X-Git-Url: https://scm.cri.mines-paristech.fr/git/linpy.git/blobdiff_plain/7fda4e3865bb7cc9b6ee15cfd3c62c207f585ec7..23922aa39e585f1e6b11f3479da002c92bebf2a1:/linpy/linexprs.py

diff --git a/linpy/linexprs.py b/linpy/linexprs.py
index b5864e1..f361218 100644
--- a/linpy/linexprs.py
+++ b/linpy/linexprs.py
@@ -62,7 +62,7 @@ class LinExpr:
         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')
@@ -76,7 +76,7 @@ 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
@@ -245,28 +245,34 @@ 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):
         """
@@ -300,7 +306,7 @@ class LinExpr:
         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
@@ -331,7 +337,7 @@ 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):
@@ -339,13 +345,13 @@ 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 = ''
@@ -371,30 +377,6 @@ 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()):
@@ -403,42 +385,43 @@ 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('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 expr
+        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):
@@ -450,6 +433,13 @@ 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.
@@ -463,12 +453,17 @@ 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):
         """
@@ -506,9 +501,6 @@ class Symbol(LinExpr):
     def __repr__(self):
         return self.name
 
-    def _repr_latex_(self):
-        return '$${}$$'.format(self.name)
-
 
 def symbols(names):
     """
@@ -553,15 +545,8 @@ 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
 
@@ -574,9 +559,6 @@ class Dummy(Symbol):
     def __repr__(self):
         return '_{}'.format(self.name)
 
-    def _repr_latex_(self):
-        return '$${}_{{{}}}$$'.format(self.name, self._index)
-
 
 class Rational(LinExpr, Fraction):
     """
@@ -586,6 +568,13 @@ 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 = {}
@@ -614,13 +603,3 @@ 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)