messy and needs reformatting but returning correct values for now

[linpy.git] / pypol / linear.py

diff --git a/pypol/linear.py b/pypol/linear.py
index fabf2a2..b40415f 100644 (file)
--- a/pypol/linear.py
+++ b/pypol/linear.py
@@ -1,16 +1,19 @@
-
+import ast

 import functools
 import numbers
 import functools
 import numbers

+import re

 
 from fractions import Fraction, gcd
 
 
 from fractions import Fraction, gcd
 

+from . import isl
+from .isl import libisl
+

 
 __all__ = [
 
 __all__ = [

-    'Expression',
-    'constant', 'symbol', 'symbols',
+    'Expression', 'Constant', 'Symbol', 'symbols',

     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',

-    'empty', 'universe'
+    'Empty', 'Universe'

 ]
 
 
 ]
 
 


@@ -20,65 +23,122 @@ def _polymorphic_method(func):
         if isinstance(b, Expression):
             return func(a, b)
         if isinstance(b, numbers.Rational):
         if isinstance(b, Expression):
             return func(a, b)
         if isinstance(b, numbers.Rational):

-            b = constant(b)
+            b = Constant(b)

             return func(a, b)
         return NotImplemented
     return wrapper
 
 def _polymorphic_operator(func):
             return func(a, b)
         return NotImplemented
     return wrapper
 
 def _polymorphic_operator(func):

+    # A polymorphic operator should call a polymorphic method, hence we just
+    # have to test the left operand.

     @functools.wraps(func)
     def wrapper(a, b):
         if isinstance(a, numbers.Rational):
     @functools.wraps(func)
     def wrapper(a, b):
         if isinstance(a, numbers.Rational):

-            a = constant(a)
-        if isinstance(b, numbers.Rational):
-            b = constant(b)
-        if isinstance(a, Expression) and isinstance(b, Expression):
+            a = Constant(a)
+            return func(a, b)
+        elif isinstance(a, Expression):

             return func(a, b)
         raise TypeError('arguments must be linear expressions')
     return wrapper
 
 
             return func(a, b)
         raise TypeError('arguments must be linear expressions')
     return wrapper
 
 

+_main_ctx = isl.Context()
+
+

 class Expression:
     """
     This class implements linear expressions.
     """
 
 class Expression:
     """
     This class implements linear expressions.
     """
 

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

     def __new__(cls, coefficients=None, constant=0):
         if isinstance(coefficients, str):
             if constant:
                 raise TypeError('too many arguments')
             return cls.fromstring(coefficients)
     def __new__(cls, coefficients=None, constant=0):
         if isinstance(coefficients, str):
             if constant:
                 raise TypeError('too many arguments')
             return cls.fromstring(coefficients)

-        self = super().__new__(cls)
-        self._coefficients = {}

         if isinstance(coefficients, dict):
             coefficients = coefficients.items()
         if isinstance(coefficients, dict):
             coefficients = coefficients.items()

-        if coefficients is not None:
-            for symbol, coefficient in coefficients:
-                if isinstance(symbol, Expression) and symbol.issymbol():
-                    symbol = str(symbol)
-                elif not isinstance(symbol, str):
-                    raise TypeError('symbols must be strings')
-                if not isinstance(coefficient, numbers.Rational):
-                    raise TypeError('coefficients must be rational numbers')
-                if coefficient != 0:
-                    self._coefficients[symbol] = coefficient
+        if coefficients is None:
+            return Constant(constant)
+        coefficients = [(symbol, coefficient)
+                for symbol, coefficient in coefficients if coefficient != 0]
+        if len(coefficients) == 0:
+            return Constant(constant)
+        elif len(coefficients) == 1 and constant == 0:
+            symbol, coefficient = coefficients[0]
+            if coefficient == 1:
+                return Symbol(symbol)
+        self = object().__new__(cls)
+        self._coefficients = {}
+        for symbol, coefficient in coefficients:
+            if isinstance(symbol, Symbol):
+                symbol = symbol.name
+            elif not isinstance(symbol, str):
+                raise TypeError('symbols must be strings or Symbol instances')
+            if isinstance(coefficient, Constant):
+                coefficient = coefficient.constant
+            if not isinstance(coefficient, numbers.Rational):
+                raise TypeError('coefficients must be rational numbers or Constant instances')
+            self._coefficients[symbol] = coefficient
+        if isinstance(constant, Constant):
+            constant = constant.constant

