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Fix Symbol creation
[linpy.git] / pypol / linear.py
diff --git a/pypol/linear.py b/pypol/linear.py
index 9584609..8f73fd3 100644 (file)
--- a/pypol/linear.py
+++ b/pypol/linear.py
@@ -1,34 +1,20 @@
+import ctypes, ctypes.util
 import functools
 import numbers
 import functools
 import numbers
-import json
-import ctypes, ctypes.util
-from pypol import isl
-from . import isl, islhelper
 
 from fractions import Fraction, gcd
 
 
 from fractions import Fraction, gcd
 
-libisl = ctypes.CDLL(ctypes.util.find_library('isl'))
+from . import isl
+from .isl import libisl
 
 
-libisl.isl_printer_get_str.restype = ctypes.c_char_p
 
 __all__ = [
 
 __all__ = [
-    'Expression',
-    'constant', 'symbol', 'symbols',
+    'Expression', 'Constant', 'Symbol', 'symbols',
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',
     'empty', 'universe'
 ]
 
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',
     'empty', 'universe'
 ]
 
-ids = {}
-
-def get_ids(co):
-    if co in ids:
-        return ids.get(co)
-    else:
-        idd = len(ids)
-        ids[co] = idd
-        #print(ids)
-        return idd
 
 def _polymorphic_method(func):
     @functools.wraps(func)
 
 def _polymorphic_method(func):
     @functools.wraps(func)
@@ -36,7 +22,7 @@ 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
             return func(a, b)
         return NotImplemented
     return wrapper
@@ -47,34 +33,15 @@ def _polymorphic_operator(func):
     @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)
+            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)
         elif isinstance(a, Expression):
             return func(a, b)
         raise TypeError('arguments must be linear expressions')
     return wrapper
 
-class Context:
-
-    __slots__ = ('_ic')
-
-    def __init__(self):
-        self._ic = libisl.isl_ctx_alloc()
-
-    @property
-    def _as_parameter_(self):
-        return self._ic
-    
-    #comment out so does not delete itself after being created 
-    #def __del__(self):
-    #   libisl.isl_ctx_free(self)
-
-    def __eq__(self, other):
-        if not isinstance(other, Context):
-            return False
-        return self._ic == other._ic
-
 
 
+_main_ctx = isl.Context()
 
 
 class Expression:
 
 
 class Expression:
@@ -87,38 +54,56 @@ class Expression:
             if constant:
                 raise TypeError('too many arguments')
             return cls.fromstring(coefficients)
             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 = str(symbol)
+            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 fromstring(cls, string):
+        raise NotImplementedError
 
 
+    @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:
@@ -126,9 +111,8 @@ class Expression:
 
     __getitem__ = coefficient
 
 
     __getitem__ = coefficient
 
-    @property
     def coefficients(self):
     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
@@ -136,30 +120,22 @@ 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 values_int(self):
-        for symbol in self.symbols():
-            return self.coefficient(symbol)
-        return int(self.constant)
-
-
+    @property
     def symbol(self):
     def symbol(self):
-        if not self.issymbol():
-            raise ValueError('not a symbol: {}'.format(self))
-        for symbol in self.symbols():
-            return symbol
+        raise ValueError('not a symbol: {}'.format(self))
 
     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)
+        True
 
     def __pos__(self):
         return self
 
     def __pos__(self):
         return self
@@ -169,8 +145,8 @@ class Expression:
 
     @_polymorphic_method
     def __add__(self, other):
 
     @_polymorphic_method
     def __add__(self, other):
-        coefficients = dict(self.coefficients)
-        for symbol, coefficient in other.coefficients:
+        coefficients = dict(self.coefficients())
+        for symbol, coefficient in other.coefficients():
             if symbol in coefficients:
                 coefficients[symbol] += coefficient
             else:
             if symbol in coefficients:
                 coefficients[symbol] += coefficient
             else:
@@ -182,8 +158,8 @@ class Expression:
 
     @_polymorphic_method
     def __sub__(self, other):
 
