rem stringlengths 1 322k | add stringlengths 0 2.05M | context stringlengths 4 228k | meta stringlengths 156 215 |
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return join(map(lambda x:self._character_to_code[x],string), '') | return "".join(map(lambda x: self._character_to_code[x], string)) | def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
Returns a decoded version of the given string corresponding to the current encoding table. INPUT: - ``string`` (string) EXAMPLE: This is how a string is encoded then decoded :: | Decode the given string using the current encoding table. INPUT: - ``string`` -- a string of Huffman encodings. OUTPUT: - The Huffman decoding of ``string``. EXAMPLES: This is how a string is encoded and then decoded:: | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
not, an exception is raised :: | not, an exception is raised:: | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
ValueError: The given string does not only contain 0 and 1 """ | ValueError: Input must be a binary string. """ | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
if i == '0': | if i == "0": | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
elif i == '1': | elif i == "1": | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
raise ValueError('The given string does not only contain 0 and 1') if not isinstance(tree,list): | raise ValueError("Input must be a binary string.") if not isinstance(tree, list): | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
return join(chars, '') | return "".join(chars) | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
Returns the current encoding table | Returns the current encoding table. INPUT: - None. | def encoding_table(self): r""" Returns the current encoding table | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
A dictionary associating its code to each trained letter of the alphabet EXAMPLE:: sage: from sage.coding.source_coding.huffman import Huffman sage: str = "Sage is my most favorite general purpose computer algebra system" sage: h = Huffman(str) sage: h.encoding_table() {'S': '00000', 'a': '1101', ' ': '101', 'c': '11... | - A dictionary associating an alphabetic symbol to a Huffman encoding. EXAMPLES:: sage: from sage.coding.source_coding.huffman import Huffman sage: str = "Sage is my most favorite general purpose computer algebra system" sage: h = Huffman(str) sage: T = sorted(h.encoding_table().items()) sage: for symbol, code in T: ... | def encoding_table(self): r""" Returns the current encoding table | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
Returns the Huffman tree corresponding to the current encoding | Returns the Huffman tree corresponding to the current encoding. INPUT: - None. | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
A tree EXAMPLE:: | - The binary tree representing a Huffman code. EXAMPLES:: | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
""" | <BLANKLINE> """ | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' | def _generate_edges(self, tree, parent="", bit=""): """ Generate the edges of the given Huffman tree. INPUT: - ``tree`` -- a Huffman binary tree. - ``parent`` -- (default: empty string) a parent vertex with exactly two children. - ``bit`` -- (default: empty string) the bit signifying either the left or right branch... | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
u = father | u = parent s = "".join([parent, bit]) | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | left = self._generate_edges(tree[0], parent=s, bit="0") right = self._generate_edges(tree[1], parent=s, bit="1") L = [(u, s)] if s != "" else [] return left + right + L | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
return [(u, self.decode(father+id)+' : '+(father+id))] | return [(u, "".join([self.decode(s), ": ", s]))] | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | d36ada9fa8d1207afa7f17ab966193d7d807e471 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d36ada9fa8d1207afa7f17ab966193d7d807e471/huffman.py |
For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. INPUT: - P = (a,b) a non-Weierstrass point on self - prec: desired precision of the local co... | For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. INPUT: - P = (a,b) a non-Weierstrass point on self - prec: desired precision of the local coordinates - name: gen of the power series ring (default: '... | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py | ||
is the local parameter at P | is the local parameter at P | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x^5-23*x^3+18*x^2+40*x) sage: P = H(1,6) sage: x,y = H.local_coordinates_at_nonweierstrass(P,prec=5) ... | sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x^5-23*x^3+18*x^2+40*x) sage: P = H(1,6) sage: x,y = H.local_coordinates_at_nonweierstrass(P,prec=5) sage: x 1 + t + O(t^5) sage: y 6 + t - 7/2*t^2 - 1/2*t^3 - 25/48*t^4 + O(t^5) sage: Q = H(-2,12) sage: x,y = H.local_coordinates_at_nonweierstrass(Q,prec=5) sage: x -2 ... | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
if d == 0: raise TypeError, "P = %s is a Weierstrass point. Use local_coordinates_at_weierstrass instead!"%P | if d == 0: raise TypeError, "P = %s is a Weierstrass point. Use local_coordinates_at_weierstrass instead!"%P | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. INPUT: | For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. INPUT: | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x^5-23*x^3+18*x^2+40*x) sage: A = H(4,0) sage: x,y = H.local_coordinates_at_weierstrass(A,prec =5) sage: x | sage: R.<x> = QQ['x'] sage: H = HyperellipticCurve(x^5-23*x^3+18*x^2+40*x) sage: A = H(4,0) sage: x,y = H.local_coordinates_at_weierstrass(A,prec =5) sage: x | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