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

-            raise TypeError('constant must be a rational number')
+            raise TypeError('constant must be a rational number or a Constant instance')

         self._constant = constant
         self._constant = constant

+        self._symbols = tuple(sorted(self._coefficients))
+        self._dimension = len(self._symbols)

         return self
 
         return self
 

+    @classmethod
+    def _fromast(cls, node):
+        if isinstance(node, ast.Module) and len(node.body) == 1:
+            return cls._fromast(node.body[0])
+        elif isinstance(node, ast.Expr):
+            return cls._fromast(node.value)
+        elif isinstance(node, ast.Name):
+            return Symbol(node.id)
+        elif isinstance(node, ast.Num):
+            return Constant(node.n)
+        elif isinstance(node, ast.UnaryOp) and isinstance(node.op, ast.USub):
+            return -cls._fromast(node.operand)
+        elif isinstance(node, ast.BinOp):
+            left = cls._fromast(node.left)
+            right = cls._fromast(node.right)
+            if isinstance(node.op, ast.Add):
+                return left + right
+            elif isinstance(node.op, ast.Sub):
+                return left - right
+            elif isinstance(node.op, ast.Mult):
+                return left * right
+            elif isinstance(node.op, ast.Div):
+                return left / right
+        raise SyntaxError('invalid syntax')
+
+    @classmethod
+    def fromstring(cls, string):
+        string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+        tree = ast.parse(string, 'eval')
+        return cls._fromast(tree)
+
+    @property

     def symbols(self):
     def symbols(self):

-        yield from sorted(self._coefficients)
+        return self._symbols

 
     @property
     def dimension(self):
 
     @property
     def dimension(self):

-        return len(list(self.symbols()))
+        return self._dimension

 
     def coefficient(self, symbol):
 
     def coefficient(self, symbol):

-        if isinstance(symbol, Expression) and symbol.issymbol():
+        if isinstance(symbol, Symbol):

             symbol = str(symbol)
         elif not isinstance(symbol, str):
             symbol = str(symbol)
         elif not isinstance(symbol, str):

-            raise TypeError('symbol must be a string')
+            raise TypeError('symbol must be a string or a Symbol instance')

         try:
             return self._coefficients[symbol]
         except KeyError:
         try:
             return self._coefficients[symbol]
         except KeyError:


@@ -87,7 +147,7 @@ class Expression:
     __getitem__ = coefficient
 
     def coefficients(self):
     __getitem__ = coefficient
 
     def coefficients(self):

-        for symbol in self.symbols():
+        for symbol in self.symbols:

             yield symbol, self.coefficient(symbol)
 
     @property
             yield symbol, self.coefficient(symbol)
 
     @property


@@ -95,24 +155,18 @@ class Expression:
         return self._constant
 
     def isconstant(self):
         return self._constant
 
     def isconstant(self):

-        return len(self._coefficients) == 0
+        return False

 
     def values(self):
 
     def values(self):

-        for symbol in self.symbols():
+        for symbol in self.symbols:

             yield self.coefficient(symbol)
         yield self.constant
 
             yield self.coefficient(symbol)
         yield self.constant
 

-    def symbol(self):
-        if not self.issymbol():
-            raise ValueError('not a symbol: {}'.format(self))
-        for symbol in self.symbols():
-            return symbol
-

     def issymbol(self):
     def issymbol(self):

-        return len(self._coefficients) == 1 and self._constant == 0
+        return False

 
     def __bool__(self):
 
     def __bool__(self):

-        return (not self.isconstant()) or bool(self.constant)
+        return True

 
     def __pos__(self):
         return self
 
     def __pos__(self):
         return self


@@ -144,7 +198,8 @@ class Expression:
         constant = self.constant - other.constant
         return Expression(coefficients, constant)
 
         constant = self.constant - other.constant
         return Expression(coefficients, constant)
 

-    __rsub__ = __sub__
+    def __rsub__(self, other):
+        return -(self - other)

