X-Git-Url: https://svn.cri.ensmp.fr/git/linpy.git/blobdiff_plain/42c85c00b3ed474312c4b66a3da0e8208c60d231..HEAD:/linpy/linexprs.py

diff --git a/linpy/linexprs.py b/linpy/linexprs.py
index e4ed1cc..ccfbbfa 100644
--- a/linpy/linexprs.py
+++ b/linpy/linexprs.py
@@ -20,14 +20,16 @@ import functools
 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',
 ]
 
 
@@ -59,10 +61,10 @@ class LinExpr:
     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')
@@ -76,12 +78,12 @@ class LinExpr:
 
         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:
@@ -105,8 +107,9 @@ class LinExpr:
             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)
@@ -223,7 +226,8 @@ class LinExpr:
         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)
@@ -236,7 +240,8 @@ class LinExpr:
         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)
@@ -245,37 +250,43 @@ class LinExpr:
     @_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),
-            [value.denominator for value in self.values()])
-        return self * lcm
+        lcd = functools.reduce(lambda a, b: a*b // gcd(a, b),
+                               [value.denominator for value in self.values()])
+        return self * lcd
 
     def subs(self, symbol, expression=None):
         """
@@ -294,21 +305,16 @@ class LinExpr:
         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 = Rational(self._constant)
+        for symbol, coefficient in self._coefficients.items():
+            expression = substitutions.get(symbol, symbol)
+            result += coefficient * expression
         return result
 
     @classmethod
@@ -336,7 +342,7 @@ class LinExpr:
                 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):
@@ -344,13 +350,13 @@ class LinExpr:
         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 = ''
@@ -376,30 +382,6 @@ class LinExpr:
             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()):
@@ -408,42 +390,45 @@ class LinExpr:
             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):
@@ -455,6 +440,13 @@ class Symbol(LinExpr):
     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.
@@ -468,12 +460,17 @@ class Symbol(LinExpr):
             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):
         """
@@ -511,9 +508,6 @@ class Symbol(LinExpr):
     def __repr__(self):
         return self.name
 
-    def _repr_latex_(self):
-        return '$${}$$'.format(self.name)
-
 
 def symbols(names):
     """
@@ -558,15 +552,8 @@ class Dummy(Symbol):
         """
         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
 
@@ -579,9 +566,6 @@ class Dummy(Symbol):
     def __repr__(self):
         return '_{}'.format(self.name)
 
-    def _repr_latex_(self):
-        return '$${}_{{{}}}$$'.format(self.name, self._index)
-
 
 class Rational(LinExpr, Fraction):
     """
@@ -591,6 +575,13 @@ class Rational(LinExpr, Fraction):
     fractions.Fraction classes.
     """
 
+    __slots__ = (
+        '_coefficients',
+        '_constant',
+        '_symbols',
+        '_dimension',
+    ) + Fraction.__slots__
+
     def __new__(cls, numerator=0, denominator=None):
         self = object().__new__(cls)
         self._coefficients = {}
@@ -619,13 +610,3 @@ 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)