X-Git-Url: https://scm.cri.mines-paristech.fr/git/linpy.git/blobdiff_plain/36156a49062f344bee22bd87310b5e03f0955c5d..2a56c56cadd9be4dd461218b1620d2617ca8a924:/pypol/linear.py?ds=sidebyside

diff --git a/pypol/linear.py b/pypol/linear.py
index e69600f..524b3cb 100644
--- a/pypol/linear.py
+++ b/pypol/linear.py
@@ -1,46 +1,21 @@
+import ast
 import functools
 import numbers
-import ctypes, ctypes.util
+import re
 
 from fractions import Fraction, gcd
 
-from . import isl, islhelper
+from pypol import isl
+from pypol.isl import libisl
 
 
-libisl = ctypes.CDLL(ctypes.util.find_library('isl'))
-
-libisl.isl_printer_get_str.restype = ctypes.c_char_p
-
 __all__ = [
-    'Expression',
-    'constant', 'symbol', 'symbols',
+    'Expression', 'Constant', 'Symbol', 'symbols',
     'eq', 'le', 'lt', 'ge', 'gt',
     'Polyhedron',
-    'empty', 'universe'
+    'Empty', 'Universe'
 ]
 
-'''
-def symbolToInt(self):
-     make dictionary of key:value (letter:integer)
-        iterate through the dictionary to find matching symbol
-        return the given integer value
-    d = {'a': 1, 'b': 2, 'c': 3, 'd': 4, 'e': 5, 'f': 6, 'g': 7, 'h': 8, 'i': 6, 'j': 10, 'k': 11, 'l': 12, 'm': 13, 'n': 14,
-         'o': 15, 'p': 16, 'q': 17, 'r': 18, 's': 19, 't': 20, 'u': 21, 'v': 22, 'w': 23, 'x': 24, 'y': 25, 'z': 26}
-    if self in d:
-        num = d.get(self)
-    return num
-'''
-
-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)
@@ -48,7 +23,7 @@ def _polymorphic_method(func):
         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
@@ -59,34 +34,15 @@ def _polymorphic_operator(func):
     @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
 
-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:
@@ -94,43 +50,97 @@ 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)
-        self = super().__new__(cls)
-        self._coefficients = {}
         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):
-            raise TypeError('constant must be a rational number')
+            raise TypeError('constant must be a rational number or a Constant instance')
         self._constant = constant
+        self._symbols = tuple(sorted(self._coefficients))
+        self._dimension = len(self._symbols)
         return self
 
+    @classmethod
+    def _fromast(cls, node):
+        if isinstance(node, ast.Module):
+            assert 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):
+            if 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):
-        yield from sorted(self._coefficients)
+        return self._symbols
 
     @property
     def dimension(self):
-        return len(list(self.symbols()))
+        return self._dimension
 
     def coefficient(self, symbol):
-        if isinstance(symbol, Expression) and symbol.issymbol():
+        if isinstance(symbol, Symbol):
             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:
@@ -139,7 +149,7 @@ class Expression:
     __getitem__ = coefficient
 
     def coefficients(self):
-        for symbol in self.symbols():
+        for symbol in self.symbols:
             yield symbol, self.coefficient(symbol)
 
     @property
@@ -147,30 +157,18 @@ class Expression:
         return self._constant
 
     def isconstant(self):
-        return len(self._coefficients) == 0
+        return False
 
     def values(self):
-        for symbol in self.symbols():
+        for symbol in self.symbols:
             yield self.coefficient(symbol)
         yield self.constant
 
-    def values_int(self):
-        for symbol in self.symbols():
-            return self.coefficient(symbol)
-        return int(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):
-        return len(self._coefficients) == 1 and self._constant == 0
+        return False
 
     def __bool__(self):
-        return (not self.isconstant()) or bool(self.constant)
+        return True
 
     def __pos__(self):
         return self
@@ -246,10 +244,9 @@ class Expression:
 
     def __str__(self):
         string = ''
-        symbols = sorted(self.symbols())
         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
@@ -298,10 +295,6 @@ class Expression:
         string += '}}, {!r})'.format(self.constant)
         return string
 
-    @classmethod
-    def fromstring(cls, string):
-        raise NotImplementedError
-
     @_polymorphic_method
     def __eq__(self, other):
         # "normal" equality
@@ -311,70 +304,112 @@ class Expression:
                 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):
-        return Polyhedron(equalities=[(self - other)._canonify()])
+        return Polyhedron(equalities=[(self - other)._toint()])
 
     @_polymorphic_method
     def __le__(self, other):
-        return Polyhedron(inequalities=[(self - other)._canonify()])
+        return Polyhedron(inequalities=[(other - self)._toint()])
 
     @_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):
-        return Polyhedron(inequalities=[(other - self)._canonify()])
+        return Polyhedron(inequalities=[(self - other)._toint()])
 
     @_polymorphic_method
     def __gt__(self, other):
-        return Polyhedron(inequalities=[(other - self)._canonify() + 1])
+        return Polyhedron(inequalities=[(self - other)._toint() - 1])
+
+
+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):
+        return '{}({!r})'.format(self.__class__.__name__, self._constant)
+
+
+class Symbol(Expression):
+
+    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=3)
-    else:
-        return Expression(constant=Fraction(numerator, denominator))
+    def issymbol(self):
+        return True
 
-def symbol(name):
-    if not isinstance(name, str):
-        raise TypeError('name must be a string')
-    return Expression(coefficients={name: 1})
+    def __repr__(self):
+        return '{}({!r})'.format(self.__class__.__name__, self._name)
 