if P[1] != 0: raise TypeError, "P = %s is not a finite Weierstrass point. Use local_coordinates_at_nonweierstrass instead!"%P | if P[1] != 0: raise TypeError, "P = %s is not a finite Weierstrass point. Use local_coordinates_at_nonweierstrass instead!"%P | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py | ||
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py | ||
sage: R.<x> = QQ['x'] | sage: R.<x> = QQ['x'] | def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
If P is not infinity, calls the appropriate local_coordinates function. INPUT: | If P is not infinity, calls the appropriate local_coordinates function. INPUT: | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
(x(t),y(t)) such that y(t)^2 = f(x(t)) and t | (x(t),y(t)) such that y(t)^2 = f(x(t)), where t | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | d7bac827859bd8b14065ddd251609f968f4b30b1 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d7bac827859bd8b14065ddd251609f968f4b30b1/hyperelliptic_generic.py |
We can plot with this transform. Remember that the independent variable is the radius, and the dependent variables are the | We can plot with this transform. Remember that the dependent variable is the radius, and the independent variables are the | 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]) | 987db773b5744546b1de73657586b7320e6c2317 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/987db773b5744546b1de73657586b7320e6c2317/plot3d.py |
We can plot with this transform. Remember that the independent variable is the height, and the dependent variables are the | We can plot with this transform. Remember that the dependent variable is the height, and the independent variables are the | def transform(self, radius=None, azimuth=None, inclination=None): """ A spherical coordinates transform. | 987db773b5744546b1de73657586b7320e6c2317 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/987db773b5744546b1de73657586b7320e6c2317/plot3d.py |
if len(xi) != n: | if len(yi) != n: | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | d092c40804aa52a738434cda3f1e697609c87ac5 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d092c40804aa52a738434cda3f1e697609c87ac5/sbox.py |
x = self.to_bits(e) | x = self.to_bits(e, m) | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | d092c40804aa52a738434cda3f1e697609c87ac5 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/d092c40804aa52a738434cda3f1e697609c87ac5/sbox.py |
Check if a sage object belongs to self. This methods is a helper for | Check if a Sage object belongs to self. This methods is a helper for | def _is_a(self, x): """ Check if a sage object belongs to self. This methods is a helper for :meth:`__contains__` and the constructor :meth:`_element_constructor_`. | 54dbc8f9d65cf0eff0b6c365ec9c632ddfd2c034 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/54dbc8f9d65cf0eff0b6c365ec9c632ddfd2c034/disjoint_union_enumerated_sets.py |
the curve, then `|h(P) - \hat{h}(P)| \leq B`, where `h(P)` is | the curve, then `h(P) \le \hat{h}(P) + B`, where `h(P)` is | def CPS_height_bound(self): r""" Return the Cremona-Prickett-Siksek height bound. This is a floating point number B such that if P is a rational point on the curve, then `|h(P) - \hat{h}(P)| \leq B`, where `h(P)` is the naive logarithmic height of `P` and `\hat{h}(P)` is the canonical height. | 44699f49bf3139d49818b64ebdefb81646859d9f /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/44699f49bf3139d49818b64ebdefb81646859d9f/ell_rational_field.py |
this function is not called) is n=15, but it might have to be | this function is not called) is ``n=15``, but it might have to be | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- `n` (long) -- real precision used for floating point | - ``n`` (long) -- real precision used for floating point | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
.. note:: This change is global and affects all of Sage. | .. warning:: This change is global and affects *all* of Sage. | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
curve using the Curvedata class from eclib, called here an 'mwrank | curve using the ``Curvedata`` class from ``eclib``, called here an 'mwrank | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. If strictly less than 5 invariants are given, then the first ones are set to 0, so, e.g., ``[3,4] means `a_1=a_2=a_3=0` and `a_4=3`, `a_6=4`. INPUT: - `ainvs` (list or tuple) -- a list of <= 5 integers, the coefficients o... | ``ainvs``, which is a list of 5 or less *integers* `a_1`, `a_2`, `a_3`, `a_4`, and `a_5`. See the docstring of this class for full documentation. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
This example illustrates that omitted $a$-invariants default to $0$:: sage: e = mwrank_EllipticCurve([3, -4]) sage: e y^2 = x^3 + 3*x - 4 sage: e.ainvs() [0, 0, 0, 3, -4] The entries of the input list are coerced to :class:`int`. If this is impossible then an error is raised:: sage: e = mwrank_EllipticCurve([3, -4.... | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py | |
if not isinstance(ainvs, list) and len(ainvs) <= 5: raise TypeError, "ainvs must be a list of length at most 5." | if not isinstance(ainvs, (list,tuple)) or not len(ainvs) <= 5: raise TypeError, "ainvs must be a list or tuple of length at most 5." | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py | ||
raise TypeError, "ainvs must be a list of integers." | raise TypeError, "ainvs must be a list or tuple of integers." | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Set the verbosity of printing of output by the 2-descent and | Set the verbosity of printing of output by the :meth:`two_descent()` and | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- `verbose` (int) -- if positive, print lots of output when | - ``verbose`` (int) -- if positive, print lots of output when | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
