rem stringlengths 1 322k | add stringlengths 0 2.05M | context stringlengths 4 228k | meta stringlengths 156 215 |
|---|---|---|---|
table), we are likely to get some random-looking string :: | table), we are likely to get some random-looking string:: | def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
... precisely what we deserved :-) INPUT: One among the following: - ``string`` -- a string from which the Huffman encoding should be created - ``frequencies`` -- a dictionary associating its frequency or its number of occurrences to each letter of the alphabet. | This does not look like our original string. Instead of using frequency, we can assign weights to each alphabetic symbol:: sage: from sage.coding.source_coding.huffman import Huffman sage: T = {"a":45, "b":13, "c":12, "d":16, "e":9, "f":5} sage: H = Huffman(table=T) sage: L = ["deaf", "bead", "fab", "bee"] sage: E = ... | def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman INPUT: One among the following: - ``string`` -- a string from which the Huffman encoding should be created - ``frequencies`` -- a dictionary associating its frequency or its number of occurrences to each letter of the alphabet. EXA... | def __init__(self, string=None, table=None): r""" Constructor for Huffman. See the docstring of this class for full documentation. 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) TESTS: If b... | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
ValueError: Exactly one of `string` or `frequencies` parameters must be defined """ | ValueError: Exactly one of 'string' and 'table' cannot be None. """ if (string is not None) and (table is not None): raise ValueError( "Exactly one of 'string' and 'table' cannot be None.") | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
if sum([string is not None, frequencies is not None]) != 1: raise ValueError("Exactly one of `string` or `frequencies` parameters must be defined") | self._tree = None self._index = None | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
elif frequencies is not None: self._build_code(frequencies) def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | elif table is not None: self._build_code(table) def _build_code_from_tree(self, tree, d, prefix): r""" Builds the Huffman code corresponding to a given tree and prefix. | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
EXAMPLE:: | EXAMPLES:: | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
sage: h._build_code_from_tree(h._tree, d) """ | sage: h._build_code_from_tree(h._tree, d, prefix="") """ | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
self._build_code_from_tree(tree[0], d, prefix=prefix+'0') self._build_code_from_tree(tree[1], d, prefix=prefix+'1') | self._build_code_from_tree(tree[0], d, prefix="".join([prefix, "0"])) self._build_code_from_tree(tree[1], d, prefix="".join([prefix, "1"])) | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
Returns a Huffman code for each one of the given elements. INPUT: - ``dic`` (dictionary) -- associates to each letter of the alphabet a frequency or a number of occurrences. | Constructs a Huffman code corresponding to an alphabet with the given weight table. INPUT: - ``dic`` -- a dictionary that associates to each symbol of an alphabet a numeric value. If we consider the frequency of each alphabetic symbol, then ``dic`` is considered as the frequency table of the alphabet with each numeri... | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py | ||
index = dic.items() | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py | |
for i,(e,w) in enumerate(index): heappush(heap, (w, i) ) while len(heap)>=2: (w1, i1) = heappop(heap) (w2, i2) = heappop(heap) heappush(heap, (w1+w2,[i1,i2])) | for i, (s, w) in enumerate(dic.items()): heappush(heap, (w, i)) for i in range(1, len(dic)): weight_a, node_a = heappop(heap) weight_b, node_b = heappop(heap) heappush(heap, (weight_a + weight_b, [node_a, node_b])) | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
self._build_code_from_tree(self._tree, d) self._index = dict([(i,e) for i,(e,w) in enumerate(index)]) self._character_to_code = dict([(e,d[i]) for i,(e,w) in enumerate(index)]) | self._build_code_from_tree(self._tree, d, prefix="") self._index = dict((i, s) for i, (s, w) in enumerate(dic.items())) self._character_to_code = dict( (s, d[i]) for i, (s, w) in enumerate(dic.items())) | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
Returns an encoding of the given string based on the current encoding table INPUT: - ``string`` (string) EXAMPLE: This is how a string is encoded then decoded :: | Encode the given string based on the current encoding table. INPUT: - ``string`` -- a string of symbols over an alphabet. OUTPUT: - A Huffman encoding of ``string``. EXAMPLES: This is how a string is encoded and then decoded:: | def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py | ||
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 | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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. | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