     @_polymorphic_method
     def __sub__(self, other):
-        coefficients = dict(self.coefficients)
-        for symbol, coefficient in other.coefficients:
+        coefficients = dict(self.coefficients())
+        for symbol, coefficient in other.coefficients():
             if symbol in coefficients:
                 coefficients[symbol] -= coefficient
             else:
             if symbol in coefficients:
                 coefficients[symbol] -= coefficient
             else:
@@ -193,11 +169,11 @@ class Expression:
 
     def __rsub__(self, other):
         return -(self - other)
 
     def __rsub__(self, other):
         return -(self - other)
-    
+
     @_polymorphic_method
     def __mul__(self, other):
         if other.isconstant():
     @_polymorphic_method
     def __mul__(self, other):
         if other.isconstant():
-            coefficients = dict(self.coefficients)
+            coefficients = dict(self.coefficients())
             for symbol in coefficients:
                 coefficients[symbol] *= other.constant
             constant = self.constant * other.constant
             for symbol in coefficients:
                 coefficients[symbol] *= other.constant
             constant = self.constant * other.constant
@@ -235,10 +211,9 @@ 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
@@ -280,17 +255,13 @@ class Expression:
 
     def __repr__(self):
         string = '{}({{'.format(self.__class__.__name__)
 
     def __repr__(self):
         string = '{}({{'.format(self.__class__.__name__)
-        for i, (symbol, coefficient) in enumerate(self.coefficients):
+        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
 
             if i != 0:
                 string += ', '
             string += '{!r}: {!r}'.format(symbol, coefficient)
         string += '}}, {!r})'.format(self.constant)
         return string
 
-    @classmethod
-    def fromstring(cls, string):
-        raise NotImplementedError
-
     @_polymorphic_method
     def __eq__(self, other):
         # "normal" equality
     @_polymorphic_method
     def __eq__(self, other):
         # "normal" equality
@@ -302,42 +273,84 @@ class Expression:
     def __hash__(self):
         return hash((self._coefficients, self._constant))
 
     def __hash__(self):
         return hash((self._coefficients, 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=[(other - self)._canonify()])
+        return Polyhedron(inequalities=[(other - self)._toint()])
 
     @_polymorphic_method
     def __lt__(self, other):
 
     @_polymorphic_method
     def __lt__(self, other):
-        return Polyhedron(inequalities=[(other - self)._canonify() - 1])
+        return Polyhedron(inequalities=[(other - self)._toint() - 1])
 
     @_polymorphic_method
     def __ge__(self, other):
 
     @_polymorphic_method
     def __ge__(self, other):
-        return Polyhedron(inequalities=[(self - other)._canonify()])
+        return Polyhedron(inequalities=[(self - other)._toint()])
 
     @_polymorphic_method
     def __gt__(self, other):
 
     @_polymorphic_method
     def __gt__(self, other):
-        return Polyhedron(inequalities=[(self - other)._canonify() - 1])
+        return Polyhedron(inequalities=[(self - other)._toint() - 1])
 
 
 
 
-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))
+class Constant(Expression):
 
 
-def symbol(name):
-    if not isinstance(name, str):
-        raise TypeError('name must be a string')
-    return Expression(coefficients={name: 1})
+    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):
+        return '{}({!r})'.format(self.__class__.__name__, self._constant)
+
+
+class Symbol(Expression):
+
+    def __new__(cls, name):
+        if isinstance(name, Symbol):
+            name = name.symbol
+        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._symbol = name
+        self._dimension = 1
+        return self
+
+    @property
+    def symbol(self):
+        return self._symbol
+
+    def issymbol(self):
+        return True
+
+    def __repr__(self):
+        return '{}({!r})'.format(self.__class__.__name__, self._symbol)
 
 def symbols(names):
     if isinstance(names, str):
 
 def symbols(names):
     if isinstance(names, str):
@@ -385,6 +398,7 @@ 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:
@@ -392,57 +406,41 @@ class Polyhedron:
                     if value.denominator != 1:
                         raise TypeError('non-integer constraint: '
                                 '{} <= 0'.format(constraint))
                     if value.denominator != 1:
                         raise TypeError('non-integer constraint: '
                                 '{} <= 0'.format(constraint))
-                self._inequalities.append(constraint)      
-        self._bset = self.to_isl()
-        #print(self._bset)
-        #put this here just to test from isl method
-        #from_isl = self.from_isl(self._bset)
-        #print(from_isl)
-        #rint(self)
-        return self 
-   
-  
+                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
+
+    @classmethod
+    def fromstring(cls, string):
+        raise NotImplementedError
+
     @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
-        
-    @property
-    def constant(self):
-        return self._constant
-
-    def isconstant(self):
-        return len(self._coefficients) == 0
-    
-        
-    def isempty(self):
-        return bool(libisl.isl_basic_set_is_empty(self._bset))
+        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())
-        return 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
-        if self._equalities or self._inequalities:
-            return False
-        else:
-            return True
-        
+        return not self.is_empty()
 