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


@@ -176,7 +231,7 @@ class Expression:
         return NotImplemented
 
     def __rtruediv__(self, other):
         return NotImplemented
 
     def __rtruediv__(self, other):

-        if isinstance(other, Rational):
+        if isinstance(other, self):

             if self.isconstant():
                 constant = Fraction(other, self.constant)
                 return Expression(constant=constant)
             if self.isconstant():
                 constant = Fraction(other, self.constant)
                 return Expression(constant=constant)


@@ -187,10 +242,9 @@ class Expression:
 
     def __str__(self):
         string = ''
 
     def __str__(self):
         string = ''

-        symbols = sorted(self.symbols())

         i = 0
         i = 0

-        for symbol in symbols:
-            coefficient = self[symbol]
+        for symbol in self.symbols:
+            coefficient = self.coefficient(symbol)

             if coefficient == 1:
                 if i == 0:
                     string += symbol
             if coefficient == 1:
                 if i == 0:
                     string += symbol


@@ -231,17 +285,7 @@ class Expression:
             return '({})'.format(string)
 
     def __repr__(self):
             return '({})'.format(string)
 
     def __repr__(self):

-        string = '{}({{'.format(self.__class__.__name__)
-        for i, (symbol, coefficient) in enumerate(self.coefficients()):
-            if i != 0:
-                string += ', '
-            string += '{!r}: {!r}'.format(symbol, coefficient)
-        string += '}}, {!r})'.format(self.constant)
-        return string
-
-    @classmethod
-    def fromstring(cls, string):
-        raise NotImplementedError
+        return '{}({!r})'.format(self.__class__.__name__, str(self))

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


@@ -252,70 +296,164 @@ class Expression:
                 self.constant == other.constant
 
     def __hash__(self):
                 self.constant == other.constant
 
     def __hash__(self):

-        return hash((self._coefficients, self._constant))
+        return hash((tuple(sorted(self._coefficients.items())), self._constant))

 
 

-    def _canonify(self):
+    def _toint(self):

         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
                 [value.denominator for value in self.values()])
         return self * lcm
 
     @_polymorphic_method
     def _eq(self, other):
         lcm = functools.reduce(lambda a, b: a*b // gcd(a, b),
                 [value.denominator for value in self.values()])
         return self * lcm
 
     @_polymorphic_method
     def _eq(self, other):

-        return Polyhedron(equalities=[(self - other)._canonify()])
+        return Polyhedron(equalities=[(self - other)._toint()])

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

-        return Polyhedron(inequalities=[(self - other)._canonify()])
+        return Polyhedron(inequalities=[(other - self)._toint()])

 
     @_polymorphic_method
     def __lt__(self, other):
 
     @_polymorphic_method
     def __lt__(self, other):

-        return Polyhedron(inequalities=[(self - other)._canonify() + 1])
+        return Polyhedron(inequalities=[(other - self)._toint() - 1])

 
     @_polymorphic_method
     def __ge__(self, other):
 
     @_polymorphic_method
     def __ge__(self, other):

-        return Polyhedron(inequalities=[(other - self)._canonify()])
+        return Polyhedron(inequalities=[(self - other)._toint()])

 
     @_polymorphic_method
     def __gt__(self, other):
 
     @_polymorphic_method
     def __gt__(self, other):