Returns the current encoding table | Returns the current encoding table. INPUT: - None. | def encoding_table(self): r""" Returns the current encoding table | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
""" | <BLANKLINE> """ | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 []) | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 []) | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 []) | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/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 []) | 08cf8218c91d92b4dcb4602a7135f1d9d706af1e /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/08cf8218c91d92b4dcb4602a7135f1d9d706af1e/huffman.py |
\log(n)` time (and in linear time if all weights are equal). On the other hand, if one is given a large (possibly | \log(n)` time (and in linear time if all weights are equal) where `n = V + E`. On the other hand, if one is given a large (possibly | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6/generic_graph.py |
sage: st = g.steiner_tree(g.vertices()[:5]) sage: st.is_tree() | sage: st = g.steiner_tree(g.vertices()[:5]) sage: st.is_tree() | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6/generic_graph.py |
sage: all([v in st for v in g.vertices()[:5] ]) | sage: all([v in st for v in g.vertices()[:5] ]) | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ab8938ee4489ea4b0bde5a6b5927cff64d96a7b6/generic_graph.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. | 09cf0daf0656159c5e2e166b299baee34935d15f /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/09cf0daf0656159c5e2e166b299baee34935d15f/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. | 09cf0daf0656159c5e2e166b299baee34935d15f /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/09cf0daf0656159c5e2e166b299baee34935d15f/sbox.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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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 | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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 | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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 | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/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. | ef7503ddc882a8693dd4b8a170c060074f3ef89b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/ef7503ddc882a8693dd4b8a170c060074f3ef89b/hyperelliptic_generic.py |
Returns a list of the immediate super categories of self. | Returns a list of the immediate super categories of ``self``. | def super_categories(self): """ Returns a list of the immediate super categories of self. | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
- often uses self.one(). | - often uses ``self.one()``. | def one(self): r""" Returns the one of the monoid, that is the unique neutral element for `*`. | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
Backward compatibility alias for :meth:`self.one()`. | Backward compatibility alias for :meth:`one`. | def one_element(self): r""" Backward compatibility alias for :meth:`self.one()`. | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
Returns the product of the elements in `args`, as an element of `self`. EXAMPLES: | Returns the product of the elements in ``args``, as an element of ``self``. EXAMPLES:: | def prod(self, args): r""" n-ary product | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
def prod(self, args): r""" n-ary product | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py | ||
Returns whether self is the one of the monoid | Returns whether ``self`` is the one of the monoid | def is_one(self): r""" Returns whether self is the one of the monoid | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
- n: a non negative integer | - ``n``: a non negative integer | def __pow__(self, n): r""" INPUTS: - n: a non negative integer | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
A naive implementation of __pow__ | A naive implementation of ``__pow__`` | def _pow_naive(self, n): r""" A naive implementation of __pow__ | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
- n: a non negative integer | - ``n``: a non negative integer | def _pow_naive(self, n): r""" A naive implementation of __pow__ | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
faster du to size explotion). | faster due to size explosion). | def _pow_naive(self, n): r""" A naive implementation of __pow__ | f7adc4547fa59894ffbc320f0b3a2c47db617853 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f7adc4547fa59894ffbc320f0b3a2c47db617853/monoids.py |
'Sphere center 1.0 2.0 3.0 Rad 0.015 texture84' | 'Sphere center 1.0 2.0 3.0 Rad 0.015 texture85' | def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using the Tachyon ray tracer. | 87327e7c8fd18e4438140ec95ad093425fb8d221 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/87327e7c8fd18e4438140ec95ad093425fb8d221/shapes2.py |
