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 + 2*y + 1 can be constructed using
one of the following instructions:
>>> 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)
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
symbol = Symbol(symbol.name)
coefficients.append((symbol, coefficient))
else:
- raise TypeError('non-linear expression: {!r}'.format(expression))
+ 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__))
+ raise TypeError('cannot convert to a {} instance'.format(
+ cls.__name__))
return expression
def tosympy(self):