index d8b020d..07d4005 100644 (file)
@@ -3,14 +3,14 @@ import functools
import numbers
import re

import numbers
import re

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

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

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

]

@@ -20,7 +20,7 @@ def _polymorphic(func):
if isinstance(right, Expression):
return func(left, right)
elif isinstance(right, numbers.Rational):
if isinstance(right, Expression):
return func(left, right)
elif isinstance(right, numbers.Rational):
-            right = Constant(right)
+            right = Rational(right)
return func(left, right)
return NotImplemented
return wrapper
return func(left, right)
return NotImplemented
return wrapper
@@ -31,72 +31,53 @@ 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')
raise TypeError('too many arguments')
-            return cls.fromstring(coefficients)
-        if isinstance(coefficients, dict):
-            coefficients = coefficients.items()
+            return Expression.fromstring(coefficients)
if coefficients is None:
if coefficients is None:
-            return Constant(constant)
-        coefficients = [(symbol, coefficient)
-            for symbol, coefficient in coefficients if coefficient != 0]
+            return Rational(constant)
+        if isinstance(coefficients, Mapping):
+            coefficients = coefficients.items()
+        coefficients = list(coefficients)
+        for symbol, coefficient in coefficients:
+            if not isinstance(symbol, Symbol):
+                raise TypeError('symbols must be Symbol instances')
+            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:
if len(coefficients) == 0:
-            return Constant(constant)
-        elif len(coefficients) == 1 and constant == 0:
+            return Rational(constant)
+        if len(coefficients) == 1 and constant == 0:
symbol, coefficient = coefficients[0]
if coefficient == 1:
symbol, coefficient = coefficients[0]
if coefficient == 1:
-                return Symbol(symbol)
+                return symbol
+        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 = object().__new__(cls)
-        self._coefficients = {}
-        for symbol, coefficient in coefficients:
-            if isinstance(symbol, Symbol):
-                symbol = symbol.name
-            elif not isinstance(symbol, str):
-                raise TypeError('symbols must be strings or Symbol instances')
-            if isinstance(coefficient, Constant):
-                coefficient = coefficient.constant
-            if not isinstance(coefficient, numbers.Rational):
-                raise TypeError('coefficients must be rational numbers '
-                    'or Constant instances')
-            self._coefficients[symbol] = coefficient
-        self._coefficients = OrderedDict(sorted(self._coefficients.items()))
-        if isinstance(constant, Constant):
-            constant = constant.constant
-        if not isinstance(constant, numbers.Rational):
-            raise TypeError('constant must be a rational number '
-                'or a Constant instance')
-        self._constant = constant
+        self._coefficients = OrderedDict(coefficients)
+        self._constant = Fraction(constant)
self._symbols = tuple(self._coefficients)
self._dimension = len(self._symbols)
return self

def coefficient(self, symbol):
self._symbols = tuple(self._coefficients)
self._dimension = len(self._symbols)
return self

def coefficient(self, symbol):
-        if isinstance(symbol, Symbol):
-            symbol = str(symbol)
-        elif not isinstance(symbol, str):
-            raise TypeError('symbol must be a string or a Symbol instance')
-        try:
-            return self._coefficients[symbol]
-        except KeyError:
-            return 0
+        if not isinstance(symbol, Symbol):
+            raise TypeError('symbol must be a Symbol instance')
+        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):
@@ -106,6 +87,9 @@ class Expression:
def dimension(self):
return self._dimension

def dimension(self):
return self._dimension

+    def __hash__(self):
+        return hash((tuple(self._coefficients.items()), self._constant))
+
def isconstant(self):
return False

def isconstant(self):
return False

@@ -113,9 +97,9 @@ class Expression:
return False

def values(self):
return False

def values(self):
-        for symbol in self.symbols:
-            yield self.coefficient(symbol)
-        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
@@ -128,106 +112,92 @@ class Expression:

