Improve error messages in linexprs.py

[linpy.git] / pypol / linexprs.py

diff --git a/pypol/linexprs.py b/pypol/linexprs.py
index 73c6b0e..229e8d9 100644 (file)
--- a/pypol/linexprs.py
+++ b/pypol/linexprs.py
@@ -3,13 +3,13 @@ import functools
 import numbers
 import re
 
 import numbers
 import re
 

-from collections import OrderedDict, defaultdict
+from collections import OrderedDict, defaultdict, Mapping

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

-    'Symbol', 'symbols',
+    'Symbol', 'Dummy', 'symbols',

     'Rational',
 ]
 
     'Rational',
 ]
 


@@ -31,27 +31,25 @@ 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')
             return Expression.fromstring(coefficients)
         if coefficients is None:
             return Rational(constant)
                 raise TypeError('too many arguments')
             return Expression.fromstring(coefficients)
         if coefficients is None:
             return Rational(constant)

-        if isinstance(coefficients, dict):
+        if isinstance(coefficients, Mapping):

             coefficients = coefficients.items()
         for symbol, coefficient in coefficients:
             if not isinstance(symbol, Symbol):
                 raise TypeError('symbols must be Symbol instances')
             coefficients = coefficients.items()
         for symbol, coefficient in coefficients:
             if not isinstance(symbol, Symbol):
                 raise TypeError('symbols must be Symbol instances')

-        coefficients = [(symbol, coefficient)
+            if not isinstance(coefficient, numbers.Rational):
+                raise TypeError('coefficients must be rational numbers')
+        coefficients = [(symbol, Fraction(coefficient))

             for symbol, coefficient in coefficients if coefficient != 0]
             for symbol, coefficient in coefficients if coefficient != 0]

+        if not isinstance(constant, numbers.Rational):
+            raise TypeError('constant must be a rational number')
+        constant = Fraction(constant)

         if len(coefficients) == 0:
             return Rational(constant)
         if len(coefficients) == 1 and constant == 0:
         if len(coefficients) == 0:
             return Rational(constant)
         if len(coefficients) == 1 and constant == 0:


@@ -59,20 +57,8 @@ class Expression:
             if coefficient == 1:
                 return symbol
         self = object().__new__(cls)
             if coefficient == 1:
                 return symbol
         self = object().__new__(cls)

-        self._coefficients = OrderedDict()
-        for symbol, coefficient in sorted(coefficients,
-                key=lambda item: item[0].sortkey()):
-            if isinstance(coefficient, Rational):
-                coefficient = coefficient.constant
-            if not isinstance(coefficient, numbers.Rational):
-                raise TypeError('coefficients must be rational numbers '
-                    'or Rational instances')
-            self._coefficients[symbol] = coefficient
-        if isinstance(constant, Rational):
-            constant = constant.constant
-        if not isinstance(constant, numbers.Rational):
-            raise TypeError('constant must be a rational number '
-                'or a Rational instance')
+        self._coefficients = OrderedDict(sorted(coefficients,
+            key=lambda item: item[0].sortkey()))

         self._constant = constant
         self._symbols = tuple(self._coefficients)
         self._dimension = len(self._symbols)
         self._constant = constant
         self._symbols = tuple(self._coefficients)
         self._dimension = len(self._symbols)


@@ -82,18 +68,19 @@ class Expression:
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
         try:
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
         try:

-            return self._coefficients[symbol]
+            return Rational(self._coefficients[symbol])

         except KeyError:
         except KeyError:

-            return 0
+            return Rational(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):


@@ -113,8 +100,9 @@ class Expression:
         return False
 
     def values(self):
         return False
 
     def values(self):

-        yield from self._coefficients.values()
-        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


@@ -127,20 +115,20 @@ class Expression:
 
     @_polymorphic
     def __add__(self, other):
 
     @_polymorphic
     def __add__(self, other):

-        coefficients = defaultdict(Rational, self.coefficients())
-        for symbol, coefficient in other.coefficients():
+        coefficients = defaultdict(Fraction, self._coefficients)
+        for symbol, coefficient in other._coefficients.items():

             coefficients[symbol] += coefficient
             coefficients[symbol] += coefficient

-        constant = self.constant + other.constant
+        constant = self._constant + other._constant

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

-        coefficients = defaultdict(Rational, self.coefficients())
-        for symbol, coefficient in other.coefficients():
+        coefficients = defaultdict(Fraction, self._coefficients)
+        for symbol, coefficient in other._coefficients.items():

             coefficients[symbol] -= coefficient
             coefficients[symbol] -= coefficient

-        constant = self.constant - other.constant
+        constant = self._constant - other._constant

         return Expression(coefficients, constant)
 
     def __rsub__(self, other):
         return Expression(coefficients, constant)
 
     def __rsub__(self, other):


