Coverage for local/lib/python2.7/site-packages/sage/rings/pari_ring.py : 40%

""" 

Ring of pari objects 

AUTHORS: 

- William Stein (2004): Initial version. 

- Simon King (2011-08-24): Use UniqueRepresentation, element_class and 

proper initialisation of elements. 

""" 

# **************************************************************************** 

# Copyright (C) 2004 William Stein <wstein@gmail.com> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# 

# The full text of the GPL is available at: 

# 

# http://www.gnu.org/licenses/ 

# **************************************************************************** 

import sage.libs.pari.all as pari 

import sage.rings.ring as ring 

from sage.structure.element import RingElement 

from sage.structure.richcmp import richcmp 

from sage.misc.fast_methods import Singleton 

class Pari(RingElement): 

""" 

Element of Pari pseudo-ring. 

""" 

def __init__(self, x, parent=None): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: f = R('x^3 + 1/2') 

sage: f 

x^3 + 1/2 

sage: type(f) 

<class 'sage.rings.pari_ring.PariRing_with_category.element_class'> 

sage: loads(f.dumps()) == f 

True 

""" 

if parent is None: 

parent = _inst 

RingElement.__init__(self, parent) 

self.__x = pari.pari(x) 

def __repr__(self): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3); a 

3 

""" 

return str(self.__x) 

def _add_(self, other): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: b = R(11) 

sage: a = R(3) 

sage: a + b 

14 

""" 

return self.__class__(self.__x + other.__x, parent=_inst) 

def _sub_(self, other): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: b = R(11) 

sage: b - a 

8 

""" 

return self.__class__(self.__x - other.__x, parent=_inst) 

def _mul_(self, other): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: b = R(11) 

sage: b * a 

33 

""" 

return self.__class__(self.__x * other.__x, parent=_inst) 

def _div_(self, other): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: b = R(11) 

sage: b / a 

11/3 

""" 

return self.__x * (~other.__x) 

def __neg__(self): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: -a 

-3 

""" 

return self.__class__(-self.__x, parent=_inst) 

def __pow__(self, other): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: a^2 

9 

""" 

if not(other in PariRing()): 

other = Pari(other) 

return self.__class__(self.__x ** other.__x, parent=_inst) 

def __invert__(self): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: ~a 

1/3 

""" 

return self.__class__(~self.__x, parent=_inst) 

def _richcmp_(self, other, op): 

""" 

EXAMPLES:: 

sage: R = PariRing() 

sage: a = R(3) 

sage: b = R(11) 

sage: a < b 

True 

sage: a == b 

False 

sage: a > b 

False 

""" 

return richcmp(self.__x, other.__x, op) 

def __int__(self): 

return int(self.__x) 

class PariRing(Singleton, ring.Ring): 

""" 

EXAMPLES:: 

sage: R = PariRing(); R 

Pseudoring of all PARI objects. 

sage: loads(R.dumps()) is R 

True 

""" 

Element = Pari 

def __init__(self): 

ring.Ring.__init__(self, self) 

def __repr__(self): 

return 'Pseudoring of all PARI objects.' 

def _element_constructor_(self, x): 

if isinstance(x, Pari): 

return x 

return self.element_class(x, parent=self) 

def is_field(self, proof=True): 

return False 

def characteristic(self): 

raise RuntimeError("Not defined.") 

def random_element(self, x=None, y=None, distribution=None): 

""" 

Return a random integer in Pari. 

.. NOTE:: 

The given arguments are passed to ``ZZ.random_element(...)``. 

INPUT: 

- `x`, `y` -- optional integers, that are lower and upper bound 

for the result. If only `x` is provided, then the result is 

between 0 and `x-1`, inclusive. If both are provided, then the 

result is between `x` and `y-1`, inclusive. 

- `distribution` -- optional string, so that ``ZZ`` can make sense 

of it as a probability distribution. 

EXAMPLES:: 

sage: R = PariRing() 

sage: R.random_element() 

-8 

sage: R.random_element(5,13) 

12 

sage: [R.random_element(distribution="1/n") for _ in range(10)] 

[0, 1, -1, 2, 1, -95, -1, -2, -12, 0] 

""" 

from sage.all import ZZ 

return self(ZZ.random_element(x, y, distribution)) 

def zeta(self): 

""" 

Return -1. 

EXAMPLES:: 

sage: R = PariRing() 

sage: R.zeta() 

-1 

""" 

return self(-1) 

_inst = PariRing()