sage: E.saturate() | sage: E.saturate() | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Returns the underlying _Curvedata class for this mwrank elliptic curve. | Returns the underlying :class:`_Curvedata` class for this mwrank elliptic curve. | def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- ``verbose`` (bool, default True) -- print what mwrank is doing - ``selmer_only`` (bool, default False) -- selmer_only switch | - ``verbose`` (bool, default ``True``) -- print what mwrank is doing. - ``selmer_only`` (bool, default ``False``) -- ``selmer_only`` switch. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
quartic point search - ``second_limit`` (int, default 8) -- bound on `\log `max(|x|,|z|)`, i.e. logarithmic | quartic point search. - ``second_limit`` (int, default 8) -- bound on `\log \max(|x|,|z|)`, i.e. logarithmic. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
quartic search. n_aux=-1 causes default (8) to be used. | quartic search. ``n_aux=-1`` causes default (8) to be used. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- ``second_descent`` (bool, default True) -- (only relevant | - ``second_descent`` (bool, default ``True``) -- (only relevant | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
descent. Default strongloy recommended. | descent. *Default strongly recommended.* | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Nothing -- nothing is returned | Nothing -- nothing is returned. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
second_descent = int(second_descent) | second_descent = int(second_descent) | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Returns the rank of this curve, computed using 2-descent. | Returns the rank of this curve, computed using :meth:`two_descent()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
upper bound may be obtained using the function rank_bound(). | upper bound may be obtained using the function :meth:`rank_bound()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
the method :meth:`certain`. | the method :meth:`certain()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
using 2-descent. | using :meth:`two_descent()`. | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
of order 4, we only obtain an upper bound of 2: | of order 4, we only obtain an upper bound of 2:: | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
In this case the value returned by :meth:`rank` is only a lower bound in general (though in this is correct):: | In this case the value returned by :meth:`rank()` is only a lower bound in general (though this is correct):: | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
the computation again but turn off the second descent:: | the computation again but turn off ``second_descent``:: | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
but with no 2-torsion, the selmer rank is strictly greater | but with no 2-torsion, the Selmer rank is strictly greater | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
primes up to bound. | primes up to ``bound``. | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- `bound` (int, default -1) -- Use `-1` (the default) to | - ``bound`` (int, default -1) -- Use `-1` (the default) to | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` | Returns ``True`` if the last :meth:`two_descent()` call provably correctly computed the rank. If :meth:`two_descent()` hasn't been called, then it is first called by :meth:`certain()` | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
The result is true if and only if the results of the methods :meth:`rank` and :meth:`rank_bound` are equal. | The result is ``True`` if and only if the results of the methods :meth:`rank()` and :meth:`rank_bound()` are equal. | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
for the curve `y^2 + y = x^3 - x^2 - 120x - 2183`.:: | for the curve `y^2 + y = x^3 - x^2 - 120x - 2183`:: | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
computing the L-function), but Sha has order 4 and the $2$-torsion is trivial, so mwrank cannot conclusively | computing the `L`-function), but Sha has order 4 and the 2-torsion is trivial, so mwrank cannot conclusively | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | floating point number `B` such that if `P` is a point on the curve, then the naive logarithmic height `h(P)` is less than `B+\hat{h}(P)`, where `\hat{h}(P)` is the canonical height of `P`. | def CPS_height_bound(self): r""" Return the Cremona-Prickett-Siksek height bound. This is a floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | number `B` such that if `P` is a point on the curve, then the naive logarithmic height `h(P)` is less than `B+\hat{h}(P)`, where `\hat{h}(P)` is the canonical height of `P`. | def silverman_bound(self): r""" Return the Silverman height bound. This is a floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
INPUT: - `curve` (:class:`mwrank_EllipticCurve`) -- the underlying elliptic curve. - `verbose` (bool, default False) -- verbosity flag (controls amount of output produced in point searches) - `pp` (int, default 1) -- process points flag (if nonzero, the points found are processed, so that at all times only a `\ZZ`-b... | See the docstring of this class for full documentation. | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Subgroup of Mordell Weil group: [] sage: EQ.search(2) The previous command produces the following output:: P1 = [0:1:0] is torsion point, order 1 P1 = [1:-1:1] is torsion point, order 2 P1 = [2:2:1] is torsion point, order 3 P1 = [9:23:1] is torsion point, order 6 sage: E = mwrank_EllipticCurve([0,0,1,-7,6]) sag... | Subgroup of Mordell-Weil group: [] | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
