X-Git-Url: https://scm.cri.ensmp.fr/git/linpy.git/blobdiff_plain/66e41ccd173874b3309e4c24be64c7b6b2ac6298..1d494bb187b70135df721c13306d7f26fdf33f50:/pypol/linear.py

diff --git a/pypol/linear.py b/pypol/linear.py
deleted file mode 100644
index b40415f..0000000
--- a/pypol/linear.py
+++ /dev/null
@@ -1,784 +0,0 @@
-import ast
-import functools
-import numbers
-import re
-
-from fractions import Fraction, gcd
-
-from . import isl
-from .isl import libisl
-
-
-__all__ = [
-    'Expression', 'Constant', 'Symbol', 'symbols',
-    'eq', 'le', 'lt', 'ge', 'gt',
-    'Polyhedron',
-    'Empty', 'Universe'
-]
-
-
-def _polymorphic_method(func):
-    @functools.wraps(func)
-    def wrapper(a, b):
-        if isinstance(b, Expression):
-            return func(a, b)
-        if isinstance(b, numbers.Rational):
-            b = Constant(b)
-            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):
-            a = Constant(a)
-            return func(a, b)
-        elif isinstance(a, Expression):
-            return func(a, b)
-        raise TypeError('arguments must be linear expressions')
-    return wrapper
-
-
-_main_ctx = isl.Context()
-
-
-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)
-        if isinstance(coefficients, dict):
-            coefficients = coefficients.items()
-        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 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) 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):
-        return self._symbols
-
-    @property
-    def dimension(self):
-        return self._dimension
-
-    def coefficient(self, symbol):
-        if isinstance(symbol, Symbol):
-            symbol = str(symbol)
-        elif not isinstance(symbol, str):
-            raise TypeError('symbol must be a string or a Symbol instance')
-        try:
-            return self._coefficients[symbol]
-        except KeyError:
-            return 0
-
-    __getitem__ = coefficient
-
-    def coefficients(self):
-        for symbol in self.symbols:
-            yield symbol, self.coefficient(symbol)
-
-    @property
-    def constant(self):
-        return self._constant
-
-    def isconstant(self):
-        return False
-
-    def values(self):
-        for symbol in self.symbols:
-            yield self.coefficient(symbol)
-        yield self.constant
-
-    def issymbol(self):
-        return False
-
-    def __bool__(self):
-        return True
-
-    def __pos__(self):
-        return self
-
-    def __neg__(self):
-        return self * -1
-
-    @_polymorphic_method
-    def __add__(self, other):
-        coefficients = dict(self.coefficients())
-        for symbol, coefficient in other.coefficients():
-            if symbol in coefficients:
-                coefficients[symbol] += coefficient
-            else:
-                coefficients[symbol] = coefficient
-        constant = self.constant + other.constant
-        return Expression(coefficients, constant)
-
-    __radd__ = __add__
-
-    @_polymorphic_method
-    def __sub__(self, other):
-        coefficients = dict(self.coefficients())
-        for symbol, coefficient in other.coefficients():
-            if symbol in coefficients:
-                coefficients[symbol] -= coefficient
-            else:
-                coefficients[symbol] = -coefficient
-        constant = self.constant - other.constant
-        return Expression(coefficients, constant)
-
-    def __rsub__(self, other):
-        return -(self - other)
-
-    @_polymorphic_method
-    def __mul__(self, other):
-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] *= other.constant
-            constant = self.constant * other.constant
-            return Expression(coefficients, constant)
-        if isinstance(other, Expression) and not self.isconstant():
-            raise ValueError('non-linear expression: '
-                    '{} * {}'.format(self._parenstr(), other._parenstr()))
-        return NotImplemented
-
-    __rmul__ = __mul__
-
-    @_polymorphic_method
-    def __truediv__(self, other):
-        if other.isconstant():
-            coefficients = dict(self.coefficients())
-            for symbol in coefficients:
-                coefficients[symbol] = \
-                        Fraction(coefficients[symbol], other.constant)
-            constant = Fraction(self.constant, other.constant)
-            return Expression(coefficients, constant)
-        if isinstance(other, Expression):
-            raise ValueError('non-linear expression: '
-                '{} / {}'.format(self._parenstr(), other._parenstr()))
-        return NotImplemented
-
-    def __rtruediv__(self, other):
-        if isinstance(other, self):
-            if self.isconstant():
-                constant = Fraction(other, self.constant)
-                return Expression(constant=constant)
-            else:
-                raise ValueError('non-linear expression: '
-                        '{} / {}'.format(other._parenstr(), self._parenstr()))
-        return NotImplemented
-
-    def __str__(self):
-        string = ''
-        i = 0
-        for symbol in self.symbols:
-            coefficient = self.coefficient(symbol)
-            if coefficient == 1:
-                if i == 0:
-                    string += symbol
-                else:
-                    string += ' + {}'.format(symbol)
-            elif coefficient == -1:
-                if i == 0:
-                    string += '-{}'.format(symbol)
-                else:
-                    string += ' - {}'.format(symbol)
-            else:
-                if i == 0:
-                    string += '{}*{}'.format(coefficient, symbol)
-                elif coefficient > 0:
-                    string += ' + {}*{}'.format(coefficient, symbol)
