Module garoupa.algebra.dihedral.d

#  Copyright (c) 2021. Davi Pereira dos Santos
#
#  Functions Based on Gabriel Dalforno code:
#  order_hist, euler
#
#  This file is part of the garoupa project.
#  Please respect the license - more about this in the section (*) below.
#
#  garoupa is free software: you can redistribute it and/or modify
#  it under the terms of the GNU General Public License as published by
#  the Free Software Foundation, either version 3 of the License, or
#  (at your option) any later version.
#
#  garoupa is distributed in the hope that it will be useful,
#  but WITHOUT ANY WARRANTY; without even the implied warranty of
#  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#  GNU General Public License for more details.
#
#  You should have received a copy of the GNU General Public License
#  along with garoupa.  If not, see <http://www.gnu.org/licenses/>.
#
#  (*) Removing authorship by any means, e.g. by distribution of derived
#  works or verbatim, obfuscated, compiled or rewritten versions of any
#  part of this work is a crime and is unethical regarding the effort and
#  time spent here.

from itertools import chain, repeat

from garoupa.algebra.dihedral.dr import Dr
from garoupa.algebra.dihedral.ds import Ds
from garoupa.algebra.matrix.group import Group
from garoupa.algebra.product.product import Product


class D(Group):
    def __init__(self, n, seed=None):
        """
        Usage:

        >>> G = D(1414343245, seed=0)
        >>> round(G.comm_degree, 2)
        0.25
        >>> G, ~G, G^2
        (D1414343245, ds1627694678, D1414343245×D1414343245)
        """
        self.r = lambda: (Dr(r, n) for r in range(n))
        self.s = lambda: (Ds(s, n) for s in range(n))
        sorted = lambda: chain(self.s(), self.r())
        super().__init__(Dr(0, n), sorted, seed)
        self.n = n

    @property
    def comm_degree(self):
        """Exact commutativity degree"""
        num = (self.n + 6) if self.n % 2 == 0 else (self.n + 3)
        den = 2 * self.order
        return num / den

    def __iter__(self):
        while True:
            yield self.rnd.choice([Dr, Ds])(self.samplei(), self.n)

    def __repr__(self):
        return f"D{self.n}"

    def __xor__(self, other):
        return Product(*repeat(self, other))

    __pow__ = __xor__

    def replace(self, *args, **kwargs):
        """
        Usage:

        >>> G = D(1414343245, seed=0)
        >>> ~G.replace(seed=1)
        dr1222356005
        """
        dic = {"n": self.n, "seed": self.seed}
        dic.update(kwargs)
        return self.__class__(**dic)

    @property
    def order_hist(self):
        """Sorted histogram of element orders.

        Based on Gabriel Dalforno code.

        Usage:

        >>> D(7).order_hist
        {1: 1, 2: 7, 7: 6}
        """
        if self._order_hist is None:
            rule = self.n % 2
            hist = {1: 1, 2: self.n if rule != 0 else self.n + 1}
            rng = range(3, self.n + 1, 2) if rule != 0 else range(3, self.n + 1)
            for d in rng:
                if self.n % d == 0:
                    hist[d] = self.euler(d)
            self._order_hist = dict(sorted(hist.items()))
        return self._order_hist

    def euler(self, d):
        """Euler Totient Function
        Based on Gabriel Dalforno code."""
        phi = 1
        for i in range(2, d):
            if self.gcd(i, d) == 1:
                phi += 1
        return phi


#     @property
#     def order_hist(self):
#         """Sorted histogram of element orders.

#         Usage
#         >>> D(7).order_hist
#         {1: 1, 2: 7, 7: 6}

#         Based on Gabriel Dalforno code."""
#         if self._order_hist is None:
#             if self.n % 2 == 0:
#                 raise Exception("Cannot calculate histogram for even n:", self.n)
#             hist = {1: 1, 2: self.n}
#             for d in range(3, self.n + 1, 2):
#                 if self.n % d == 0:
#                     hist[d] = self.euler
#             self._order_hist = dict(sorted(hist.items()))
#         return self._order_hist

#     @property
#     def euler(self):
#         """Euler Totient Function

#         Based on Gabriel Dalforno code."""
#         if self._euler is None:
#             self._euler = 1
#             for i in range(2, self.n):
#                 if self.gcd(i, self.n) == 1:
#                     self._euler += 1
#         return self._euler