Make Expression.subs() always return a LinExpr instance

[linpy.git] / linpy / linexprs.py

diff --git a/linpy/linexprs.py b/linpy/linexprs.py
index ab5d344c8006d9394500ec74d741d2692db5e34d..f3612185455a4afac95278af032cdaf481cc0d06 100644 (file)
--- 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.
 
         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')
         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:
 
 
         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
 
         A linear expression with a single symbol of coefficient 1 and no
         constant term is automatically subclassed as a Symbol instance. A linear


@@ -178,8 +178,7 @@ class LinExpr:
         Iterate over the coefficient values in the expression, and the constant
         term.
         """
         Iterate over the coefficient values in the expression, and the constant
         term.
         """

-        for coefficient in self._coefficients.values():
-            yield coefficient
+        yield from self._coefficients.values()

         yield self._constant
 
     def __bool__(self):
         yield self._constant
 
     def __bool__(self):


@@ -246,36 +245,43 @@ class LinExpr:
     @_polymorphic
     def __eq__(self, other):
         """
     @_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.

         """
         """

-        return isinstance(other, LinExpr) and \
-            self._coefficients == other._coefficients and \
+        return self._coefficients == other._coefficients and \

             self._constant == other._constant
 
             self._constant == other._constant
 

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

     def __lt__(self, other):
     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):
     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):
     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.
         """
 
     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),
+        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 * lcm
+        return self * lcd

 
     def subs(self, symbol, expression=None):
         """
 
     def subs(self, symbol, expression=None):
         """


@@ -294,21 +300,16 @@ class LinExpr:
         2*x + y + 1
         """
         if expression is None:
         2*x + y + 1
         """
         if expression is None:

-            if isinstance(symbol, Mapping):
-                symbol = symbol.items()
-            substitutions = symbol
+            substitutions = dict(symbol)

         else:
         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')
             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
         return result
 
     @classmethod


@@ -336,7 +337,7 @@ class LinExpr:
                 return left / right
         raise SyntaxError('invalid syntax')
 
                 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):
 
     @classmethod
     def fromstring(cls, string):


@@ -344,13 +345,13 @@ class LinExpr:
         Create an expression from a string. Raise SyntaxError if the string is
         not properly formatted.
         """
         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')
         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')
             raise SyntaxError('invalid syntax')

-        return expr
+        return expression

 
     def __repr__(self):
         string = ''
 
     def __repr__(self):
         string = ''


@@ -376,30 +377,6 @@ class LinExpr:
             string += ' - {}'.format(-constant)
         return string
 
             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()):
     def _parenstr(self, always=False):
         string = str(self)
         if not always and (self.isconstant() or self.issymbol()):


@@ -408,42 +385,43 @@ class LinExpr:
             return '({})'.format(string)
 
     @classmethod
             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
         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):
             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('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__))
             raise TypeError('cannot convert to a {} instance'.format(cls.__name__))

-        return expr
+        return expression

 
     def tosympy(self):
         """
 
     def tosympy(self):
         """

-        Convert the linear expression to a sympy expression.
+        Convert the linear expression to a SymPy expression.

         """
         import sympy
         """
         import sympy

-        expr = 0
+        expression = 0

         for symbol, coefficient in self.coefficients():
             term = coefficient * sympy.Symbol(symbol.name)
         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):
 
 
 class Symbol(LinExpr):


@@ -455,6 +433,13 @@ class Symbol(LinExpr):
     Two instances of Symbol are equal if they have the same name.
     """
 
     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.
     def __new__(cls, name):
         """
         Return a symbol with the name string given in argument.


@@ -468,12 +453,17 @@ class Symbol(LinExpr):
             raise SyntaxError('invalid syntax')
         self = object().__new__(cls)
         self._name = name
             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
 
         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):
         """
     @property
     def name(self):
         """


@@ -498,7 +488,9 @@ class Symbol(LinExpr):
         return True
 
     def __eq__(self, other):
         return True
 
     def __eq__(self, other):

-        return self.sortkey() == other.sortkey()
+        if isinstance(other, Symbol):
+            return self.sortkey() == other.sortkey()
+        return NotImplemented

 
     def asdummy(self):
         """
 
     def asdummy(self):
         """


@@ -509,9 +501,6 @@ class Symbol(LinExpr):
     def __repr__(self):
         return self.name
 
     def __repr__(self):
         return self.name
 

-    def _repr_latex_(self):
-        return '$${}$$'.format(self.name)
-

 
 def symbols(names):
     """
 
 def symbols(names):
     """


@@ -556,15 +545,8 @@ class Dummy(Symbol):
         """
         if name is None:
             name = 'Dummy_{}'.format(Dummy._count)
         """
         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._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
 


@@ -577,9 +559,6 @@ class Dummy(Symbol):
     def __repr__(self):
         return '_{}'.format(self.name)
 
     def __repr__(self):
         return '_{}'.format(self.name)
 

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

 
 class Rational(LinExpr, Fraction):
     """
 
 class Rational(LinExpr, Fraction):
     """


@@ -589,6 +568,13 @@ class Rational(LinExpr, Fraction):
     fractions.Fraction classes.
     """
 
     fractions.Fraction classes.
     """
 

+    __slots__ = (
+        '_coefficients',
+        '_constant',
+        '_symbols',
+        '_dimension',
+    ) + Fraction.__slots__
+

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


@@ -617,13 +603,3 @@ class Rational(LinExpr, Fraction):
             return '{!r}'.format(self.numerator)
         else:
             return '{!r}/{!r}'.format(self.numerator, self.denominator)
             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)