index f3cff23..07d4005 100644 (file)
@@ -3,13 +3,13 @@ import functools
import numbers
import re

import numbers
import re

-from collections import OrderedDict, defaultdict
+from collections import OrderedDict, defaultdict, Mapping
from fractions import Fraction, gcd

__all__ = [
'Expression',
from fractions import Fraction, gcd

__all__ = [
'Expression',
-    'Symbol', 'symbols', 'Dummy',
+    'Symbol', 'Dummy', 'symbols',
'Rational',
]

'Rational',
]

@@ -31,49 +31,35 @@ class Expression:
This class implements linear expressions.
"""

This class implements linear expressions.
"""

-    __slots__ = (
-        '_coefficients',
-        '_constant',
-        '_symbols',
-        '_dimension',
-    )
-
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
def __new__(cls, coefficients=None, constant=0):
if isinstance(coefficients, str):
-            if constant:
+            if constant != 0:
raise TypeError('too many arguments')
return Expression.fromstring(coefficients)
if coefficients is None:
return Rational(constant)
raise TypeError('too many arguments')
return Expression.fromstring(coefficients)
if coefficients is None:
return Rational(constant)
-        if isinstance(coefficients, dict):
+        if isinstance(coefficients, Mapping):
coefficients = coefficients.items()
coefficients = coefficients.items()
+        coefficients = list(coefficients)
for symbol, coefficient in coefficients:
if not isinstance(symbol, Symbol):
raise TypeError('symbols must be Symbol instances')
for symbol, coefficient in coefficients:
if not isinstance(symbol, Symbol):
raise TypeError('symbols must be Symbol instances')
-        coefficients = [(symbol, coefficient)
-            for symbol, coefficient in coefficients if coefficient != 0]
+            if not isinstance(coefficient, numbers.Rational):
+                raise TypeError('coefficients must be rational numbers')
+        if not isinstance(constant, numbers.Rational):
+            raise TypeError('constant must be a rational number')
if len(coefficients) == 0:
return Rational(constant)
if len(coefficients) == 1 and constant == 0:
symbol, coefficient = coefficients
if coefficient == 1:
return symbol
if len(coefficients) == 0:
return Rational(constant)
if len(coefficients) == 1 and constant == 0:
symbol, coefficient = coefficients
if coefficient == 1:
return symbol
+        coefficients = [(symbol, Fraction(coefficient))
+            for symbol, coefficient in coefficients if coefficient != 0]
+        coefficients.sort(key=lambda item: item.sortkey())
self = object().__new__(cls)
self = object().__new__(cls)
-        self._coefficients = OrderedDict()
-        for symbol, coefficient in sorted(coefficients,
-                key=lambda item: item.sortkey()):
-            if isinstance(coefficient, Rational):
-                coefficient = coefficient.constant
-            if not isinstance(coefficient, numbers.Rational):
-                raise TypeError('coefficients must be rational numbers '
-                    'or Rational instances')
-            self._coefficients[symbol] = coefficient
-        if isinstance(constant, Rational):
-            constant = constant.constant
-        if not isinstance(constant, numbers.Rational):
-            raise TypeError('constant must be a rational number '
-                'or a Rational instance')
-        self._constant = constant
+        self._coefficients = OrderedDict(coefficients)
+        self._constant = Fraction(constant)
self._symbols = tuple(self._coefficients)
self._dimension = len(self._symbols)
return self
self._symbols = tuple(self._coefficients)
self._dimension = len(self._symbols)
return self
@@ -81,19 +67,17 @@ class Expression:
def coefficient(self, symbol):
if not isinstance(symbol, Symbol):
raise TypeError('symbol must be a Symbol instance')
def coefficient(self, symbol):
if not isinstance(symbol, Symbol):
raise TypeError('symbol must be a Symbol instance')
-        try:
-            return self._coefficients[symbol]
-        except KeyError:
-            return 0
+        return Rational(self._coefficients.get(symbol, 0))

__getitem__ = coefficient

def coefficients(self):

__getitem__ = coefficient

def coefficients(self):
-        yield from self._coefficients.items()
+        for symbol, coefficient in self._coefficients.items():
+            yield symbol, Rational(coefficient)

@property
def constant(self):

@property
def constant(self):
-        return self._constant
+        return Rational(self._constant)

@property
def symbols(self):

