pari_group.py

r"""
PARI Groups
"""

import group
from sage.libs.all import pari_gen
from sage.rings.all import Integer
from sage.structure.parent import Parent

class PariGroup(group.Group):
    def __init__(self, x, degree=None):
        """
        EXAMPLES::

            sage: R.<x> = PolynomialRing(QQ)
            sage: f = x^4 - 17*x^3 - 2*x + 1
            sage: G = f.galois_group(pari_group=True); G
            PARI group [24, -1, 5, "S4"] of degree 4
            sage: G.category()
            Category of finite groups

        Caveat: fix those tests and/or document precisely that this is
        an abstract group without explicit elements::

            sage: TestSuite(G).run()
            Failure in
            ...
            The following tests failed: _test_an_element, _test_associativity, _test_elements, _test_elements_eq, _test_enumerated_set_contains, _test_enumerated_set_iter_cardinality, _test_enumerated_set_iter_list, _test_inverse, _test_one, _test_prod, _test_some_elements
        """
        if not isinstance(x, pari_gen):
            raise TypeError, "x (=%s) must be a PARI gen"%x
        self.__x = x
        self.__degree = degree
        from sage.categories.finite_groups import FiniteGroups
        Parent.__init__(self, category = FiniteGroups())

    def __repr__(self):
        return "PARI group %s of degree %s"%(self.__x, self.__degree)

    def __cmp__(self, other):
        if not isinstance(other, PariGroup):
            return cmp(type(self), type(other))
        return cmp((self.__x, self.__degree), (other.__x, other.__degree))

    def _pari_(self):
        return self.__x

    def degree(self):
        return self.__degree

    def order(self):
        return Integer(self.__x[0])

    def permutation_group(self):
        if self.__degree is None:
            raise NotImplementedError
        import perm_gps.permgroup_named
        return perm_gps.permgroup_named.TransitiveGroup(self.__degree, self.__x[2])
    
    _permgroup_ = permutation_group