-        return Polyhedron(inequalities=[(other - self)._canonify() + 1])
+        return Polyhedron(inequalities=[(self - other)._toint() - 1])
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        coefficients = {}
+        constant = 0
+        for symbol, coefficient in expr.as_coefficients_dict().items():
+            coefficient = Fraction(coefficient.p, coefficient.q)
+            if symbol == sympy.S.One:
+                constant = coefficient
+            elif isinstance(symbol, sympy.Symbol):
+                symbol = symbol.name
+                coefficients[symbol] = coefficient
+            else:
+                raise ValueError('non-linear expression: {!r}'.format(expr))
+        return cls(coefficients, constant)
+
+    def tosympy(self):
+        import sympy
+        expr = 0
+        for symbol, coefficient in self.coefficients():
+            term = coefficient * sympy.Symbol(symbol)
+            expr += term
+        expr += self.constant
+        return expr
+
+
+class Constant(Expression):
+
+    def __new__(cls, numerator=0, denominator=None):
+        self = object().__new__(cls)
+        if denominator is None:
+            if isinstance(numerator, numbers.Rational):
+                self._constant = numerator
+            elif isinstance(numerator, Constant):
+                self._constant = numerator.constant
+            else:
+                raise TypeError('constant must be a rational number or a Constant instance')
+        else:
+            self._constant = Fraction(numerator, denominator)
+        self._coefficients = {}
+        self._symbols = ()
+        self._dimension = 0
+        return self
+
+    def isconstant(self):
+        return True
+
+    def __bool__(self):
+        return bool(self.constant)
+
+    def __repr__(self):
+        if self.constant.denominator == 1:
+            return '{}({!r})'.format(self.__class__.__name__, self.constant)
+        else:
+            return '{}({!r}, {!r})'.format(self.__class__.__name__,
+                self.constant.numerator, self.constant.denominator)
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        if isinstance(expr, sympy.Rational):
+            return cls(expr.p, expr.q)
+        elif isinstance(expr, numbers.Rational):
+            return cls(expr)
+        else:
+            raise TypeError('expr must be a sympy.Rational instance')
+
+
+class Symbol(Expression):
+
+    __slots__ = Expression.__slots__ + (
+        '_name',
+    )
+
+    def __new__(cls, name):
+        if isinstance(name, Symbol):
+            name = name.name
+        elif not isinstance(name, str):
+            raise TypeError('name must be a string or a Symbol instance')
+        self = object().__new__(cls)
+        self._coefficients = {name: 1}
+        self._constant = 0
+        self._symbols = tuple(name)
+        self._name = name
+        self._dimension = 1
+        return self

 
 

+    @property
+    def name(self):
+        return self._name

 
 

-def constant(numerator=0, denominator=None):
-    if denominator is None and isinstance(numerator, numbers.Rational):
-        return Expression(constant=numerator)
-    else:
-        return Expression(constant=Fraction(numerator, denominator))
+    def issymbol(self):
+        return True
+
+    def __repr__(self):
+        return '{}({!r})'.format(self.__class__.__name__, self._name)
+
+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        if isinstance(expr, sympy.Symbol):
+            return cls(expr.name)
+        else:
+            raise TypeError('expr must be a sympy.Symbol instance')

 
 

-def symbol(name):
-    if not isinstance(name, str):
-        raise TypeError('name must be a string')
-    return Expression(coefficients={name: 1})

 
 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()
 
 def symbols(names):
     if isinstance(names, str):
         names = names.replace(',', ' ').split()

-    return (symbol(name) for name in names)
+    return (Symbol(name) for name in names)

 
 
 @_polymorphic_operator
 def eq(a, b):
 
 
 @_polymorphic_operator
 def eq(a, b):

-    return a._eq(b)
+    return a.__eq__(b)

 
 @_polymorphic_operator
 def le(a, b):
 
 @_polymorphic_operator
 def le(a, b):

-    return a <= b
+    return a.__le__(b)

 
 @_polymorphic_operator
 def lt(a, b):
 
 @_polymorphic_operator
 def lt(a, b):

-    return a < b
+    return a.__lt__(b)

 
 @_polymorphic_operator
 def ge(a, b):
 
 @_polymorphic_operator
 def ge(a, b):

-    return a >= b
+    return a.__ge__(b)

 
 @_polymorphic_operator
 def gt(a, b):
 
 @_polymorphic_operator
 def gt(a, b):

-    return a > b
+    return a.__gt__(b)

 
 
 class Polyhedron:
 
 
 class Polyhedron:


@@ -323,6 +461,13 @@ class Polyhedron:
     This class implements polyhedrons.
     """
 
     This class implements polyhedrons.
     """
 

+    __slots__ = (
+        '_equalities',
+        '_inequalities',
+        '_constraints',
+        '_symbols',
+    )
+

     def __new__(cls, equalities=None, inequalities=None):
         if isinstance(equalities, str):
             if inequalities is not None:
     def __new__(cls, equalities=None, inequalities=None):
         if isinstance(equalities, str):
             if inequalities is not None:


@@ -337,6 +482,7 @@ class Polyhedron:
                         raise TypeError('non-integer constraint: '
                                 '{} == 0'.format(constraint))
                 self._equalities.append(constraint)
                         raise TypeError('non-integer constraint: '
                                 '{} == 0'.format(constraint))
                 self._equalities.append(constraint)

+        self._equalities = tuple(self._equalities)

         self._inequalities = []
         if inequalities is not None:
             for constraint in inequalities:
         self._inequalities = []
         if inequalities is not None:
             for constraint in inequalities:


@@ -345,59 +491,127 @@ class Polyhedron:
                         raise TypeError('non-integer constraint: '
                                 '{} <= 0'.format(constraint))
                 self._inequalities.append(constraint)
                         raise TypeError('non-integer constraint: '
                                 '{} <= 0'.format(constraint))
                 self._inequalities.append(constraint)

+        self._inequalities = tuple(self._inequalities)
+        self._constraints = self._equalities + self._inequalities
+        self._symbols = set()
+        for constraint in self._constraints:
+            self.symbols.update(constraint.symbols)
+        self._symbols = tuple(sorted(self._symbols))

         return self
 
         return self
 

+    @classmethod
+    def _fromast(cls, node):
+        if isinstance(node, ast.Module) and len(node.body) == 1:
+            return cls._fromast(node.body[0])
+        elif isinstance(node, ast.Expr):
+            return cls._fromast(node.value)
+        elif isinstance(node, ast.BinOp) and isinstance(node.op, ast.BitAnd):
+            equalities1, inequalities1 = cls._fromast(node.left)
+            equalities2, inequalities2 = cls._fromast(node.right)
+            equalities = equalities1 + equalities2
+            inequalities = inequalities1 + inequalities2
+            return equalities, inequalities
+        elif isinstance(node, ast.Compare):
+            equalities = []
+            inequalities = []
+            left = Expression._fromast(node.left)
+            for i in range(len(node.ops)):
+                op = node.ops[i]
+                right = Expression._fromast(node.comparators[i])
+                if isinstance(op, ast.Lt):
+                    inequalities.append(right - left - 1)
+                elif isinstance(op, ast.LtE):
+                    inequalities.append(right - left)
+                elif isinstance(op, ast.Eq):
+                    equalities.append(left - right)
+                elif isinstance(op, ast.GtE):
+                    inequalities.append(left - right)
+                elif isinstance(op, ast.Gt):
+                    inequalities.append(left - right - 1)
+                else:
+                    break
+                left = right
+            else:
+                return equalities, inequalities
+        raise SyntaxError('invalid syntax')
+
+    @classmethod
+    def fromstring(cls, string):
+        string = string.strip()
+        string = re.sub(r'^\{\s*|\s*\}$', '', string)
+        string = re.sub(r'([^<=>])=([^<=>])', r'\1==\2', string)
+        string = re.sub(r'(\d+|\))\s*([^\W\d_]\w*|\()', r'\1*\2', string)
+        tokens = re.split(r',|;|and|&&|/\\|∧', string, flags=re.I)
+        tokens = ['({})'.format(token) for token in tokens]
+        string = ' & '.join(tokens)
+        tree = ast.parse(string, 'eval')
+        equalities, inequalities = cls._fromast(tree)
+        return cls(equalities, inequalities)
+

     @property
     def equalities(self):
     @property
     def equalities(self):

-        yield from self._equalities
+        return self._equalities

 
     @property
     def inequalities(self):
 
     @property
     def inequalities(self):

-        yield from self._inequalities
+        return self._inequalities

 
 

+    @property

     def constraints(self):
     def constraints(self):

-        yield from self.equalities
-        yield from self.inequalities
+        return self._constraints

 
 

+    @property

     def symbols(self):
     def symbols(self):

-        s = set()
-        for constraint in self.constraints():
-            s.update(constraint.symbols)
-        yield from sorted(s)
+        return self._symbols

 
     @property
     def dimension(self):
 
     @property
     def dimension(self):

-        return len(self.symbols())
+        return len(self.symbols)

 
     def __bool__(self):
 
     def __bool__(self):

