bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def show(self, **kwds): """ Show this graphics image with the default image viewer. | def show(self, **kwds): """ Show this graphics image with the default image viewer. | 461,100 |
def replace_parens(x): r""" A map from '(' to open_symbol and ')' to close_symbol and otherwise an error is raised. EXAMPLES:: sage: from sage.combinat.dyck_word import replace_parens sage: replace_parens('(') 1 sage: replace_parens(')') 0 sage: replace_parens(1) Traceback (most recent call last): ... ValueError """ ... | def replace_parens(x): r""" A map from ``'('`` to ``open_symbol`` and ``')'`` to ``close_symbol`` and otherwise an error is raised. The values of the constants ``open_symbol`` and ``close_symbol`` are subject to change. This is the inverse map of :func:`replace_symbols`. INPUT: - ``x`` -- either an opening or closing... | 461,101 |
def replace_symbols(x): r""" A map from open_symbol to '(' and close_symbol to ')' and otherwise an error is raised. EXAMPLES:: sage: from sage.combinat.dyck_word import replace_symbols sage: replace_symbols(1) '(' sage: replace_symbols(0) ')' sage: replace_symbols(3) Traceback (most recent call last): ... ValueError... | def replace_symbols(x): r""" A map from ``open_symbol`` to ``'('`` and ``close_symbol`` to ``')'`` and otherwise an error is raised. The values of the constants ``open_symbol`` and ``close_symbol`` are subject to change. This is the inverse map of :func:`replace_parens`. INPUT: - ``x`` -- either ``open_symbol`` or ``... | 461,102 |
def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete. EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyc... | 461,103 |
def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | 461,104 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 461,105 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 461,106 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 461,107 |
def to_noncrossing_partition(self): r""" Bijection of Biane from Dyck words to non crossing partitions Thanks to Mathieu Dutour for describing the bijection. EXAMPLES:: sage: DyckWord([]).to_noncrossing_partition() [] sage: DyckWord([1, 0]).to_noncrossing_partition() [[1]] sage: DyckWord([1, 1, 0, 0]).to_noncrossing_... | def to_noncrossing_partition(self): r""" Bijection of Biane from Dyck words to non-crossing partitions. Thanks to Mathieu Dutour for describing the bijection. EXAMPLES:: sage: DyckWord([]).to_noncrossing_partition() [] sage: DyckWord([1, 0]).to_noncrossing_partition() [[1]] sage: DyckWord([1, 1, 0, 0]).to_noncrossing... | 461,108 |
def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | 461,109 |
def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | 461,110 |
def a_statistic(self): """ Returns the a-statistic for the Dyck word correspond to the area of the Dyck path. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(1,0)` and '0's represent steps in the direction `(0,1)`. The... | def a_statistic(self): """ Returns the a-statistic for the Dyck word corresponding to the area of the Dyck path. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(1,0)` and '0's represent steps in the direction `(0,1)`. ... | 461,111 |
def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(0,1)` and '0's represent steps in the direct... | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(0,1)` and '0's represent steps in the direct... | 461,112 |
def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(0,1)` and '0's represent steps in the direct... | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. One can view a balanced Dyck word as a lattice path from `(0,0)` to `(n,n)` in the first quadrant by letting '1's represent steps in the direction `(0,1)` and '0's represent steps in the direct... | 461,113 |
def list(self): """ Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. EXAMPLES:: sage: DyckWords(0).list() [[]] sage: DyckWords(1).list() [[1, 0]] sage: DyckWords(2).list() [[1, 0, 1, 0], [1, 1, 0, 0]] """ return list(self) | def list(self): """ Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. EXAMPLES:: sage: DyckWords(0).list() [[]] sage: DyckWords(1).list() [[1, 0]] sage: DyckWords(2).list() [[1, 0, 1, 0], [1, 1, 0, 0]] """ return list(self) | 461,114 |
def __iter__(self): r""" Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. EXAMPLES:: sage: [ w for w in DyckWords(0) ] [[]] sage: [ w for w in DyckWords(1) ] [[1, 0]] sage: [ w for w in DyckWords(2) ] [[1, 0, 1, 0], [1, 1, 0, 0]] sage: len([ 'x' for _ in DyckWords(5) ]) 42 """ if... | def __iter__(self): r""" Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. EXAMPLES:: sage: [ w for w in DyckWords(0) ] [[]] sage: [ w for w in DyckWords(1) ] [[1, 0]] sage: [ w for w in DyckWords(2) ] [[1, 0, 1, 0], [1, 1, 0, 0]] sage: len([ 'x' for _ in DyckWords(5) ]) 42 """ if... | 461,115 |