@property
def symbols(self):
@@ -113,8 +97,9 @@ class Expression:
return False

def values(self):
return False

def values(self):
-        yield from self._coefficients.values()
-        yield self.constant
+        for coefficient in self._coefficients.values():
+            yield Rational(coefficient)
+        yield Rational(self._constant)

def __bool__(self):
return True

def __bool__(self):
return True
@@ -127,86 +112,64 @@ class Expression:

@_polymorphic

@_polymorphic
-        coefficients = defaultdict(Rational, self.coefficients())
-        for symbol, coefficient in other.coefficients():
+        coefficients = defaultdict(Fraction, self._coefficients)
+        for symbol, coefficient in other._coefficients.items():
coefficients[symbol] += coefficient
coefficients[symbol] += coefficient
-        constant = self.constant + other.constant
+        constant = self._constant + other._constant
return Expression(coefficients, constant)

@_polymorphic
def __sub__(self, other):
return Expression(coefficients, constant)

@_polymorphic
def __sub__(self, other):
-        coefficients = defaultdict(Rational, self.coefficients())
-        for symbol, coefficient in other.coefficients():
+        coefficients = defaultdict(Fraction, self._coefficients)
+        for symbol, coefficient in other._coefficients.items():
coefficients[symbol] -= coefficient
coefficients[symbol] -= coefficient
-        constant = self.constant - other.constant
+        constant = self._constant - other._constant
return Expression(coefficients, constant)

return Expression(coefficients, constant)

+    @_polymorphic
def __rsub__(self, other):
def __rsub__(self, other):
-        return -(self - other)
+        return other - self

-    @_polymorphic
def __mul__(self, other):
def __mul__(self, other):
-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] *= other.constant
-            constant = self.constant * other.constant
+        if isinstance(other, numbers.Rational):
+            coefficients = ((symbol, coefficient * other)
+                for symbol, coefficient in self._coefficients.items())
+            constant = self._constant * other
return Expression(coefficients, constant)
return Expression(coefficients, constant)
-        if isinstance(other, Expression) and not self.isconstant():
-            raise ValueError('non-linear expression: '
-                    '{} * {}'.format(self._parenstr(), other._parenstr()))
return NotImplemented

__rmul__ = __mul__

return NotImplemented

__rmul__ = __mul__

-    @_polymorphic
def __truediv__(self, other):
def __truediv__(self, other):
-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] = Rational(coefficients[symbol], other.constant)
-            constant = Rational(self.constant, other.constant)
+        if isinstance(other, numbers.Rational):
+            coefficients = ((symbol, coefficient / other)
+                for symbol, coefficient in self._coefficients.items())
+            constant = self._constant / other
return Expression(coefficients, constant)
return Expression(coefficients, constant)
-        if isinstance(other, Expression):
-            raise ValueError('non-linear expression: '
-                '{} / {}'.format(self._parenstr(), other._parenstr()))
-        return NotImplemented
-
-    def __rtruediv__(self, other):
-        if isinstance(other, self):
-            if self.isconstant():
-                return Rational(other, self.constant)
-            else:
-                raise ValueError('non-linear expression: '
-                        '{} / {}'.format(other._parenstr(), self._parenstr()))
return NotImplemented

@_polymorphic
def __eq__(self, other):
return NotImplemented

@_polymorphic
def __eq__(self, other):
-        # "normal" equality
+        # returns a boolean, not a constraint
# see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
return isinstance(other, Expression) and \
self._coefficients == other._coefficients and \
# see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
return isinstance(other, Expression) and \
self._coefficients == other._coefficients and \
-            self.constant == other.constant
+            self._constant == other._constant

-    @_polymorphic
def __le__(self, other):
from .polyhedra import Le
return Le(self, other)

def __le__(self, other):
from .polyhedra import Le
return Le(self, other)

-    @_polymorphic
def __lt__(self, other):
from .polyhedra import Lt
return Lt(self, other)

def __lt__(self, other):
from .polyhedra import Lt
return Lt(self, other)

-    @_polymorphic
def __ge__(self, other):
from .polyhedra import Ge
return Ge(self, other)

def __ge__(self, other):
from .polyhedra import Ge
return Ge(self, other)