@@ -148,40 +136,19 @@ class Expression:
 
     @_polymorphic
     def __mul__(self, other):
 
     @_polymorphic
     def __mul__(self, other):

-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] *= other.constant
-            constant = self.constant * other.constant
-            return Expression(coefficients, constant)
-        if isinstance(other, Expression) and not self.isconstant():
-            raise ValueError('non-linear expression: '
-                    '{} * {}'.format(self._parenstr(), other._parenstr()))
+        if isinstance(other, Rational):
+            return other.__rmul__(self)

         return NotImplemented
 
     __rmul__ = __mul__
 
     @_polymorphic
     def __truediv__(self, other):
         return NotImplemented
 
     __rmul__ = __mul__
 
     @_polymorphic
     def __truediv__(self, other):

-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] = Rational(coefficients[symbol], other.constant)
-            constant = Rational(self.constant, other.constant)
-            return Expression(coefficients, constant)
-        if isinstance(other, Expression):
-            raise ValueError('non-linear expression: '
-                '{} / {}'.format(self._parenstr(), other._parenstr()))
+        if isinstance(other, Rational):
+            return other.__rtruediv__(self)

         return NotImplemented
 
         return NotImplemented
 

-    def __rtruediv__(self, other):
-        if isinstance(other, self):
-            if self.isconstant():
-                return Rational(other, self.constant)
-            else:
-                raise ValueError('non-linear expression: '
-                        '{} / {}'.format(other._parenstr(), self._parenstr()))
-        return NotImplemented
+    __rtruediv__ = __truediv__

 
     @_polymorphic
     def __eq__(self, other):
 
     @_polymorphic
     def __eq__(self, other):


@@ -189,7 +156,7 @@ class Expression:
         # see http://docs.sympy.org/dev/tutorial/gotchas.html#equals-signs
         return isinstance(other, Expression) and \
             self._coefficients == other._coefficients 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._constant == other._constant

 
     @_polymorphic
     def __le__(self, other):
 
     @_polymorphic
     def __le__(self, other):


@@ -218,18 +185,20 @@ class Expression:
 
     def subs(self, symbol, expression=None):
         if expression is None:
 
     def subs(self, symbol, expression=None):
         if expression is None:

-            if isinstance(symbol, dict):
+            if isinstance(symbol, Mapping):

                 symbol = symbol.items()
             substitutions = symbol
         else:
             substitutions = [(symbol, expression)]
         result = self
         for symbol, expression in substitutions:
                 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)
             coefficients = [(othersymbol, coefficient)

-                for othersymbol, coefficient in result.coefficients()
+                for othersymbol, coefficient in result._coefficients.items()

                 if othersymbol != symbol]
                 if othersymbol != symbol]

-            coefficient = result.coefficient(symbol)
-            constant = result.constant
+            coefficient = result._coefficients.get(symbol, 0)
+            constant = result._constant

             result = Expression(coefficients, constant) + coefficient*expression
         return result
 
             result = Expression(coefficients, constant) + coefficient*expression
         return result
 


@@ -269,39 +238,27 @@ class Expression:
 
     def __repr__(self):
         string = ''
 
     def __repr__(self):
         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.name
-                else:
-                    string += ' + {}'.format(symbol)
+                string += '' if i == 0 else ' + '
+                string += '{!r}'.format(symbol)

             elif coefficient == -1:
             elif coefficient == -1:

-                if i == 0:
-                    string += '-{}'.format(symbol)
-                else:
-                    string += ' - {}'.format(symbol)
+                string += '-' if i == 0 else ' - '
+                string += '{!r}'.format(symbol)

             else:
                 if i == 0:
             else:
                 if i == 0:

-                    string += '{}*{}'.format(coefficient, symbol)
+                    string += '{}*{!r}'.format(coefficient, symbol)

                 elif coefficient > 0:
                 elif coefficient > 0:

-                    string += ' + {}*{}'.format(coefficient, symbol)
+                    string += ' + {}*{!r}'.format(coefficient, symbol)

                 else:
                 else:

-                    assert coefficient < 0
-                    coefficient *= -1
-                    string += ' - {}*{}'.format(coefficient, symbol)
-            i += 1
+                    string += ' - {}*{!r}'.format(-coefficient, 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
 
     def _parenstr(self, always=False):
         return string
 
     def _parenstr(self, always=False):


@@ -339,15 +296,15 @@ class Expression:
 
 class Symbol(Expression):
 
 
 class Symbol(Expression):
 

-    __slots__ = (
-        '_name',
-    )
-

     def __new__(cls, name):
         if not isinstance(name, str):
             raise TypeError('name must be a string')
         self = object().__new__(cls)
         self._name = name.strip()
     def __new__(cls, name):
         if not isinstance(name, str):
             raise TypeError('name must be a string')
         self = object().__new__(cls)
         self._name = name.strip()

