symbols to their coefficients, and a constant term. The coefficients and
the constant term must be rational numbers.
- For example, the linear expression x + 2y + 1 can be constructed using
+ For example, the linear expression x + 2*y + 1 can be constructed using
one of the following instructions:
>>> x, y = symbols('x y')
Alternatively, linear expressions can be constructed from a string:
- >>> LinExpr('x + 2*y + 1')
+ >>> LinExpr('x + 2y + 1')
A linear expression with a single symbol of coefficient 1 and no
constant term is automatically subclassed as a Symbol instance. A linear
@_polymorphic
def __eq__(self, other):
"""
- Test whether two linear expressions are equal.
+ Test whether two linear expressions are equal. Unlike methods
+ LinExpr.__lt__(), LinExpr.__le__(), LinExpr.__ge__(), LinExpr.__gt__(),
+ the result is a boolean value, not a polyhedron. To express that two
+ linear expressions are equal or not equal, use functions Eq() and Ne()
+ instead.
"""
- if isinstance(other, LinExpr):
- return self._coefficients == other._coefficients and \
- self._constant == other._constant
- return NotImplemented
-
- def __le__(self, other):
- from .polyhedra import Le
- return Le(self, other)
+ return self._coefficients == other._coefficients and \
+ self._constant == other._constant
+ @_polymorphic
def __lt__(self, other):
- from .polyhedra import Lt
- return Lt(self, other)
+ from .polyhedra import Polyhedron
+ return Polyhedron([], [other - self - 1])
+ @_polymorphic
+ def __le__(self, other):
+ from .polyhedra import Polyhedron
+ return Polyhedron([], [other - self])
+
+ @_polymorphic
def __ge__(self, other):
- from .polyhedra import Ge
- return Ge(self, other)
+ from .polyhedra import Polyhedron
+ return Polyhedron([], [self - other])
+ @_polymorphic
def __gt__(self, other):
- from .polyhedra import Gt
- return Gt(self, other)
+ from .polyhedra import Polyhedron
+ return Polyhedron([], [self - other - 1])
def scaleint(self):
"""
Return the expression multiplied by its lowest common denominator to
make all values integer.
"""
- lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
+ lcd = functools.reduce(lambda a, b: a*b // gcd(a, b),
[value.denominator for value in self.values()])
- return self * lcm
+ return self * lcd
def subs(self, symbol, expression=None):
"""
2*x + y + 1
"""
if expression is None:
- if isinstance(symbol, Mapping):
- symbol = symbol.items()
- substitutions = symbol
+ substitutions = dict(symbol)
else:
- substitutions = [(symbol, expression)]
- result = self
- for symbol, expression in substitutions:
+ substitutions = {symbol: expression}
+ for symbol in substitutions:
if not isinstance(symbol, Symbol):
raise TypeError('symbols must be Symbol instances')
- coefficients = [(othersymbol, coefficient)
- for othersymbol, coefficient in result._coefficients.items()
- if othersymbol != symbol]
- coefficient = result._coefficients.get(symbol, 0)
- constant = result._constant
- result = LinExpr(coefficients, constant) + coefficient*expression
+ result = self._constant
+ for symbol, coefficient in self._coefficients.items():
+ expression = substitutions.get(symbol, symbol)
+ result += coefficient * expression
return result
@classmethod
return left / right
raise SyntaxError('invalid syntax')
- _RE_NUM_VAR = re.compile(r'(\d+|\))\s*([^\W\d_]\w*|\()')
+ _RE_NUM_VAR = re.compile(r'(\d+|\))\s*([^\W\d]\w*|\()')
@classmethod
def fromstring(cls, string):
Create an expression from a string. Raise SyntaxError if the string is
not properly formatted.
"""
- # add implicit multiplication operators, e.g. '5x' -> '5*x'
+ # Add implicit multiplication operators, e.g. '5x' -> '5*x'.
string = LinExpr._RE_NUM_VAR.sub(r'\1*\2', string)
tree = ast.parse(string, 'eval')
expr = cls._fromast(tree)
@classmethod
def fromsympy(cls, expr):
"""
- Create a linear expression from a sympy expression. Raise TypeError is
+ Create a linear expression from a SymPy expression. Raise TypeError is
the sympy expression is not linear.
"""
import sympy
if symbol == sympy.S.One:
constant = coefficient
elif isinstance(symbol, sympy.Dummy):
- # we cannot properly convert dummy symbols
+ # We cannot properly convert dummy symbols with respect to
+ # symbol equalities.
raise TypeError('cannot convert dummy symbols')
elif isinstance(symbol, sympy.Symbol):
symbol = Symbol(symbol.name)
def tosympy(self):
"""
- Convert the linear expression to a sympy expression.
+ Convert the linear expression to a SymPy expression.
"""
import sympy
expr = 0
Two instances of Symbol are equal if they have the same name.
"""
+ __slots__ = (
+ '_name',
+ '_constant',
+ '_symbols',
+ '_dimension',
+ )
+
def __new__(cls, name):
"""
Return a symbol with the name string given in argument.
raise SyntaxError('invalid syntax')
self = object().__new__(cls)
self._name = name
- self._coefficients = {self: Fraction(1)}
self._constant = Fraction(0)
self._symbols = (self,)
self._dimension = 1
return self
+ @property
+ def _coefficients(self):
+ # This is not implemented as an attribute, because __hash__ is not
+ # callable in __new__ in class Dummy.
+ return {self: Fraction(1)}
+
@property
def name(self):
"""
"""
if name is None:
name = 'Dummy_{}'.format(Dummy._count)
- elif not isinstance(name, str):
- raise TypeError('name must be a string')
- self = object().__new__(cls)
+ self = super().__new__(cls, name)
self._index = Dummy._count
- self._name = name.strip()
- self._coefficients = {self: Fraction(1)}
- self._constant = Fraction(0)
- self._symbols = (self,)
- self._dimension = 1
Dummy._count += 1
return self
fractions.Fraction classes.
"""
+ __slots__ = (
+ '_coefficients',
+ '_constant',
+ '_symbols',
+ '_dimension',
+ ) + Fraction.__slots__
+
def __new__(cls, numerator=0, denominator=None):
self = object().__new__(cls)
self._coefficients = {}
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