['g obj_1', 'usemtl texture86'] | ['g obj_1', 'usemtl texture87'] | def obj_repr(self, render_params): """ Returns complete representation of the point as a sphere. | 87327e7c8fd18e4438140ec95ad093425fb8d221 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/87327e7c8fd18e4438140ec95ad093425fb8d221/shapes2.py |
'FCylinder base 1.0 0.0 0.0 apex 0.999950000417 0.00999983333417 0.0001 rad 0.005 texture126' | 'FCylinder base 1.0 0.0 0.0 apex 0.999950000417 0.00999983333417 0.0001 rad 0.005 texture127' | def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using the Tachyon ray tracer. | 87327e7c8fd18e4438140ec95ad093425fb8d221 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/87327e7c8fd18e4438140ec95ad093425fb8d221/shapes2.py |
linewidths = options['linewidths'] | linewidths = options.get('linewidths',None) | def _render_on_subplot(self, subplot): """ TESTS: | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
linestyles = options['linestyles'] | linestyles = options.get('linestyles',None) | def _render_on_subplot(self, subplot): """ TESTS: | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
@suboptions('label', fontsize=9, colors=None, inline=None, inline_spacing=3, fmt="%1.2f") | @suboptions('label', fontsize=9, colors='blue', inline=None, inline_spacing=3, fmt="%1.2f") | def _render_on_subplot(self, subplot): """ TESTS: | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
If fill is True (the default), then we may have to color the labels so that we can see them:: | We can change the color of the labels if so desired:: | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
g.add_primitive(ContourPlot(xy_data_array, xrange,yrange, dict(contours=[-1e307, 0, 1e307], cmap=cmap, fill=True, labels=False, **options))) | g.add_primitive(ContourPlot(xy_data_array, xrange,yrange, dict(contours=[-1e307, 0, 1e307], cmap=cmap, fill=True, labels=False, **options))) | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
g.add_primitive(ContourPlot(xy_data_array, xrange, yrange, dict( linestyles=linestyles, linewidths=linewidths, contours=[0], cmap=[bordercol], fill=False, labels=False, **options))) | g.add_primitive(ContourPlot(xy_data_array, xrange, yrange, dict(linestyles=linestyles, linewidths=linewidths, contours=[0], cmap=[bordercol], fill=False, labels=False, **options))) | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 267857a0698745b43920a2cd088b4c002a62b836 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/267857a0698745b43920a2cd088b4c002a62b836/contour_plot.py |
gens = [ "()" ] | k = max(self.entries()) gens = [range(1,k+1)] | def row_stabilizer(self): """ Return the PermutationGroup corresponding to the row stabilizer of self. | 607f3bf91afb925b159d15574764be8ff24b5e0a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/607f3bf91afb925b159d15574764be8ff24b5e0a/tableau.py |
A map from '(' to open_symbol and ')' to close_symbol and otherwise an error is raised. | 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 parenthesis. OUTPUT: - If... | 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 """ ... | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
A map from open_symbol to '(' and close_symbol to ')' and otherwise an error is raised. | 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 ``close_symbol``. OUTPUT: - I... | 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... | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete | Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete. | 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... | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
TODO: In functions where a Dyck word is necessary, an error should be raised (e.g. a_statistic, b_statistic)? | TODO: In functions where a Dyck word is necessary, an error should be raised (e.g. ``a_statistic``, ``b_statistic``)? | 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... | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
report the position for the parenthesis that matches the one at position ``pos`` | 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`` | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
- ``pos`` - the index of the parenthesis in the list | - ``pos`` - the index of the parenthesis in the list. | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
integer representing the index of the matching parenthesis. If no parenthesis matches nothing is returned | Integer representing the index of the matching parenthesis. If no parenthesis matches, return ``None``. | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Bijection of Biane from Dyck words to non crossing partitions | Bijection of Biane from Dyck words to non-crossing partitions. | def to_noncrossing_partition(self): r""" Bijection of Biane from Dyck words to non crossing partitions Thanks to Mathieu Dutour for describing the bijection. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