+        self._coefficients = {self: 1}
+        self._constant = 0
+        self._symbols = (self,)
+        self._dimension = 1

         return self
 
     @property
         return self
 
     @property


@@ -355,30 +312,7 @@ class Symbol(Expression):
         return self._name
 
     def __hash__(self):
         return self._name
 
     def __hash__(self):

-        return hash(self._name)
-
-    def coefficient(self, symbol):
-        if not isinstance(symbol, Symbol):
-            raise TypeError('symbol must be a Symbol instance')
-        if symbol == self:
-            return 1
-        else:
-            return 0
-
-    def coefficients(self):
-        yield self, 1
-
-    @property
-    def constant(self):
-        return 0
-
-    @property
-    def symbols(self):
-        return self,
-
-    @property
-    def dimension(self):
-        return 1
+        return hash(self.sortkey())

 
     def sortkey(self):
         return self.name,
 
     def sortkey(self):
         return self.name,


@@ -386,11 +320,12 @@ class Symbol(Expression):
     def issymbol(self):
         return True
 
     def issymbol(self):
         return True
 

-    def values(self):
-        yield 1
-

     def __eq__(self, other):
     def __eq__(self, other):

-        return isinstance(other, Symbol) and self.name == other.name
+        return not isinstance(other, Dummy) and isinstance(other, Symbol) \
+            and self.name == other.name
+
+    def asdummy(self):
+        return Dummy(self.name)

 
     @classmethod
     def _fromast(cls, node):
 
     @classmethod
     def _fromast(cls, node):


@@ -402,66 +337,94 @@ class Symbol(Expression):
             return Symbol(node.id)
         raise SyntaxError('invalid syntax')
 
             return Symbol(node.id)
         raise SyntaxError('invalid syntax')
 

+    def __repr__(self):
+        return self.name
+

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

-            return Symbol(expr.name)
+            return cls(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)
+        self = object().__new__(cls)
+        self._index = Dummy._count
+        self._name = name.strip()
+        self._coefficients = {self: 1}
+        self._constant = 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 __eq__(self, other):
+        return isinstance(other, Dummy) and self._index == other._index
+
+    def __repr__(self):
+        return '_{}'.format(self.name)
+
+

 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()
     return tuple(Symbol(name) for name in names)
 
 
 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()
     return tuple(Symbol(name) for name in names)
 
 

-class Rational(Expression):
-
-    __slots__ = (
-        '_constant',
-    )
+class Rational(Expression, Fraction):

 
     def __new__(cls, numerator=0, denominator=None):
 
     def __new__(cls, numerator=0, denominator=None):

-        self = object().__new__(cls)
-        if denominator is None and isinstance(numerator, Rational):
-            self._constant = numerator.constant
-        else:
-            self._constant = Fraction(numerator, denominator)
+        self = Fraction.__new__(cls, numerator, denominator)
+        self._coefficients = {}
+        self._constant = Fraction(self)
+        self._symbols = ()
+        self._dimension = 0

         return self
 
     def __hash__(self):
         return self
 
     def __hash__(self):

-        return hash(self.constant)
-
-    def coefficient(self, symbol):
-        if not isinstance(symbol, Symbol):
-            raise TypeError('symbol must be a Symbol instance')
-        return 0
-
-    def coefficients(self):
-        yield from ()
-
-    @property
-    def symbols(self):
-        return ()
+        return Fraction.__hash__(self)

 
     @property
 
     @property

-    def dimension(self):
-        return 0
+    def constant(self):
+        return self

 
     def isconstant(self):
         return True
 
 
     def isconstant(self):
         return True
 

-    def values(self):
-        yield self._constant
+    def __bool__(self):
+        return Fraction.__bool__(self)

 
     @_polymorphic
 
     @_polymorphic

-    def __eq__(self, other):
-        return isinstance(other, Rational) and self.constant == other.constant
+    def __mul__(self, other):
+        coefficients = dict(other._coefficients)
+        for symbol in coefficients:
+            coefficients[symbol] *= self._constant
+        constant = other._constant * self._constant
+        return Expression(coefficients, constant)

 
 

-    def __bool__(self):
-        return self.constant != 0
+    __rmul__ = __mul__
+
+    @_polymorphic
+    def __rtruediv__(self, other):
+        coefficients = dict(other._coefficients)
+        for symbol in coefficients:
+            coefficients[symbol] /= self._constant
+        constant = other._constant / self._constant
+        return Expression(coefficients, constant)

 
     @classmethod
     def fromstring(cls, string):
 
     @classmethod
     def fromstring(cls, string):