def from_noncrossing_partition(ncp): r""" converts a non-crossing partition to a Dyck word TESTS:: sage: DyckWord(noncrossing_partition=[[1,2]]) # indirect doctest [1, 1, 0, 0] sage: DyckWord(noncrossing_partition=[[1],[2]]) [1, 0, 1, 0] :: sage: dws = DyckWords(5).list() sage: ncps = map( lambda x: x.to_noncrossin... | def from_noncrossing_partition(ncp): r""" Converts a non-crossing partition to a Dyck word. TESTS:: sage: DyckWord(noncrossing_partition=[[1,2]]) # indirect doctest [1, 1, 0, 0] sage: DyckWord(noncrossing_partition=[[1],[2]]) [1, 0, 1, 0] :: sage: dws = DyckWords(5).list() sage: ncps = map( lambda x: x.to_noncrossi... | 461,116 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality u... | 461,117 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns ``True`` if `n` is prime, and ``False`` otherwise. AUTHORS: - Kevin Stueve kstueve@uw.edu (2010-01-17): delegated calculation to ``n.is_prime()`` INPUT: - ``n`` - the object for which to determine primality OUTPUT: - ``bool`` - True or False .. note:: We do not consid... | 461,118 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | 461,119 |
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify pri... | 461,120 |
def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If ... | 461,121 |
def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | def _compute_dim(self, compute_vertices): r""" Compute the dimension of this polytope and its vertices, if necessary. If ``compute_vertices`` is ``True``, then ``self._vertices`` should contain points whose convex hull will be computed and placed back into ``self._vertices``. If the dimension of this polytope is not ... | 461,122 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 461,123 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 461,124 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 461,125 |
def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | def facet_constant(self, i): r""" Return the constant in the ``i``-th facet inequality of this polytope. The i-th facet inequality is given by self.facet_normal(i) * X + self.facet_constant(i) >= 0. INPUT: - ``i`` - integer, the index of the facet OUTPUT: - integer -- the constant in the ``i``-th facet inequality.... | 461,126 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be orthogonal to the integer kernel of the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- th... | 461,127 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 461,128 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 461,129 |
def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | def facet_normal(self, i): r""" Return the inner normal to the ``i``-th facet of this polytope. If this polytope is not full-dimensional, facet normals will be parallel to the affine subspace spanned by this polytope. INPUT: - ``i`` -- integer, the index of the facet OUTPUT: - vectors -- the inner normal of the ``... | 461,130 |
def overlap_partition(self, other, delay=0, p=None, involution=None) : r""" Returns the partition of the alphabet induced by the overlap of self and other with the given delay. | def overlap_partition(self, other, delay=0, p=None, involution=None) : r""" Returns the partition of the alphabet induced by the overlap of self and other with the given delay. | 461,131 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,132 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,133 |
def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | def bezier3d(path, **options): """ Draws a 3-dimensional bezier path. Input is similar to bezier_path, but each point in the path and each control point is required to have 3 coordinates. INPUT: - ``path`` - a list of curves, which each is a list of points. See further detail below. - ``thickness`` - (default: 2)... | 461,134 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3-D. Primarily used as a helper function for creating frames for 3-D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple... | 461,135 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple,... | 461,136 |
def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, ... | def frame3d(lower_left, upper_right, **kwds): """ Draw a frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple,... | 461,137 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3-D. Primarily used as a helper function for creating frames for 3-D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the l... | 461,138 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,139 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,140 |