     def __contains__(self, value):
         # is the value in the polyhedron?
 
     def __contains__(self, value):
         # is the value in the polyhedron?
@@ -451,11 +449,12 @@ class Polyhedron:
     def __eq__(self, other):
         raise NotImplementedError
 
     def __eq__(self, other):
         raise NotImplementedError
 
-    def is_empty(self):
-        return
+    def isempty(self):
+        bset = self._toisl()
+        return bool(libisl.isl_basic_set_is_empty(bset))
 
     def isuniverse(self):
 
     def isuniverse(self):
-        return self == universe
+        raise NotImplementedError
 
     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
@@ -472,11 +471,6 @@ class Polyhedron:
 
     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
-        for value in other:
-            if value == self.constraints():
-                return True 
-            else:
-                return False     
         raise NotImplementedError
 
     def __ge__(self, other):
         raise NotImplementedError
 
     def __ge__(self, other):
@@ -530,87 +524,75 @@ class Polyhedron:
         return '{}(equalities={!r}, inequalities={!r})' \
                 ''.format(self.__class__.__name__, equalities, inequalities)
 
         return '{}(equalities={!r}, inequalities={!r})' \
                 ''.format(self.__class__.__name__, equalities, inequalities)
 
-    @classmethod
-    def fromstring(cls, string):
-        raise NotImplementedError
-    
-    def _symbolunion(self, *others): 
-        print(self)
-        symbols = set(self.symbols())
+    def _symbolunion(self, *others):
+        symbols = set(self.symbols)
         for other in others:
         for other in others:
-            symbols.update(other.symbols())
+            symbols.update(other.symbols)
         return sorted(symbols)
         return sorted(symbols)
-    
-    def to_isl(self, symbols=None):
+
+    def _toisl(self, symbols=None):
         if symbols is None:
         if symbols is None:
-            symbols = self.symbols()
-            print(symbols)
-        print('>>>', self)
-        print('eq:', list(self.equalities))
-        print('ineq:', list(self.inequalities)) 
+            symbols = self.symbols
         num_coefficients = len(symbols)
         num_coefficients = len(symbols)
-        ctx = Context()
-        space = libisl.isl_space_set_alloc(ctx, 0, num_coefficients)
-        bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space)) 
+        space = libisl.isl_space_set_alloc(_main_ctx, 0, num_coefficients)
+        bset = libisl.isl_basic_set_universe(libisl.isl_space_copy(space))
         ls = libisl.isl_local_space_from_space(space)
         ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
         cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
         '''if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set'''
         if list(self.equalities): #check if any equalities exist
             for eq in self.equalities:
         ls = libisl.isl_local_space_from_space(space)
         ceq = libisl.isl_equality_alloc(libisl.isl_local_space_copy(ls))
         cin = libisl.isl_inequality_alloc(libisl.isl_local_space_copy(ls))
         '''if there are equalities/inequalities, take each constant and coefficient and add as a constraint to the basic set'''
         if list(self.equalities): #check if any equalities exist
             for eq in self.equalities:
-                coeff_eq = dict(eq.coefficients)
+                coeff_eq = dict(eq.coefficients())
                 if eq.constant:
                     value = eq.constant
                     ceq = libisl.isl_constraint_set_constant_si(ceq, value)
                 for eq in coeff_eq:
                     num = coeff_eq.get(eq)
                     iden = symbols.index(eq)
                 if eq.constant:
                     value = eq.constant
                     ceq = libisl.isl_constraint_set_constant_si(ceq, value)
                 for eq in coeff_eq:
                     num = coeff_eq.get(eq)
                     iden = symbols.index(eq)
