(cls, partition, integer=None)
return obj
Generates a new IntegerPartition object from a list or dictionary.

        The partition can be given as a list of positive integers or a
        dictionary of (integer, multiplicity) items. If the partition is
        preceeded by an integer an error will be raised if the partition
        does not sum to that given integer.

        Examples
        ========

        >>> from sympy.combinatorics.partitions import IntegerPartition
        >>> a = IntegerPartition([5, 4, 3, 1, 1])
        >>> a
        IntegerPartition(14, (5, 4, 3, 1, 1))
        >>> print(a)
        [5, 4, 3, 1, 1]
        >>> IntegerPartition({1:3, 2:1})
        IntegerPartition(5, (2, 1, 1, 1))

        If the value that the partion should sum to is given first, a check
        will be made to see n error will be raised if there is a discrepancy:
        >>> IntegerPartition(10, [5, 4, 3, 1])
        Traceback (most recent call last):
        ...
        ValueError: The partition is not valid
Generates a new IntegerPartition object from a list or dictionary.
Generates a new IntegerPartition object from a list or dictionary .
def __new__(cls, partition, integer=None):
        """
        Generates a new IntegerPartition object from a list or dictionary.

        The partition can be given as a list of positive integers or a
        dictionary of (integer, multiplicity) items. If the partition is
        preceeded by an integer an error will be raised if the partition
        does not sum to that given integer.

        Examples
        ========

        >>> from sympy.combinatorics.partitions import IntegerPartition
        >>> a = IntegerPartition([5, 4, 3, 1, 1])
        >>> a
        IntegerPartition(14, (5, 4, 3, 1, 1))
        >>> print(a)
        [5, 4, 3, 1, 1]
        >>> IntegerPartition({1:3, 2:1})
        IntegerPartition(5, (2, 1, 1, 1))

        If the value that the partion should sum to is given first, a check
        will be made to see n error will be raised if there is a discrepancy:
        >>> IntegerPartition(10, [5, 4, 3, 1])
        Traceback (most recent call last):
        ...
        ValueError: The partition is not valid

        """
        if integer is not None:
            integer, partition = partition, integer
        if isinstance(partition, (dict, Dict)):
            _ = []
            for k, v in sorted(list(partition.items()), reverse=True):
                if not v:
                    continue
                k, v = as_int(k), as_int(v)
                _.extend([k]*v)
            partition = tuple(_)
        else:
            partition = tuple(sorted(map(as_int, partition), reverse=True))
        sum_ok = False
        if integer is None:
            integer = sum(partition)
            sum_ok = True
        else:
            integer = as_int(integer)

        if not sum_ok and sum(partition) != integer:
            raise ValueError("Partition did not add to %s" % integer)
        if any(i < 1 for i in partition):
            raise ValueError("The summands must all be positive.")

        obj = Basic.__new__(cls, integer, partition)
        obj.partition = list(partition)
        obj.integer = integer
        return obj
def __new__ ( cls , partition , integer = None ) : if integer is not None : integer , partition = partition , integer if isinstance ( partition , ( dict , Dict ) ) : _ = [ ] for k , v in sorted ( list ( partition . items ( ) ) , reverse = True ) : if not v : continue k , v = as_int ( k ) , as_int ( v ) _ . extend ( [ k ] * v ) partition = tuple ( _ ) else : partition = tuple ( sorted ( map ( as_int , partition ) , reverse = True ) ) sum_ok = False if integer is None : integer = sum ( partition ) sum_ok = True else : integer = as_int ( integer ) if not sum_ok and sum ( partition ) != integer : raise ValueError ( "Partition did not add to %s" % integer ) if any ( i < 1 for i in partition ) : raise ValueError ( "The summands must all be positive." ) obj = Basic . __new__ ( cls , integer , partition ) obj . partition = list ( partition ) obj . integer = integer return obj