Add GPL License

[linpy.git] / pypol / linexprs.py

diff --git a/pypol/linexprs.py b/pypol/linexprs.py
index e73449e..3dd03ef 100644 (file)
--- a/pypol/linexprs.py
+++ b/pypol/linexprs.py
@@ -1,3 +1,20 @@
+"""
+    This file is part of Linpy.
+
+    Linpy is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    Linpy is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with Linpy.  If not, see <http://www.gnu.org/licenses/>.
+"""
+

 import ast
 import functools
 import numbers
 import ast
 import functools
 import numbers


@@ -40,26 +57,26 @@ class Expression:
             return Rational(constant)
         if isinstance(coefficients, Mapping):
             coefficients = coefficients.items()
             return Rational(constant)
         if isinstance(coefficients, Mapping):
             coefficients = coefficients.items()

+        coefficients = list(coefficients)

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

-                raise TypeError('coefficients must be Rational instances')
-        coefficients = [(symbol, Fraction(coefficient))
-            for symbol, coefficient in coefficients if coefficient != 0]
+                raise TypeError('coefficients must be rational numbers')

         if not isinstance(constant, numbers.Rational):
         if not isinstance(constant, numbers.Rational):

-            raise TypeError('constant must be a Rational instance')
-        constant = Fraction(constant)
+            raise TypeError('constant must be a rational number')

         if len(coefficients) == 0:
             return Rational(constant)
         if len(coefficients) == 1 and constant == 0:
             symbol, coefficient = coefficients[0]
             if coefficient == 1:
                 return symbol
         if len(coefficients) == 0:
             return Rational(constant)
         if len(coefficients) == 1 and constant == 0:
             symbol, coefficient = coefficients[0]
             if coefficient == 1:
                 return symbol

+        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 = object().__new__(cls)

-        self._coefficients = OrderedDict(sorted(coefficients,
-            key=lambda item: item[0].sortkey()))
-        self._constant = constant
+        self._coefficients = OrderedDict(coefficients)
+        self._constant = Fraction(constant)

         self._symbols = tuple(self._coefficients)
         self._dimension = len(self._symbols)
         return self
         self._symbols = tuple(self._coefficients)
         self._dimension = len(self._symbols)
         return self


@@ -67,10 +84,7 @@ class Expression:
     def coefficient(self, symbol):
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')
     def coefficient(self, symbol):
         if not isinstance(symbol, Symbol):
             raise TypeError('symbol must be a Symbol instance')

-        try:
-            return Rational(self._coefficients[symbol])
-        except KeyError:
-            return Rational(0)
+        return Rational(self._coefficients.get(symbol, 0))

 
     __getitem__ = coefficient
 
 
     __getitem__ = coefficient
 


@@ -131,49 +145,48 @@ class Expression:
         constant = self._constant - other._constant
         return Expression(coefficients, constant)
 
         constant = self._constant - other._constant
         return Expression(coefficients, constant)
 

+    @_polymorphic

     def __rsub__(self, other):
     def __rsub__(self, other):

-        return -(self - other)
+        return other - self

 
 

-    @_polymorphic

     def __mul__(self, other):
     def __mul__(self, other):

-        if isinstance(other, Rational):
-            return other.__rmul__(self)
+        if isinstance(other, numbers.Rational):
+            coefficients = ((symbol, coefficient * other)
+                for symbol, coefficient in self._coefficients.items())
+            constant = self._constant * other
+            return Expression(coefficients, constant)

         return NotImplemented
 
     __rmul__ = __mul__
 
         return NotImplemented
 
     __rmul__ = __mul__
 

-    @_polymorphic

     def __truediv__(self, other):
     def __truediv__(self, other):

-        if isinstance(other, Rational):
-            return other.__rtruediv__(self)
+        if isinstance(other, numbers.Rational):
+            coefficients = ((symbol, coefficient / other)
+                for symbol, coefficient in self._coefficients.items())
+            constant = self._constant / other
+            return Expression(coefficients, constant)

         return NotImplemented
 
         return NotImplemented
 

-    __rtruediv__ = __truediv__
-

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

-        # "normal" equality
+        # returns a boolean, not a constraint

         # 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
 
         # 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
 

-    @_polymorphic

     def __le__(self, other):
         from .polyhedra import Le
         return Le(self, other)
 
     def __le__(self, other):
         from .polyhedra import Le
         return Le(self, other)
 

-    @_polymorphic

     def __lt__(self, other):
         from .polyhedra import Lt
         return Lt(self, other)
 
     def __lt__(self, other):
         from .polyhedra import Lt
         return Lt(self, other)
 

-    @_polymorphic

     def __ge__(self, other):
         from .polyhedra import Ge
         return Ge(self, other)
 
     def __ge__(self, other):
         from .polyhedra import Ge
         return Ge(self, other)
 

-    @_polymorphic

     def __gt__(self, other):
         from .polyhedra import Gt
         return Gt(self, other)
     def __gt__(self, other):
         from .polyhedra import Gt
         return Gt(self, other)


@@ -240,18 +253,17 @@ class Expression:
         string = ''
         for i, (symbol, coefficient) in enumerate(self.coefficients()):
             if coefficient == 1:
         string = ''
         for i, (symbol, coefficient) in enumerate(self.coefficients()):
             if coefficient == 1:

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

             elif coefficient == -1:
                 string += '-' if i == 0 else ' - '
             elif coefficient == -1:
                 string += '-' if i == 0 else ' - '

-                string += '{!r}'.format(symbol)
+            elif i == 0:
+                string += '{}*'.format(coefficient)
+            elif coefficient > 0:
+                string += ' + {}*'.format(coefficient)

             else:
             else:

-                if i == 0:
-                    string += '{}*{!r}'.format(coefficient, symbol)
-                elif coefficient > 0:
-                    string += ' + {}*{!r}'.format(coefficient, symbol)
-                else:
-                    string += ' - {}*{!r}'.format(-coefficient, symbol)
+                string += ' - {}*'.format(-coefficient)
+            string += '{}'.format(symbol)

         constant = self.constant
         if len(string) == 0:
             string += '{}'.format(constant)
         constant = self.constant
         if len(string) == 0:
             string += '{}'.format(constant)


@@ -261,6 +273,30 @@ class Expression:
             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()):


@@ -301,8 +337,8 @@ class Symbol(Expression):
             raise TypeError('name must be a string')
         self = object().__new__(cls)
         self._name = name.strip()
             raise TypeError('name must be a string')
         self = object().__new__(cls)
         self._name = name.strip()

-        self._coefficients = {self: 1}
-        self._constant = 0
+        self._coefficients = {self: Fraction(1)}
+        self._constant = Fraction(0)

         self._symbols = (self,)
         self._dimension = 1
         return self
         self._symbols = (self,)
         self._dimension = 1
         return self


@@ -321,8 +357,7 @@ class Symbol(Expression):
         return True
 
     def __eq__(self, other):
         return True
 
     def __eq__(self, other):

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

 
     def asdummy(self):
         return Dummy(self.name)
 
     def asdummy(self):
         return Dummy(self.name)


@@ -340,11 +375,16 @@ class Symbol(Expression):
     def __repr__(self):
         return self.name
 
     def __repr__(self):
         return self.name
 

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

     @classmethod
     def fromsympy(cls, expr):
         import sympy
     @classmethod
     def fromsympy(cls, expr):
         import sympy

-        if isinstance(expr, sympy.Symbol):
-            return cls(expr.name)
+        if isinstance(expr, sympy.Dummy):
+            return Dummy(expr.name)
+        elif isinstance(expr, sympy.Symbol):
+            return Symbol(expr.name)

         else:
             raise TypeError('expr must be a sympy.Symbol instance')
 
         else:
             raise TypeError('expr must be a sympy.Symbol instance')
 


@@ -356,11 +396,13 @@ class Dummy(Symbol):
     def __new__(cls, name=None):
         if name is None:
             name = 'Dummy_{}'.format(Dummy._count)
     def __new__(cls, name=None):
         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._index = Dummy._count
         self._name = name.strip()
         self = object().__new__(cls)
         self._index = Dummy._count
         self._name = name.strip()

-        self._coefficients = {self: 1}
-        self._constant = 0
+        self._coefficients = {self: Fraction(1)}
+        self._constant = Fraction(0)

         self._symbols = (self,)
         self._dimension = 1
         Dummy._count += 1
         self._symbols = (self,)
         self._dimension = 1
         Dummy._count += 1


@@ -372,12 +414,12 @@ class Dummy(Symbol):
     def sortkey(self):
         return self._name, self._index
 
     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 __repr__(self):
         return '_{}'.format(self.name)
 

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

 
 def symbols(names):
     if isinstance(names, str):
 
 def symbols(names):
     if isinstance(names, str):


@@ -388,11 +430,13 @@ def symbols(names):
 class Rational(Expression, Fraction):
 
     def __new__(cls, numerator=0, denominator=None):
 class Rational(Expression, Fraction):
 
     def __new__(cls, numerator=0, denominator=None):

-        self = Fraction.__new__(cls, numerator, denominator)
+        self = object().__new__(cls)

         self._coefficients = {}
         self._coefficients = {}

-        self._constant = Fraction(self)
+        self._constant = Fraction(numerator, denominator)

         self._symbols = ()
         self._dimension = 0
         self._symbols = ()
         self._dimension = 0

+        self._numerator = self._constant.numerator
+        self._denominator = self._constant.denominator

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


@@ -408,29 +452,21 @@ class Rational(Expression, Fraction):
     def __bool__(self):
         return Fraction.__bool__(self)
 
     def __bool__(self):
         return Fraction.__bool__(self)
 

-    @_polymorphic
-    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)
-
-    __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):
-        if not isinstance(string, str):
-            raise TypeError('string must be a string instance')
-        return Rational(Fraction(string))
+    def __repr__(self):
+        if self.denominator == 1:
+            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)

 
     @classmethod
     def fromsympy(cls, expr):
 
     @classmethod
     def fromsympy(cls, expr):


@@ -441,3 +477,5 @@ class Rational(Expression, Fraction):
             return Rational(expr)
         else:
             raise TypeError('expr must be a sympy.Rational instance')
             return Rational(expr)
         else:
             raise TypeError('expr must be a sympy.Rational instance')

+            
+# Copyright 2014 MINES ParisTech