def __init__(self, poly, prec, print_mode, names, element_class): """ Initializes self INPUTS:: - poly -- Polynomial defining this extension. - prec -- The precision cap - print_mode -- a dictionary with print options - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name) - element_class -- the class for elements of this unramified extension. EXAMPLES:: sage: R.<a> = Zq(27) #indirect doctest """ # base = poly.base_ring() # if base.is_field(): # self._PQR = pqr.PolynomialQuotientRing_field(poly.parent(), poly, name = names) # else: # self._PQR = pqr.PolynomialQuotientRing_domain(poly.parent(), poly, name = names) pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class) self._res_field = GF( self.prime_pow.pow_Integer_Integer(poly.degree()), name=names[1], modulus=poly.change_ring(poly.base_ring().residue_field()), )
def __init__(self, poly, prec, print_mode, names, element_class): """ Initializes self INPUT: - poly -- Polynomial defining this extension. - prec -- The precision cap - print_mode -- a dictionary with print options - names -- a 4-tuple, (variable_name, residue_name, unramified_subextension_variable_name, uniformizer_name) - element_class -- the class for elements of this unramified extension. EXAMPLES:: sage: R.<a> = Zq(27) #indirect doctest """ #base = poly.base_ring() #if base.is_field(): # self._PQR = pqr.PolynomialQuotientRing_field(poly.parent(), poly, name = names) #else: # self._PQR = pqr.PolynomialQuotientRing_domain(poly.parent(), poly, name = names) pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class) self._res_field = GF(self.prime_pow.pow_Integer_Integer(poly.degree()), name=names[1], modulus=poly.change_ring( poly.base_ring().residue_field()))
def __init__(self, poly, prec, print_mode, names, element_class): """ Initializes self. EXAMPLES:: sage: A = Zp(7,10) sage: S.<x> = A[] sage: B.<t> = A.ext(x^2+7) #indirect doctest """ pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)
def __init__(self, poly, prec, print_mode, names, element_class): """ Initializes self. EXAMPLES:: sage: A = Zp(7,10) sage: S.<x> = A[] sage: B.<t> = A.ext(x^2+7) #indirect doctest """ pAdicExtensionGeneric.__init__(self, poly, prec, print_mode, names, element_class)