Remove Arch Linux installation of isl in the doc

[linpy.git] / linpy / linexprs.py

diff --git a/linpy/linexprs.py b/linpy/linexprs.py
index 38fa7a1..f361218 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


@@ -122,7 +122,7 @@ class LinExpr:
         """
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
         """
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')

-        return Rational(self._coefficients.get(symbol, 0))
+        return self._coefficients.get(symbol, Fraction(0))

 
     __getitem__ = coefficient
 
 
     __getitem__ = coefficient
 


@@ -131,15 +131,14 @@ class LinExpr:
         Iterate over the pairs (symbol, value) of linear terms in the
         expression. The constant term is ignored.
         """
         Iterate over the pairs (symbol, value) of linear terms in the
         expression. The constant term is ignored.
         """

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

 
     @property
     def constant(self):
         """
         The constant term of the expression.
         """
 
     @property
     def constant(self):
         """
         The constant term of the expression.
         """

-        return Rational(self._constant)
+        return self._constant

 
     @property
     def symbols(self):
 
     @property
     def symbols(self):


@@ -179,9 +178,8 @@ 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 Rational(coefficient)
-        yield Rational(self._constant)
+        yield from self._coefficients.values()
+        yield self._constant

 
     def __bool__(self):
         return True
 
     def __bool__(self):
         return True


@@ -247,36 +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):
         """


@@ -295,21 +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


@@ -337,7 +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):


@@ -345,13 +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 = ''


@@ -377,30 +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()):


@@ -409,42 +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):


@@ -456,6 +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.


@@ -469,12 +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):
         """


@@ -499,7 +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):
         """


@@ -510,9 +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):
     """


@@ -557,15 +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
 


@@ -578,9 +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):
     """


@@ -590,6 +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 = {}


@@ -618,13 +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)