-                else:
-                    assert coefficient < 0
-                    coefficient *= -1
-                    string += ' - {}*{}'.format(coefficient, symbol)
-            i += 1
-        constant = self.constant
-        if constant != 0 and i == 0:
-            string += '{}'.format(constant)
-        elif constant > 0:
-            string += ' + {}'.format(constant)
-        elif constant < 0:
-            constant *= -1
-            string += ' - {}'.format(constant)
-        if string == '':
-            string = '0'
-        return string
-
-    def _parenstr(self, always=False):
-        string = str(self)
-        if not always and (self.isconstant() or self.issymbol()):
-            return string
-        else:
-            return '({})'.format(string)
-
-    def __repr__(self):
-        return '{}({!r})'.format(self.__class__.__name__, str(self))
-
-    @_polymorphic_method
-    def __eq__(self, other):
-        # "normal" equality
-        # 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
-
-    def __hash__(self):
-        return hash((tuple(sorted(self._coefficients.items())), self._constant))
-
-    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)._toint()])
-
-    @_polymorphic_method
-    def __le__(self, other):
-        return Polyhedron(inequalities=[(other - self)._toint()])
-
-    @_polymorphic_method
-    def __lt__(self, other):
-        return Polyhedron(inequalities=[(other - self)._toint() - 1])
-
-    @_polymorphic_method
-    def __ge__(self, other):
-        return Polyhedron(inequalities=[(self - other)._toint()])
-
-    @_polymorphic_method
-    def __gt__(self, other):
-        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 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 symbols(names):
-    if isinstance(names, str):
-        names = names.replace(',', ' ').split()
-    return (Symbol(name) for name in names)
-
-
-@_polymorphic_operator
-def eq(a, b):
-    return a.__eq__(b)
-
-@_polymorphic_operator
-def le(a, b):
-    return a.__le__(b)
-
-@_polymorphic_operator
-def lt(a, b):
-    return a.__lt__(b)
-
-@_polymorphic_operator
-def ge(a, b):
-    return a.__ge__(b)
-
-@_polymorphic_operator
-def gt(a, b):
-    return a.__gt__(b)
-
-
-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:
-                raise TypeError('too many arguments')
-            return cls.fromstring(equalities)
-        self = super().__new__(cls)
-        self._equalities = []
-        if equalities is not None:
-            for constraint in equalities:
-                for value in constraint.values():
-                    if value.denominator != 1:
-                        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:
-                for value in constraint.values():
-                    if value.denominator != 1:
-                        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
-
-    @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):
-        return self._equalities
-
-    @property
-    def inequalities(self):
-        return self._inequalities
-
-    @property
-    def constraints(self):
-        return self._constraints
-
-    @property
-    def symbols(self):
-        return self._symbols
-
-    @property
-    def dimension(self):
-        return len(self.symbols)
-
-    def __bool__(self):
-        return not self.is_empty()
-
-    def __contains__(self, value):
-        # is the value in the polyhedron?
-        raise NotImplementedError
-
-    def __eq__(self, other):
-        # 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):
-        bset = self._toisl()
-        return bool(libisl.isl_basic_set_is_empty(bset))
-
-    def isuniverse(self):
-        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
-        #symbols = self._symbolunion(other)
-        bset = self._toisl()
-        other = other._toisl()
-        return bool(libisl.isl_set_is_disjoint(bset, other))
-
-    def issubset(self, other):
-        # 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):
-        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
-        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):
-        # return a new polyhedron with elements from the polyhedron and all
-        # others (convex union)
-        raise NotImplementedError
-
-    def __or__(self, other):
-        return self.union(other)
-
-    def intersection(self, *others):
-        # return a new polyhedron with elements common to the polyhedron and all
-        # others
-        # a poor man's implementation could be:
-        # equalities = list(self.equalities)
-        # inequalities = list(self.inequalities)
-        # for other in others:
-        #     equalities.extend(other.equalities)
-        #     inequalities.extend(other.inequalities)
-        # return self.__class__(equalities, inequalities)
-        raise NotImplementedError
-
-    def __and__(self, other):
-        return self.intersection(other)
-
-    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 __str__(self):
-        constraints = []
-        for constraint in self.equalities:
-            constraints.append('{} == 0'.format(constraint))
-        for constraint in self.inequalities:
-            constraints.append('{} >= 0'.format(constraint))
-        return '{}'.format(', '.join(constraints))
-
-    def __repr__(self):
-        if self.isempty():
-            return 'Empty'
-        elif self.isuniverse():
-            return 'Universe'
-        else:
-            return '{}({!r})'.format(self.__class__.__name__, str(self))
-
-    @classmethod
-    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)
-
-    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
-
-    @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())