import numbers
import re
-from collections import OrderedDict, defaultdict, Mapping
+from collections import defaultdict, Mapping, OrderedDict
from fractions import Fraction, gcd
__all__ = [
+ 'Dummy',
'LinExpr',
- 'Symbol', 'Dummy', 'symbols',
'Rational',
+ 'Symbol',
+ 'symbols',
]
def __new__(cls, coefficients=None, constant=0):
"""
Return a linear expression from a dictionary or a sequence, that maps
- symbols to their coefficients, and a constant term. The coefficients and
- the constant term must be rational numbers.
+ 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
- expression with no symbol, only a constant term, is automatically
- subclassed as a Rational instance.
+ constant term is automatically subclassed as a Symbol instance. A
+ linear expression with no symbol, only a constant term, is
+ automatically subclassed as a Rational instance.
"""
if isinstance(coefficients, str):
if constant != 0:
symbol, coefficient = coefficients[0]
if coefficient == 1:
return symbol
- coefficients = [(symbol, Fraction(coefficient))
- for symbol, coefficient in coefficients if coefficient != 0]
+ coefficients = [(symbol_, Fraction(coefficient_))
+ for symbol_, coefficient_ in coefficients
+ if coefficient_ != 0]
coefficients.sort(key=lambda item: item[0].sortkey())
self = object().__new__(cls)
self._coefficients = OrderedDict(coefficients)
Return the product of the linear expression by a rational.
"""
if isinstance(other, numbers.Rational):
- coefficients = ((symbol, coefficient * other)
+ coefficients = (
+ (symbol, coefficient * other)
for symbol, coefficient in self._coefficients.items())
constant = self._constant * other
return LinExpr(coefficients, constant)
Return the quotient of the linear expression by a rational.
"""
if isinstance(other, numbers.Rational):
- coefficients = ((symbol, coefficient / other)
+ coefficients = (
+ (symbol, coefficient / other)
for symbol, coefficient in self._coefficients.items())
constant = self._constant / other
return LinExpr(coefficients, constant)
@_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):
"""
make all values integer.
"""
lcd = functools.reduce(lambda a, b: a*b // gcd(a, b),
- [value.denominator for value in self.values()])
+ [value.denominator for value in self.values()])
return self * lcd
def subs(self, symbol, expression=None):
for symbol in substitutions:
if not isinstance(symbol, Symbol):
raise TypeError('symbols must be Symbol instances')
- result = self._constant
+ result = Rational(self._constant)
for symbol, coefficient in self._coefficients.items():
expression = substitutions.get(symbol, symbol)
result += coefficient * expression
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)
- if not isinstance(expr, cls):
+ expression = cls._fromast(tree)
+ if not isinstance(expression, cls):
raise SyntaxError('invalid syntax')
- return expr
+ return expression
def __repr__(self):
string = ''
string += ' - {}'.format(-constant)
return string
- def _repr_latex_(self):
- string = ''
- for i, (symbol, coefficient) in enumerate(self.coefficients()):
- if coefficient == 1:
- if i != 0:
- string += ' + '
- elif coefficient == -1:
- string += '-' if i == 0 else ' - '
- elif i == 0:
- string += '{}'.format(coefficient._repr_latex_().strip('$'))
- elif coefficient > 0:
- string += ' + {}'.format(coefficient._repr_latex_().strip('$'))
- elif coefficient < 0:
- string += ' - {}'.format((-coefficient)._repr_latex_().strip('$'))
- string += '{}'.format(symbol._repr_latex_().strip('$'))
- constant = self.constant
- if len(string) == 0:
- string += '{}'.format(constant._repr_latex_().strip('$'))
- elif constant > 0:
- string += ' + {}'.format(constant._repr_latex_().strip('$'))
- elif constant < 0:
- string += ' - {}'.format((-constant)._repr_latex_().strip('$'))
- return '$${}$$'.format(string)
-
def _parenstr(self, always=False):
string = str(self)
if not always and (self.isconstant() or self.issymbol()):
return '({})'.format(string)
@classmethod
- def fromsympy(cls, expr):
+ def fromsympy(cls, expression):
"""
- 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
coefficients = []
constant = 0
- for symbol, coefficient in expr.as_coefficients_dict().items():
+ for symbol, coefficient in expression.as_coefficients_dict().items():
coefficient = Fraction(coefficient.p, coefficient.q)
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)
coefficients.append((symbol, coefficient))
else:
- raise TypeError('non-linear expression: {!r}'.format(expr))
- expr = LinExpr(coefficients, constant)
- if not isinstance(expr, cls):
- raise TypeError('cannot convert to a {} instance'.format(cls.__name__))
- return expr
+ raise TypeError('non-linear expression: {!r}'.format(
+ expression))
+ expression = LinExpr(coefficients, constant)
+ if not isinstance(expression, cls):
+ raise TypeError('cannot convert to a {} instance'.format(
+ cls.__name__))
+ return expression
def tosympy(self):
"""
- Convert the linear expression to a sympy expression.
+ Convert the linear expression to a SymPy expression.
"""
import sympy
- expr = 0
+ expression = 0
for symbol, coefficient in self.coefficients():
term = coefficient * sympy.Symbol(symbol.name)
- expr += term
- expr += self.constant
- return expr
+ expression += term
+ expression += self.constant
+ return expression
class Symbol(LinExpr):
@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 __repr__(self):
return self.name
- def _repr_latex_(self):
- return '$${}$$'.format(self.name)
-
def symbols(names):
"""
def __repr__(self):
return '_{}'.format(self.name)
- def _repr_latex_(self):
- return '$${}_{{{}}}$$'.format(self.name, self._index)
-
class Rational(LinExpr, Fraction):
"""
return '{!r}'.format(self.numerator)
else:
return '{!r}/{!r}'.format(self.numerator, self.denominator)
-
- def _repr_latex_(self):
- if self.denominator == 1:
- return '$${}$$'.format(self.numerator)
- elif self.numerator < 0:
- return '$$-\\frac{{{}}}{{{}}}$$'.format(-self.numerator,
- self.denominator)
- else:
- return '$$\\frac{{{}}}{{{}}}$$'.format(self.numerator,
- self.denominator)
projects / linpy.git / blobdiff