-        # return false if the polyhedron is empty, true otherwise
-        raise NotImplementedError
+        return not self.is_empty()

 
     def __contains__(self, value):
         # is the value in the polyhedron?
         raise NotImplementedError
 
     def __eq__(self, other):
 
     def __contains__(self, value):
         # is the value in the polyhedron?
         raise NotImplementedError
 
     def __eq__(self, other):

-        raise NotImplementedError
+        # works correctly when symbols is not passed
+        # should be equal if values are the same even if symbols are different
+        bset = self._toisl()
+        other = other._toisl()
+        return bool(libisl.isl_basic_set_plain_is_equal(bset, other))

 
     def isempty(self):
 
     def isempty(self):

-        return self == empty
+        bset = self._toisl()
+        return bool(libisl.isl_basic_set_is_empty(bset))

 
     def isuniverse(self):
 
     def isuniverse(self):

-        return self == universe
+        bset = self._toisl()
+        return bool(libisl.isl_basic_set_is_universe(bset))

 
     def isdisjoint(self, other):
         # return true if the polyhedron has no elements in common with other
 
     def isdisjoint(self, other):
         # return true if the polyhedron has no elements in common with other

-        raise NotImplementedError
+        #symbols = self._symbolunion(other)
+        bset = self._toisl()
+        other = other._toisl()
+        return bool(libisl.isl_set_is_disjoint(bset, other))

 
     def issubset(self, other):
 
     def issubset(self, other):

-        raise NotImplementedError
+        # check if self(bset) is a subset of other
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        return bool(libisl.isl_set_is_strict_subset(other, bset))

 
     def __le__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):
 
     def __le__(self, other):
         return self.issubset(other)
 
     def __lt__(self, other):

-        raise NotImplementedError
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        return bool(libisl.isl_set_is_strict_subset(other, bset))

 
     def issuperset(self, other):
         # test whether every element in other is in the polyhedron
 
     def issuperset(self, other):
         # test whether every element in other is in the polyhedron


@@ -407,6 +621,10 @@ class Polyhedron:
         return self.issuperset(other)
 
     def __gt__(self, other):
         return self.issuperset(other)
 
     def __gt__(self, other):

+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        bool(libisl.isl_set_is_strict_subset(other, bset))

         raise NotImplementedError
 
     def union(self, *others):
         raise NotImplementedError
 
     def union(self, *others):


@@ -432,10 +650,13 @@ class Polyhedron:
     def __and__(self, other):
         return self.intersection(other)
 
     def __and__(self, other):
         return self.intersection(other)
 

-    def difference(self, *others):
-        # return a new polyhedron with elements in the polyhedron that are not
-        # in the others
-        raise NotImplementedError
+    def difference(self, other):
+        # return a new polyhedron with elements in the polyhedron that are not in the other
+        symbols = self._symbolunion(other)
+        bset = self._toisl(symbols)
+        other = other._toisl(symbols)
+        difference = libisl.isl_set_subtract(bset, other)
+        return difference

 
     def __sub__(self, other):
         return self.difference(other)
 
     def __sub__(self, other):
         return self.difference(other)


@@ -445,20 +666,119 @@ class Polyhedron:
         for constraint in self.equalities:
             constraints.append('{} == 0'.format(constraint))
         for constraint in self.inequalities:
         for constraint in self.equalities:
             constraints.append('{} == 0'.format(constraint))
         for constraint in self.inequalities:

-            constraints.append('{} <= 0'.format(constraint))
-        return '{{{}}}'.format(', '.join(constraints))
+            constraints.append('{} >= 0'.format(constraint))
+        return '{}'.format(', '.join(constraints))

 
     def __repr__(self):
 
     def __repr__(self):

-        equalities = list(self.equalities)
-        inequalities = list(self.inequalities)
-        return '{}(equalities={!r}, inequalities={!r})' \
-                ''.format(self.__class__.__name__, equalities, inequalities)
+        if self.isempty():
+            return 'Empty'
+        elif self.isuniverse():
+            return 'Universe'
+        else:
+            return '{}({!r})'.format(self.__class__.__name__, str(self))