 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):
-    return a._eq(b)
+    return a.__eq__(b)
 
 @_polymorphic_operator
 def le(a, b):
-    return a <= b
+    return a.__le__(b)
 
 @_polymorphic_operator
 def lt(a, b):
-    return a < b
+    return a.__lt__(b)
 
 @_polymorphic_operator
 def ge(a, b):
-    return a >= b
+    return a.__ge__(b)
 
 @_polymorphic_operator
 def gt(a, b):
-    return a > b
+    return a.__gt__(b)
 
 
 class Polyhedron:
@@ -382,6 +417,13 @@ class Polyhedron:
     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:
@@ -396,6 +438,7 @@ class Polyhedron:
                         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:
@@ -404,96 +447,128 @@ class Polyhedron:
                         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._bset
+        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):
+        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)
+        equalities = []
+        inequalities = []
+        for cstr in re.split(r',|;|and|&&|/\\|∧', string, flags=re.I):
+            tree = ast.parse(cstr.strip(), 'eval')
+            if not isinstance(tree, ast.Module) or len(tree.body) != 1:
+                raise SyntaxError('invalid syntax')
+            node = tree.body[0]
+            if not isinstance(node, ast.Expr):
+                raise SyntaxError('invalid syntax')
+            node = node.value
+            if not isinstance(node, ast.Compare):
+                raise SyntaxError('invalid syntax')
+            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:
+                    raise SyntaxError('invalid syntax')
+                left = right
+        return cls(equalities, inequalities)
 
     @property
     def equalities(self):
-        yield from self._equalities
+        return self._equalities
 
     @property
     def inequalities(self):
-        yield from self._inequalities
+        return 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))
-
     def constraints(self):
-        yield from self.equalities
-        yield from self.inequalities
-
+        return self._constraints
 
+    @property
     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):
-        return len(self.symbols())
+        return len(self.symbols)
 
     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?
         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 is_empty(self):
-        return
+    def isempty(self):
+        bset = self._toisl()
+        return bool(libisl.isl_basic_set_is_empty(bset))
 
     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
-        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):
-        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):
-        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
-        for value in other:
-            if value == self.constraints():
-                return True
-            else:
-                return False
         raise NotImplementedError
 
     def __ge__(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):
@@ -519,10 +594,13 @@ class Polyhedron:
     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)
@@ -532,70 +610,77 @@ class Polyhedron:
         for constraint in self.equalities:
             constraints.append('{} == 0'.format(constraint))
         for constraint in self.inequalities:
-            constraints.append('{} <= 0'.format(constraint))
+            constraints.append('{} >= 0'.format(constraint))
         return '{{{}}}'.format(', '.join(constraints))
 
     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:
+            equalities = list(self.equalities)
+            inequalities = list(self.inequalities)
+            return '{}(equalities={!r}, inequalities={!r})' \
+                    ''.format(self.__class__.__name__, equalities, inequalities)
+
+    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
 
     @classmethod
-    def fromstring(cls, string):
+    def _fromisl(cls, bset, symbols):
         raise NotImplementedError
-
-    def to_isl(self):
-        #d = Expression().__dict__  #write expression values to dictionary in form {'_constant': value, '_coefficients': value}
-        d = {'_constant': 2, '_coefficients': {'b':1}}
-        coeff = d.get('_coefficients')
-        num_coefficients = len(coeff)
-        space = libisl.isl_space_set_alloc(Context(), 0, num_coefficients)
-        bset = libisl.isl_basic_set_empty(libisl.isl_space_copy(space))
-        ls = libisl.isl_local_space_from_space(libisl.isl_space_copy(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
-        need to change the symbols method to a lookup table for the integer value for each letter that could be a symbol'''
-        if self._equalities:
-            if '_constant' in d:
-                value = d.get('_constant')
-                ceq = libisl.isl_constraint_set_constant_si(ceq, value)
-            if '_coefficients' in d:
-                value_co = d.get('_coefficients')
-                for co in value_co:
-                    num = value_co.get(co)
-                    ceq = libisl.isl_constraint_set_coefficient_si(ceq, islhelper.isl_dim_set, get_ids(co), num)
-            bset = libisl.isl_set_add_constraint(bset, ceq)
-
-        if self._inequalities:
-            if '_constant' in d:
-                value = d.get('_constant')
-                cin = libisl.isl_constraint_set_constant_si(cin, value)
-            if '_coefficients' in d:
-                value_co = d.get('_coefficients')
-                for co in value_co:
-                    num = value_co.get(co)
-                    if value_co: #if dictionary not empty add coefficient as to constraint
-                        cin = libisl.isl_constraint_set_coefficient_si(cin, islhelper.isl_dim_set, get_ids(co), num)
-            bset = libisl.isl_set_add_constraint(bset, cin)
-        ip = libisl.isl_printer_to_str(Context()) #create string printer
-        ip = libisl.isl_printer_print_set(ip, bset) #print set to printer
-        string = libisl.isl_printer_get_str(ip)   #get string from printer
-        string = str(string)
-        print(string)
-        return string
-
-
-    def from_isl(self, bset):
-        '''takes basic set in isl form and puts back into python version of polyhedron
-        isl example code gives idl form as:
-            "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");'''
-
-        poly = 0
-        return poly
-
-empty = eq(1,1)
-
-
-universe = Polyhedron()
+        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__':
+    p1 = Polyhedron('2a + 2b + 1 == 0') # empty
+    print(p1._toisl())
+    p2 = Polyhedron('3x + 2y + 3 == 0') # not empty
+    print(p2._toisl())