def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | def frame_labels(lower_left, upper_right, label_lower_left, label_upper_right, eps = 1, **kwds): """ Draw correct labels for a given frame in 3D. Primarily used as a helper function for creating frames for 3D graphics viewing - do not use directly unless you know what you are doing! INPUT: - ``lower_left`` - the low... | 461,141 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3-D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of ma... | 461,142 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector. - ``end`` - the end of the ruler, as a list, tuple, or vector. - ``ticks`` - (default: 4) the number of m... | 461,143 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector. - ``end`` - the end of the ruler, as a list, tuple, or vector. - ``ticks`` - (default: 4) the number of m... | 461,144 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,145 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,146 |
def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | def ruler(start, end, ticks=4, sub_ticks=4, absolute=False, snap=False, **kwds): """ Draw a ruler in 3D, with major and minor ticks. INPUT: - ``start`` - the beginning of the ruler, as a list, tuple, or vector - ``end`` - the end of the ruler, as a list, tuple, or vector - ``ticks`` - (default: 4) the number of maj... | 461,147 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3-D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``... | 461,148 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector. - `... | 461,149 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector. - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector. - `... | 461,150 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,151 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,152 |
def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | def ruler_frame(lower_left, upper_right, ticks=4, sub_ticks=4, **kwds): """ Draw a frame made of 3D rulers, with major and minor ticks. INPUT: - ``lower_left`` - the lower left corner of the frame, as a list, tuple, or vector - ``upper_right`` - the upper right corner of the frame, as a list, tuple, or vector - ``t... | 461,153 |
def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | 461,154 |
def text3d(txt, (x,y,z), **kwds): r""" Display 3d text. INPUT: - ``txt`` - some text - ``(x,y,z)`` - position - ``**kwds`` - standard 3d graphics options .. note:: There is no way to change the font size or opacity yet. EXAMPLES: We write the word Sage in red at position (1,2,3):: sage: text3d("Sage", (1,2... | deftext3d(txt,(x,y,z),**kwds):r"""Display3dtext.INPUT:-``txt``-sometext-``(x,y,z)``-position-``**kwds``-standard3dgraphicsoptions..note::Thereisnowaytochangethefontsizeoropacityyet.EXAMPLES:WewritethewordSageinredatposition(1,2,3)::sage:text3d("Sage",(1,2,3),color=(0.5,0,0))Wedrawamulticolorspiralofnumbers::sage:sum([t... | 461,155 |
def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3D. See the docstring of this class for full documentation. | def __init__(self, center, size=1, **kwds): """ Create the graphics primitive :class:`Point` in 3-D. See the docstring of this class for full documentation. | 461,156 |
def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we simply return the center of the point. | def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we simply return the center of the point. | 461,157 |
def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using Tachyon ray tracer. | 461,158 |
def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3D. See the docstring of this class for full documentation. | def __init__(self, points, thickness=5, corner_cutoff=.5, arrow_head=False, **kwds): """ Create the graphics primitive :class:`Line` in 3-D. See the docstring of this class for full documentation. | 461,159 |
def bounding_box(self): """ Returns the lower and upper corners of a 3D bounding box for self. This is used for rendering and self should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points. | def bounding_box(self): """ Returns the lower and upper corners of a 3-D bounding box for ``self``. This is used for rendering and ``self`` should fit entirely within this box. In this case, we return the highest and lowest values of each coordinate among all points. | 461,160 |
def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using Tachyon ray tracer. | 461,161 |
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | 461,162 |
def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | def is_homogeneous(self, polynomial): r""" Check if ``polynomial`` is homogeneous. | 461,163 |
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("<... | 461,164 |
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 | 461,165 |
def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation | def from_polynomial_exp(self, p): r""" Conversion from polynomial in exponential notation | 461,166 |
