() | def rank(self): r""" Return the rank of ``self``. OUTPUT: Integer. The dimension of the free part of the quotient. EXAMPLES:: sage: N = ToricLattice(3) sage: Ns = N.submodule([N(2,4,0), N(9,12,0)]) sage: Q = N/Ns sage: Q.rank() 1 sage: Ns = N.submodule([N(1,4,0)]) sage: Q = N/Ns sage: Q.rank() 2 """ return self.V()... | 460,887 |
def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | 460,888 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points_iterator(self): r""" Return the rational points on this curve computed via enumeration. | 460,889 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,890 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,891 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,892 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,893 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,894 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,895 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,896 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 460,897 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | defrational_points(self,algorithm="enum",sort=True):r"""Returntherationalpointsonthiscurvecomputedviaenumeration. | 460,898 |
def __classcall_private__(cls, fam, facade=True, keepkey=False): # was *args, **options): """ Normalization of arguments; see :cls:`UniqueRepresentation`. | def __classcall_private__(cls, fam, facade=True, keepkey=False): # was *args, **options): """ Normalization of arguments; see :cls:`UniqueRepresentation`. | 460,899 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.