-    @_polymorphic
def __gt__(self, other):
from .polyhedra import Gt
return Gt(self, other)
def __gt__(self, other):
from .polyhedra import Gt
return Gt(self, other)
@@ -218,18 +181,20 @@ class Expression:

def subs(self, symbol, expression=None):
if expression is None:

def subs(self, symbol, expression=None):
if expression is None:
-            if isinstance(symbol, dict):
+            if isinstance(symbol, Mapping):
symbol = symbol.items()
substitutions = symbol
else:
substitutions = [(symbol, expression)]
result = self
for symbol, expression in substitutions:
symbol = symbol.items()
substitutions = symbol
else:
substitutions = [(symbol, expression)]
result = self
for symbol, expression in substitutions:
+            if not isinstance(symbol, Symbol):
+                raise TypeError('symbols must be Symbol instances')
coefficients = [(othersymbol, coefficient)
coefficients = [(othersymbol, coefficient)
-                for othersymbol, coefficient in result.coefficients()
+                for othersymbol, coefficient in result._coefficients.items()
if othersymbol != symbol]
if othersymbol != symbol]
-            coefficient = result.coefficient(symbol)
-            constant = result.constant
+            coefficient = result._coefficients.get(symbol, 0)
+            constant = result._constant
result = Expression(coefficients, constant) + coefficient*expression
return result

result = Expression(coefficients, constant) + coefficient*expression
return result

@@ -269,41 +234,52 @@ class Expression:

def __repr__(self):
string = ''

def __repr__(self):
string = ''
-        i = 0
-        for symbol in self.symbols:
-            coefficient = self.coefficient(symbol)
+        for i, (symbol, coefficient) in enumerate(self.coefficients()):
if coefficient == 1:
if coefficient == 1:
-                if i == 0:
-                    string += symbol.name
-                else:
-                    string += ' + {}'.format(symbol)
+                if i != 0:
+                    string += ' + '
elif coefficient == -1:
elif coefficient == -1:
-                if i == 0:
-                    string += '-{}'.format(symbol)
-                else:
-                    string += ' - {}'.format(symbol)
+                string += '-' if i == 0 else ' - '
+            elif i == 0:
+                string += '{}*'.format(coefficient)
+            elif coefficient > 0:
+                string += ' + {}*'.format(coefficient)
else:
else:
-                if i == 0:
-                    string += '{}*{}'.format(coefficient, symbol)
-                elif coefficient > 0:
-                    string += ' + {}*{}'.format(coefficient, symbol)
-                else:
-                    assert coefficient < 0
-                    coefficient *= -1
-                    string += ' - {}*{}'.format(coefficient, symbol)
-            i += 1
+                string += ' - {}*'.format(-coefficient)
+            string += '{}'.format(symbol)
constant = self.constant
constant = self.constant
-        if constant != 0 and i == 0:
+        if len(string) == 0:
string += '{}'.format(constant)
elif constant > 0:
string += ' + {}'.format(constant)
elif constant < 0:
string += '{}'.format(constant)
elif constant > 0:
string += ' + {}'.format(constant)
elif constant < 0:
-            constant *= -1
-            string += ' - {}'.format(constant)
-        if string == '':
-            string = '0'
+            string += ' - {}'.format(-constant)
return string

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()):
def _parenstr(self, always=False):
string = str(self)
if not always and (self.isconstant() or self.issymbol()):
@@ -339,15 +315,15 @@ class Expression:

class Symbol(Expression):

class Symbol(Expression):

-    __slots__ = (
-        '_name',
-    )
-
def __new__(cls, name):
if not isinstance(name, str):
raise TypeError('name must be a string')
self = object().__new__(cls)
self._name = name.strip()
def __new__(cls, name):
if not isinstance(name, str):
raise TypeError('name must be a string')
self = object().__new__(cls)
self._name = name.strip()
+        self._coefficients = {self: Fraction(1)}
+        self._constant = Fraction(0)
+        self._symbols = (self,)
+        self._dimension = 1
return self

@property
return self

@property
@@ -357,41 +333,14 @@ class Symbol(Expression):
def __hash__(self):
return hash(self.sortkey())

def __hash__(self):
return hash(self.sortkey())

