def is_ordered(self, letter=None):
if letter is None:
return all(self.is_ordered(l) for l in self.letters)
elif not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return True
def is_ordered(degrees, reverse=False, reverse_diff=False):
diff = 1
if reverse:
degrees.reverse()
if reverse_diff:
diff = -1
for i, d in enumerate(degrees):
if i == len(degrees) - 1:
break
if degrees[i + 1] not in (d, d - diff):
return False
return True
degrees = list(self.all_letter_degrees[letter])
return is_ordered(degrees, False, False) or\
is_ordered(degrees, True, False) or\
is_ordered(degrees, True, True) or\
is_ordered(degrees, False, True)
def max_degree_of_letter(self, letter):
if not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return 0
all_vars = (l for c, l in self._monomials)
return max(d for v in all_vars for l, d in iteritems(v) if l == letter)
def is_complete(self, letter=None):
if letter is None:
return all(self.is_complete(l) for l in self.letters)
elif not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return True
return set(self.all_letter_degrees[letter]) ==\
set(range_(self.max_degree_of_letter(letter) + 1))
def sort(self, letter=None, reverse=False):
if letter is not None and (not is_letter_valid(letter) or\
letter not in self.letters):
raise ValueError("The letter must be a single letter from the "
"alphabet contained in the Polynomial.")
elif len(self) in (0, 1):
return
elif self.is_constant():
return
def _sort(monomials, letter=None):
if letter is None:
return sorted((m for m in monomials if not m[1]),
key=lambda m: m[0], reverse=True)
return sorted((m for m in monomials if letter in m[1]),
key=lambda m: m[1][letter], reverse=True)
degrees = self.all_max_letter_degrees
letters = sorted(iterkeys(degrees),
key=lambda l: (degrees[l], 255 - ord(l)),
reverse=True)
preferenced_letters = sorted(l for l in letters\
if l in self.preferenced_letters)
if preferenced_letters and letter is None:
letter = preferenced_letters.pop(0)
elif letter is None:
letter = letters[0]
letters.remove(letter)
lower_letters = [l for l in letters\
if l.islower() and l not in preferenced_letters]
upper_letters = [l for l in letters\
if l.isupper() and l not in preferenced_letters]
letters = [letter] + preferenced_letters +\
lower_letters + upper_letters
monomials = []
for l in letters:
for m in _sort(self._monomials, l):
if m not in monomials:
monomials.append(m)
for m in _sort(self._monomials):
if m not in monomials:
monomials.append(m)
if reverse:
monomials.reverse()
self._monomials = monomials
def complete(self, letter=None):
if letter is None:
for l in self.letters:
self.complete(l)
return
elif not is_letter_valid(letter):
raise ValueError("The letter must be a single letter from the "
"alphabet.")
elif letter not in self.letters:
return
degrees = set(self.all_letter_degrees[letter])
for d in set(range_(self.max_degree_of_letter(letter))) - degrees:
self._monomials.append([0, {letter: d}])
self.sort()
def check_and_convert_iterable(iterable):
monos = []
for c, letters in iterable:
if not isinstance(c, numbers.Number):
raise ValueError("The coefficient must be a number.")
vars_ = {}
it = iteritems(letters) if isinstance(letters, dict)\
else letters
for letter, degree in it:
if not is_letter_valid(letter):
raise ValueError("All letters must be a single letter "
"from the alphabet.")
elif not is_degree_valid(degree):
raise ValueError("The degree of each variable must be "
"a positive integer.")
vars_[letter] = degree
monos.append([fractions.Fraction(str(c)), vars_])
return monos