@_polymorphic

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

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

@_polymorphic
def __sub__(self, other):
-        coefficients = dict(self.coefficients())
-        for symbol, coefficient in other.coefficients():
-            if symbol in coefficients:
-                coefficients[symbol] -= coefficient
-            else:
-                coefficients[symbol] = -coefficient
-        constant = self.constant - other.constant
+        coefficients = defaultdict(Fraction, self._coefficients)
+        for symbol, coefficient in other._coefficients.items():
+            coefficients[symbol] -= coefficient
+        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] = \
-                        Fraction(coefficients[symbol], other.constant)
-            constant = Fraction(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():
-                constant = Fraction(other, self.constant)
-                return Expression(constant=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 \
# 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._coefficients == other._coefficients and \
+            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)

-    def __hash__(self):
-        return hash((tuple(self.coefficients()), self._constant))
-
-    def _toint(self):
+    def scaleint(self):
lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
[value.denominator for value in self.values()])
return self * lcm

lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
[value.denominator for value in self.values()])
return self * lcm

+    def subs(self, symbol, expression=None):
+        if expression is None:
+            if isinstance(symbol, Mapping):
+                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)
+                for othersymbol, coefficient in result._coefficients.items()
+                if othersymbol != symbol]
+            coefficient = result._coefficients.get(symbol, 0)
+            constant = result._constant
+            result = Expression(coefficients, constant) + coefficient*expression
+        return result
+
@classmethod
def _fromast(cls, node):
if isinstance(node, ast.Module) and len(node.body) == 1:
@classmethod
def _fromast(cls, node):
if isinstance(node, ast.Module) and len(node.body) == 1:
@@ -237,7 +207,7 @@ class Expression:
elif isinstance(node, ast.Name):
return Symbol(node.id)
elif isinstance(node, ast.Num):
elif isinstance(node, ast.Name):
return Symbol(node.id)
elif isinstance(node, ast.Num):
-            return Constant(node.n)
+            return Rational(node.n)
elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
return -cls._fromast(node.operand)
elif isinstance(node, ast.BinOp):
elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
return -cls._fromast(node.operand)
elif isinstance(node, ast.BinOp):
@@ -258,47 +228,58 @@ class Expression:
@classmethod
def fromstring(cls, string):
# add implicit multiplication operators, e.g. '5x' -> '5*x'
@classmethod
def fromstring(cls, string):
# add implicit multiplication operators, e.g. '5x' -> '5*x'
-        string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
+        string = Expression._RE_NUM_VAR.sub(r'\1*\2', string)
tree = ast.parse(string, 'eval')
return cls._fromast(tree)

tree = ast.parse(string, 'eval')
return cls._fromast(tree)

-    def __str__(self):
+    def __repr__(self):
string = ''
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
-                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()):
@@ -306,30 +287,27 @@ class Expression:
else:
return '({})'.format(string)

else:
return '({})'.format(string)

-    def __repr__(self):
-        return '{}({!r})'.format(self.__class__.__name__, str(self))
-
@classmethod
def fromsympy(cls, expr):
import sympy
@classmethod
def fromsympy(cls, expr):
import sympy
-        coefficients = {}
+        coefficients = []
constant = 0
for symbol, coefficient in expr.as_coefficients_dict().items():
coefficient = Fraction(coefficient.p, coefficient.q)
if symbol == sympy.S.One:
constant = coefficient
elif isinstance(symbol, sympy.Symbol):
constant = 0
for symbol, coefficient in expr.as_coefficients_dict().items():
coefficient = Fraction(coefficient.p, coefficient.q)
if symbol == sympy.S.One:
constant = coefficient
elif isinstance(symbol, sympy.Symbol):
-                symbol = symbol.name
-                coefficients[symbol] = coefficient
+                symbol = Symbol(symbol.name)
+                coefficients.append((symbol, coefficient))
else:
raise ValueError('non-linear expression: {!r}'.format(expr))
else:
raise ValueError('non-linear expression: {!r}'.format(expr))
-        return cls(coefficients, constant)
+        return Expression(coefficients, constant)

def tosympy(self):
import sympy
expr = 0
for symbol, coefficient in self.coefficients():

def tosympy(self):
import sympy
expr = 0
for symbol, coefficient in self.coefficients():
-            term = coefficient * sympy.Symbol(symbol)
+            term = coefficient * sympy.Symbol(symbol.name)
expr += term
expr += self.constant
return expr
expr += term
expr += self.constant
return expr
@@ -337,21 +315,14 @@ class Expression:

class Symbol(Expression):

class Symbol(Expression):