def example(self): """ Returns an example of finite permutation group, as per :meth:`Category.example`. | def example(self): """ Returns an example of finite permutation group, as per :meth:`Category.example`. | 461,167 |
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... | 461,168 |
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... | 461,169 |
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... | 461,170 |
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... | 461,171 |
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... | 461,172 |
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... | 461,173 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,174 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,175 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,176 |
def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | def bound_kato(self): r""" Returns a list `p` of primes such that the theorems of Kato's [Ka] and others (e.g., as explained in a paper/thesis of Grigor Grigorov [Gri]) imply that if `p` divides the order of Sha(E) then `p` is in the list. | 461,177 |
def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. NOTES: * Evaluating on a vertex returns `A\vec{x}+b` * Evaluating on a ray returns `A\vec{r}`. Only the sign or whether it is zero is meaningful. * Evaluating on a line returns `A\vec{l}`. Only whether it is zero or not... | def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. NOTES: * Evaluating on a vertex returns `A\vec{x}+b` * Evaluating on a ray returns `A\vec{r}`. Only the sign or whether it is zero is meaningful. * Evaluating on a line returns `A\vec{l}`. Only whether it is zero or not... | 461,178 |
def is_inequality(self): """ Returns True since this is, by construction, an inequality. | def is_inequality(self): """ Returns True since this is, by construction, an inequality. | 461,179 |
def interior_contains(self, Vobj): """ Tests whether the interior of the halfspace (excluding its boundary) defined by the inequality contains the given vertex/ray/line. | def interior_contains(self, Vobj): If you pass a vector, it is assumed to be the coordinate vector of a point:: sage: P = Polyhedron(vertices=[[1,1],[1,-1],[-1,1],[-1,-1]]) sage: p = vector(ZZ, [1,0] ) sage: [ ieq.interior_contains(p) for ieq in P.inequality_generator() ] [True, True, True, False] """ try: if Vobj.is... | 461,180 |
def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | 461,181 |
def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | 461,182 |
def is_ray(self): """ Tests if this object is a ray. Always True by construction. | def is_ray(self): """ Tests if this object is a ray. Always True by construction. | 461,183 |
def is_line(self): """ Tests if the object is a line. By construction it must be. | def is_line(self): """ Tests if the object is a line. By construction it must be. | 461,184 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 461,185 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 461,186 |
... def __repr__(self): | ... def __repr__(self): | 461,187 |
... def __repr__(self): | ... def __repr__(self): | 461,188 |
... def __repr__(self): | ... def __repr__(self): | 461,189 |
... def __repr__(self): | ... def __repr__(self): | 461,190 |
... def __repr__(self): | ... def __repr__(self): | 461,191 |
... def __repr__(self): | ... def __repr__(self): | 461,192 |
def __mod__(self, args): """ Binds the lazy format with its parameters | def __mod__(self, args): """ Binds the lazy format with its parameters | 461,193 |
def height(self): r""" Returns the height of self. | def height(self): r""" Returns the height of self. | 461,194 |
def width(self): r""" Returns the width of self. | def width(self): r""" Returns the width of self. | 461,195 |
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. | 461,196 |
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. | 461,197 |
def __init__(self): r""" The inverse of the hyperbolic secant function. | def __init__(self): r""" The inverse of the hyperbolic secant function. | 461,198 |
def is_square(self): r""" Returns True if self is a square, and False otherwise. EXAMPLES:: sage: Word([1,0,0,1]).is_square() False sage: W = Words('123') sage: W('1212').is_square() True sage: W('1213').is_square() False sage: W('12123').is_square() False sage: W().is_square() True """ if self.length() % 2 != 0: ret... | def is_square(self): r""" Returns True if self is a square, and False otherwise. EXAMPLES:: sage: Word([1,0,0,1]).is_square() False sage: Word('1212').is_square() True sage: Word('1213').is_square() False sage: Word('12123').is_square() False sage: Word().is_square() True """ if self.length() % 2 != 0: return False e... | 461,199 |
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