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 | 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 | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
TODO: better name? to_standard_tableau? and should *actually* return a Tableau object? | TODO: better name? ``to_standard_tableau``? and should *actually* return a Tableau object? | 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 | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Returns the a-statistic for the Dyck word correspond to the area of the Dyck path. | Returns the a-statistic for the Dyck word corresponding to the area of the Dyck path. | def a_statistic(self): """ Returns the a-statistic for the Dyck word correspond to the area of the Dyck path. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
$(0, 0), (j_1, j_1), (j_2, j_2), ... , (j_r-1, j_r-1), (j_r, j_r) = (n, n).$ | .. MATH:: (0, 0), (j_1, j_1), (j_2, j_2), \dots , (j_r-1, j_r-1), (j_r, j_r) = (n, n). | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. | Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. | def list(self): """ Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. | Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. | def __iter__(self): r""" Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
converts a non-crossing partition to a Dyck word | Converts a non-crossing partition to a Dyck word. | 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... | 7e1334f768dfbfef3881c254af52ae022484f92b /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/7e1334f768dfbfef3881c254af52ae022484f92b/dyck_word.py |
This is called "massaging" in [CB07]_. | This is called "massaging" in [CBJ07]_. | def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | 71b8ab98c7e082f651a26f77147d1a3febc1b513 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/71b8ab98c7e082f651a26f77147d1a3febc1b513/mpolynomialsystem.py |
return HeckeModuleElement.__mul__(self, other) | return element.HeckeModuleElement.__mul__(self, other) | def __mul__(self, other): r""" Calculate the product self * other. | 3e9710c9379eb051cee450f01fed94d93593b590 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/3e9710c9379eb051cee450f01fed94d93593b590/element.py |
def order(self, *gens, **kwds): | def order(self, *args, **kwds): | def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. | 65d29c8a95ea9faea3800f96c664e08c7f675ca2 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/65d29c8a95ea9faea3800f96c664e08c7f675ca2/number_field.py |
""" | sage: K.<a> = NumberField(x^3 - 2) sage: ZZ[a] Order in Number Field in a0 with defining polynomial x^3 - 2 TESTS: We verify that trac sage: K.<a> = NumberField(x^4 + 4*x^2 + 2) sage: B = K.integral_basis() sage: K.order(*B) Order in Number Field in a with defining polynomial x^4 + 4*x^2 + 2 sage: K.order(B) Order ... | def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. | 65d29c8a95ea9faea3800f96c664e08c7f675ca2 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/65d29c8a95ea9faea3800f96c664e08c7f675ca2/number_field.py |
-0.530637530952518 + 1.11851787964371*I | 0.530637530952518 - 1.11851787964371*I | def __init__(self): r""" The inverse of the hyperbolic secant function. | 76b69b5c65d8bfde141c23aa1ee93d46e12acda4 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/76b69b5c65d8bfde141c23aa1ee93d46e12acda4/hyperbolic.py |
""" return Vobj.evaluated_on(self) | If you pass a vector, it is assumed to be the coordinate vector of a point:: sage: ineq.eval( vector(ZZ, [3,2]) ) -4 """ try: return Vobj.evaluated_on(self) except AttributeError: return self.A() * Vobj + self.b() | def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py |
is_inequality.__doc__ = Hrepresentation.is_inequality.__doc__ | def is_inequality(self): """ Returns True since this is, by construction, an inequality. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py | |
""" | 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_vector(): return self.polyhedron()... | 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. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py |
is_equation.__doc__ = Hrepresentation.is_equation.__doc__ | def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py | |
is_vertex.__doc__ = Vrepresentation.is_vertex.__doc__ | def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py | |
is_ray.__doc__ = Vrepresentation.is_ray.__doc__ | def is_ray(self): """ Tests if this object is a ray. Always True by construction. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py | |
is_line.__doc__ = Vrepresentation.is_line.__doc__ | def is_line(self): """ Tests if the object is a line. By construction it must be. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py | |
Returns the identity projection. | Returns the identity projection of the polyhedron. | def identity(self): """ Returns the identity projection. | 346f358354c345210a872f113663df4917187850 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/346f358354c345210a872f113663df4917187850/polyhedra.py |
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