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

self._dimension = 1
return self

@@ -359,9 +330,21 @@ class Symbol(Expression):
def name(self):
return self._name

def name(self):
return self._name

+    def __hash__(self):
+        return hash(self.sortkey())
+
+    def sortkey(self):
+        return self.name,
+
def issymbol(self):
return True

def issymbol(self):
return True

+    def __eq__(self, other):
+        return self.sortkey() == other.sortkey()
+
+    def asdummy(self):
+        return Dummy(self.name)
+
@classmethod
def _fromast(cls, node):
if isinstance(node, ast.Module) and len(node.body) == 1:
@classmethod
def _fromast(cls, node):
if isinstance(node, ast.Module) and len(node.body) == 1:
@@ -373,63 +356,107 @@ class Symbol(Expression):
raise SyntaxError('invalid syntax')

def __repr__(self):
raise SyntaxError('invalid syntax')

def __repr__(self):
-        return '{}({!r})'.format(self.__class__.__name__, self._name)
+        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):
-            return cls(expr.name)
+        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')

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

+class Dummy(Symbol):
+
+    _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._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
+
+    def __hash__(self):
+        return hash(self.sortkey())
+
+    def sortkey(self):
+        return self._name, self._index
+
+    def __repr__(self):
+        return '_{}'.format(self.name)
+
+    def _repr_latex_(self):
+        return '$${}_{{{}}}$$'.format(self.name, self._index)
+
+
def symbols(names):
if isinstance(names, str):
names = names.replace(',', ' ').split()
def symbols(names):
if isinstance(names, str):
names = names.replace(',', ' ').split()
-    return (Symbol(name) for name in names)
+    return tuple(Symbol(name) for name in names)

-class Constant(Expression):
+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, Constant):
-            self._constant = numerator.constant
-        else:
-            self._constant = Fraction(numerator, denominator)
self._coefficients = {}
self._coefficients = {}
+        self._constant = Fraction(numerator, denominator)
self._symbols = ()
self._dimension = 0
self._symbols = ()
self._dimension = 0
+        self._numerator = self._constant.numerator
+        self._denominator = self._constant.denominator
+        return self
+
+    def __hash__(self):
+        return Fraction.__hash__(self)
+
+    @property
+    def constant(self):
return self

def isconstant(self):
return True

def __bool__(self):
return self

def isconstant(self):
return True

def __bool__(self):
-        return self.constant != 0
-
-    @classmethod
-    def fromstring(cls, string):
-        if isinstance(string, str):
-            return Constant(Fraction(string))
-        else:
-            raise TypeError('string must be a string instance')
+        return Fraction.__bool__(self)

def __repr__(self):

def __repr__(self):
-        if self.constant.denominator == 1:
-            return '{}({!r})'.format(self.__class__.__name__,
-                self.constant.numerator)
+        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:
else:
-            return '{}({!r}, {!r})'.format(self.__class__.__name__,
-                self.constant.numerator, self.constant.denominator)
+            return '$$\\frac{{{}}}{{{}}}$$'.format(self.numerator,
+                self.denominator)

@classmethod
def fromsympy(cls, expr):
import sympy
if isinstance(expr, sympy.Rational):

@classmethod
def fromsympy(cls, expr):
import sympy
if isinstance(expr, sympy.Rational):
-            return cls(expr.p, expr.q)
+            return Rational(expr.p, expr.q)
elif isinstance(expr, numbers.Rational):
elif isinstance(expr, numbers.Rational):
-            return cls(expr)
+            return Rational(expr)
else:
raise TypeError('expr must be a sympy.Rational instance')
else:
raise TypeError('expr must be a sympy.Rational instance')