-    def coefficient(self, symbol):
-        if not isinstance(symbol, Symbol):
-            raise TypeError('symbol must be a Symbol instance')
-        if symbol == self:
-            return 1
-        else:
-            return 0
-
-    def coefficients(self):
-        yield self, 1
-
-    @property
-    def constant(self):
-        return 0
-
-    @property
-    def symbols(self):
-        return self,
-
-    @property
-    def dimension(self):
-        return 1
-
def sortkey(self):
return self.name,

def issymbol(self):
return True

def sortkey(self):
return self.name,

def issymbol(self):
return True

-    def values(self):
-        yield 1
-
def __eq__(self, other):
def __eq__(self, other):
-        return not isinstance(other, Dummy) and isinstance(other, Symbol) \
-            and self.name == other.name
+        return self.sortkey() == other.sortkey()

def asdummy(self):
return Dummy(self.name)

def asdummy(self):
return Dummy(self.name)
@@ -406,36 +355,39 @@ class Symbol(Expression):
return Symbol(node.id)
raise SyntaxError('invalid syntax')

return Symbol(node.id)
raise SyntaxError('invalid syntax')

+    def __repr__(self):
+        return self.name
+
+    def _repr_latex_(self):
+        return '$${}$$'.format(self.name)
+
@classmethod
def fromsympy(cls, expr):
import sympy
@classmethod
def fromsympy(cls, expr):
import sympy
-        if isinstance(expr, sympy.Symbol):
+        if isinstance(expr, sympy.Dummy):
+            return Dummy(expr.name)
+        elif isinstance(expr, sympy.Symbol):
return Symbol(expr.name)
else:
raise TypeError('expr must be a sympy.Symbol instance')

return Symbol(expr.name)
else:
raise TypeError('expr must be a sympy.Symbol instance')

-def symbols(names):
-    if isinstance(names, str):
-        names = names.replace(',', ' ').split()
-    return tuple(Symbol(name) for name in names)
-
-
class Dummy(Symbol):

class Dummy(Symbol):

-    __slots__ = (
-        '_name',
-        '_index',
-    )
-
_count = 0

def __new__(cls, name=None):
if name is None:
name = 'Dummy_{}'.format(Dummy._count)
_count = 0

def __new__(cls, name=None):
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 = object().__new__(cls)
-        self._name = name.strip()
self._index = Dummy._count
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

Dummy._count += 1
return self

@@ -445,61 +397,59 @@ class Dummy(Symbol):
def sortkey(self):
return self._name, self._index

def sortkey(self):
return self._name, self._index

-    def __eq__(self, other):
-        return isinstance(other, Dummy) and self._index == other._index
+    def __repr__(self):
+        return '_{}'.format(self.name)

+    def _repr_latex_(self):
+        return '$${}_{{{}}}$$'.format(self.name, self._index)

-class Rational(Expression):

-    __slots__ = (
-        '_constant',
-    )
+def symbols(names):
+    if isinstance(names, str):
+        names = names.replace(',', ' ').split()
+    return tuple(Symbol(name) for name in names)
+
+
+class Rational(Expression, Fraction):

def __new__(cls, numerator=0, denominator=None):
self = object().__new__(cls)

def __new__(cls, numerator=0, denominator=None):
self = object().__new__(cls)
-        if denominator is None and isinstance(numerator, Rational):
-            self._constant = numerator.constant
-        else:
-            self._constant = Fraction(numerator, denominator)
+        self._coefficients = {}
+        self._constant = Fraction(numerator, denominator)
+        self._symbols = ()
+        self._dimension = 0
+        self._numerator = self._constant.numerator
+        self._denominator = self._constant.denominator
return self

def __hash__(self):
return self

def __hash__(self):
-        return hash(self.constant)
-
-    def coefficient(self, symbol):
-        if not isinstance(symbol, Symbol):
-            raise TypeError('symbol must be a Symbol instance')
-        return 0
-
-    def coefficients(self):
-        yield from ()
+        return Fraction.__hash__(self)

@property

@property
-    def symbols(self):
-        return ()
-
-    @property
-    def dimension(self):
-        return 0
+    def constant(self):
+        return self

def isconstant(self):
return True

def isconstant(self):
return True

-    def values(self):
-        yield self._constant
-
-    @_polymorphic
-    def __eq__(self, other):
-        return isinstance(other, Rational) and self.constant == other.constant
-
def __bool__(self):
def __bool__(self):
-        return self.constant != 0
+        return Fraction.__bool__(self)

-    @classmethod
-    def fromstring(cls, string):
-        if not isinstance(string, str):
-            raise TypeError('string must be a string instance')
-        return Rational(Fraction(string))
+    def __repr__(self):
+        if self.denominator == 1:
+            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)

@classmethod
def fromsympy(cls, expr):

@classmethod
def fromsympy(cls, expr):