 
     @classmethod
 
     @classmethod

-    def fromstring(cls, string):
-        raise NotImplementedError
+    def _fromsympy(cls, expr):
+        import sympy
+        equalities = []
+        inequalities = []
+        if expr.func == sympy.And:
+            for arg in expr.args:
+                arg_eqs, arg_ins = cls._fromsympy(arg)
+                equalities.extend(arg_eqs)
+                inequalities.extend(arg_ins)
+        elif expr.func == sympy.Eq:
+            expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+            equalities.append(expr)
+        else:
+            if expr.func == sympy.Lt:
+                expr = Expression.fromsympy(expr.args[1] - expr.args[0] - 1)
+            elif expr.func == sympy.Le:
+                expr = Expression.fromsympy(expr.args[1] - expr.args[0])
+            elif expr.func == sympy.Ge:
+                expr = Expression.fromsympy(expr.args[0] - expr.args[1])
+            elif expr.func == sympy.Gt:
+                expr = Expression.fromsympy(expr.args[0] - expr.args[1] - 1)
+            else:
+                raise ValueError('non-polyhedral expression: {!r}'.format(expr))
+            inequalities.append(expr)
+        return equalities, inequalities

 
 

+    @classmethod
+    def fromsympy(cls, expr):
+        import sympy
+        equalities, inequalities = cls._fromsympy(expr)
+        return cls(equalities, inequalities)

 
 

-empty = le(1, 0)
+    def tosympy(self):
+        import sympy
+        constraints = []
+        for equality in self.equalities:
+            constraints.append(sympy.Eq(equality.tosympy(), 0))
+        for inequality in self.inequalities:
+            constraints.append(sympy.Ge(inequality.tosympy(), 0))
+        return sympy.And(*constraints)
+
+    def _symbolunion(self, *others):
+        symbols = set(self.symbols)
+        for other in others:
+            symbols.update(other.symbols)
+        return sorted(symbols)
+
+    def _toisl(self, symbols=None):
+        if symbols is None:
+            symbols = self.symbols
+        dimension = len(symbols)
+        space = libisl.isl_space_set_alloc(_main_ctx, 0, dimension)
+        bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
+        ls = libisl.isl_local_space_from_space(space)
+        for equality in self.equalities:
+            ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
+            for symbol, coefficient in equality.coefficients():
+                val = str(coefficient).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                dim = symbols.index(symbol)
+                ceq = libisl.isl_constraint_set_coefficient_val(ceq, libisl.isl_dim_set, dim, val)
+            if equality.constant != 0:
+                val = str(equality.constant).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                ceq = libisl.isl_constraint_set_constant_val(ceq, val)
+            bset = libisl.isl_basic_set_add_constraint(bset, ceq)
+        for inequality in self.inequalities:
+            cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
+            for symbol, coefficient in inequality.coefficients():
+                val = str(coefficient).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                dim = symbols.index(symbol)
+                cin = libisl.isl_constraint_set_coefficient_val(cin, libisl.isl_dim_set, dim, val)
+            if inequality.constant != 0:
+                val = str(inequality.constant).encode()
+                val = libisl.isl_val_read_from_str(_main_ctx, val)
+                cin = libisl.isl_constraint_set_constant_val(cin, val)
+            bset = libisl.isl_basic_set_add_constraint(bset, cin)
+        bset = isl.BasicSet(bset)
+        return bset

 
 

-universe = Polyhedron()
+    @classmethod
+    def _fromisl(cls, bset, symbols):
+        raise NotImplementedError
+        equalities = ...
+        inequalities = ...
+        return cls(equalities, inequalities)
+        '''takes basic set  in isl form and puts back into python version of polyhedron
+        isl example code gives isl form as:
+            "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
+            our printer is giving form as:
+            { [i0, i1] : 2i1 >= -2 - i0 } '''
+
+Empty = eq(0,1)
+
+Universe = Polyhedron()
+
+
+if __name__ == '__main__':
+    #p = Polyhedron('2a + 2b + 1 == 0') # empty
+    p = Polyhedron('3x + 2y + 3 == 0, y == 0') # not empty
+    ip = p._toisl()
+    print(ip)
+    print(ip.constraints())