-                    print('id of var {} is {}, coeff is {}'.format(eq, iden, num))
-                    ceq = libisl.isl_constraint_set_coefficient_si(ceq, islhelper.isl_dim_set, iden, num)  #use 3 for type isl_dim_set 
-            bset = libisl.isl_basic_set_add_constraint(bset, ceq)                   
+                    ceq = libisl.isl_constraint_set_coefficient_si(ceq, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
+            bset = libisl.isl_basic_set_add_constraint(bset, ceq)
         if list(self.inequalities): #check if any inequalities exist
             for ineq in self.inequalities:
         if list(self.inequalities): #check if any inequalities exist
             for ineq in self.inequalities:
-                coeff_in = dict(ineq.coefficients)
+                coeff_in = dict(ineq.coefficients())
                 if ineq.constant:
                     value = ineq.constant
                     cin = libisl.isl_constraint_set_constant_si(cin, value)
                 for ineq in coeff_in:
                     num = coeff_in.get(ineq)
                     iden = symbols.index(ineq)
                 if ineq.constant:
                     value = ineq.constant
                     cin = libisl.isl_constraint_set_constant_si(cin, value)
                 for ineq in coeff_in:
                     num = coeff_in.get(ineq)
                     iden = symbols.index(ineq)
-                    print('id of var {} is {}, coeff is {}'.format(ineq, iden, num))
-                    cin = libisl.isl_constraint_set_coefficient_si(cin, islhelper.isl_dim_set, iden, num)  #use 3 for type isl_dim_set 
-            bset = libisl.isl_basic_set_add_constraint(bset, cin)                   
-        ip = libisl.isl_printer_to_str(ctx) #create string printer
-        ip = libisl.isl_printer_print_basic_set(ip, bset) #print basic set to printer 
-        string = libisl.isl_printer_get_str(ip)   #get string from printer
-        string = str(string.decode())    
-        print(string)
+                    cin = libisl.isl_constraint_set_coefficient_si(cin, libisl.isl_dim_set, iden, num)  #use 3 for type isl_dim_set
+            bset = libisl.isl_basic_set_add_constraint(bset, cin)
+        bset = isl.BasicSet(bset)
         return bset
         return bset
-    
-    
-    def from_isl(self, bset):
-        '''takes basic set in isl form and puts back into python version of polyhedron
+
+    @classmethod
+    def _fromisl(cls, bset):
+        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:
             b'{ [i0] : 1 = 0 }' '''
         #bset = self
         isl example code gives isl form as:
             "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}")
             our printer is giving form as:
             b'{ [i0] : 1 = 0 }' '''
         #bset = self
-        if self._equalities:
-            constraints = libisl.isl_basic_set_equalities_matrix(bset, 3) 
-        elif self._inequalities:
-            constraints = libisl.isl_basic_set_inequalities_matrix(bset, 3)    
-        print(constraints)
-        return constraints
+        # if self._equalities:
+        #     constraints = libisl.isl_basic_set_equalities_matrix(bset, 3)
+        # elif self._inequalities:
+        #     constraints = libisl.isl_basic_set_inequalities_matrix(bset, 3)
+        # print(constraints)
+        # return constraints
+
+empty = None #eq(0,1)
+universe = None #Polyhedron()
 
 
-#empty = eq(0,1)
-empty = None
-universe = None
 
 if __name__ == '__main__':
     ex1 = Expression(coefficients={'a': 1, 'x': 2}, constant=2)
     ex2 = Expression(coefficients={'a': 3  , 'b': 2}, constant=3)
     p = Polyhedron(inequalities=[ex1, ex2])
 
 if __name__ == '__main__':
     ex1 = Expression(coefficients={'a': 1, 'x': 2}, constant=2)
     ex2 = Expression(coefficients={'a': 3  , 'b': 2}, constant=3)
     p = Polyhedron(inequalities=[ex1, ex2])
-    #p = eq(ex2, 0)# 2a+4 = 0, in fact 6a+3 = 0
-    #p.to_isl()
-
-#universe = Polyhedron()
+    bs = p._toisl()
+    print(bs)
+    print('empty ?', p.isempty())
+    print('empty ?', eq(0, 1).isempty())
A polyhedral library based on ISL