Module garoupa.algebra.abs.element

Classes

class Element (i: int, order: int)

Expand source code

@dataclass
class Element(ABC):
    i: int
    order: int
    _id = None
    _hosh = None

    def __post_init__(self):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**2, 64**32).bits - 1
        192.0
        """
        self.name = f"{self.__class__.__name__.lower()}_{self.i}"
        self.bits = log(self.order, 2)

    @abstractmethod
    def __mul__(self, other):
        pass

    def __xor__(self, other):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**2,64**5) ^ 3
        ds4096
        """
        return reduce(operator.mul, [self] * other)

    __pow__ = __xor__

    def __repr__(self):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**3, 64**5) ^ 3
        ds262144
        """
        return self.name

    def __eq__(self, other):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**2, 64**5) ^ 3 == Ds(4096, 64**5)
        True
        """
        return self.name == other.name

    def __hash__(self):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> isinstance(hash(Ds(64**2,64**5)), int)
        True
        """
        return hash(repr(self))

    @property
    def hosh(self):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**2,64**5).hosh.id
        '0_000100000_____________________________'
        """
        if self._hosh is None:
            self._hosh = Hosh.fromn(self.i)
        return self._hosh

    @property
    def id(self):
        """
        Usage:

        >>> from garoupa.algebra.dihedral import Ds
        >>> Ds(64**2,64**5).id
        '0_000100000_____________________________'
        """
        if self._id is None:
            self._id = self.hosh.id
        return self._id

Element(i: int, order: int)

Ancestors

• abc.ABC

Subclasses

• Nat
• Natm
• Dr
• Ds
• Mat
• Mat128bit
• Mat8bit
• Tuple
• Perm

Instance variables

prop hosh

Expand source code

@property
def hosh(self):
    """
    Usage:

    >>> from garoupa.algebra.dihedral import Ds
    >>> Ds(64**2,64**5).hosh.id
    '0_000100000_____________________________'
    """
    if self._hosh is None:
        self._hosh = Hosh.fromn(self.i)
    return self._hosh

Usage:

>>> from garoupa.algebra.dihedral import Ds
>>> Ds(64**2,64**5).hosh.id
'0_000100000_____________________________'

var i : int

prop id

Expand source code

@property
def id(self):
    """
    Usage:

    >>> from garoupa.algebra.dihedral import Ds
    >>> Ds(64**2,64**5).id
    '0_000100000_____________________________'
    """
    if self._id is None:
        self._id = self.hosh.id
    return self._id

Usage:

>>> from garoupa.algebra.dihedral import Ds
>>> Ds(64**2,64**5).id
'0_000100000_____________________________'

var order : int