'Subgroup of Mordell Weil group: []' | 'Subgroup of Mordell-Weil group: []' | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
'Subgroup of Mordell Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]]' """ return "Subgroup of Mordell Weil group: %s"%self.__mw | 'Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]]' """ return "Subgroup of Mordell-Weil group: %s"%self.__mw | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
This function allows one to add points to a mwrank_MordellWeil object. Process points in the list v, with saturation at primes up to sat. If sat = 0 (the default), do no saturation. | This function allows one to add points to a :class:`mwrank_MordellWeil` object. Process points in the list ``v``, with saturation at primes up to ``sat``. If ``sat`` is zero (the default), do no saturation. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- `v` (list of 3-tuples or lists of ints or Integers) -- a | - ``v`` (list of 3-tuples or lists of ints or Integers) -- a | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- `sat` (int, default 0) --saturate at primes up to sat, or at all primes if sat=0. | - ``sat`` (int, default 0) -- saturate at primes up to ``sat``, or at *all* primes if ``sat`` is zero. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
None. But note that if the verbose flag is set, then there | None. But note that if the ``verbose`` flag is set, then there | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Example to illustrate the saturation parameter:: | Example to illustrate the saturation parameter ``sat``:: | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
raise TypeError, "v (=%s) must be a list of 3-tuples of ints"%v | raise TypeError, "v (=%s) must be a list of 3-tuples (or 3-element lists) of ints"%v | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
but the interface currently returns the output as a float. | but the interface currently returns the output as a ``float``. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
(float) the regulator of the points in this subgroup. | (float) The regulator of the points in this subgroup. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
OUTPUT: (int) The rank of this subgroup of the Mordell-Weil group. | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py | |
Subgroup of Mordell Weil group: [] | Subgroup of Mordell-Weil group: [] | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Subgroup of Mordell Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] | Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
all primes up to `max_prime`. If `-1` (default) then an | all primes up to ``max_prime``. If `-1` (the default), an | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
computed bound is greater than a value set by the eclib | computed bound is greater than a value set by the ``eclib`` | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- ``odd_primes_only`` (bool, default False) -- only do | - ``odd_primes_only`` (bool, default ``False``) -- only do | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
via 2-descent they should alreday be 2-saturated.) | via :meth:``two_descent()`` they should already be 2-saturated.) | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- ``ok`` (bool) is True if and only if the saturation was | - ``ok`` (bool) -- ``True`` if and only if the saturation was | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
the computed saturation bound being too high, then True indicates that the subgroup is saturated at `\emph{all}` | the computed saturation bound being too high, then ``True`` indicates that the subgroup is saturated at *all* | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
- ``index`` (int) is the index of the group generated by the | - ``index`` (int) -- the index of the group generated by the | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
uses floating points methods based on elliptic logarithms to | uses floating point methods based on elliptic logarithms to | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
We emphasize that if this function returns True as the first return argument, and if the default was used for the parameter ``sat_bnd``, then the points in the basis after calling this function are saturated at `\emph{all}` primes, | We emphasize that if this function returns ``True`` as the first return argument (``ok``), and if the default was used for the parameter ``max_prime``, then the points in the basis after calling this function are saturated at *all* primes, | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
saturate up to, and that prime is `\leq` ``max_prime``. | saturate up to, and that prime might be smaller than ``max_prime``. | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
calling search. So calling search up to height 20 then calling saturate results in another search up to height 18. | calling :meth:`search()`. So calling :meth:`search()` up to height 20 then calling :meth:`saturate()` results in another search up to height 18. | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Subgroup of Mordell Weil group: [[1547:-2967:343], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | Subgroup of Mordell-Weil group: [[1547:-2967:343], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
Subgroup of Mordell Weil group: [[-2:3:1], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | Subgroup of Mordell-Weil group: [[-2:3:1], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 8b53e056cc765e689493ec9632c441ee03a3206a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9890/8b53e056cc765e689493ec9632c441ee03a3206a/interface.py |
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