def points(self):
"""
Return a list of the generating points in this Mordell-Weil
group.
OUTPUT:
(list) A list of lists of length 3, each holding the
primitive integer coordinates `[x,y,z]` of a generating
point.
EXAMPLES::
sage: E = mwrank_EllipticCurve([0,0,1,-7,6])
sage: EQ = mwrank_MordellWeil(E)
sage: EQ.search(1)
P1 = [0:1:0] is torsion point, order 1
P1 = [-3:0:1] is generator number 1
...
P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion)
sage: EQ.points()
[[1, -1, 1], [-2, 3, 1], [-14, 25, 8]]
"""
from sage.misc.all import preparse
from sage.rings.all import Integer
return eval(preparse(self.__mw.getbasis().replace(":", ",")))
def points(self):
"""
Return a list of the generating points in this Mordell-Weil
group.
OUTPUT:
(list) A list of lists of length 3, each holding the
primitive integer coordinates `[x,y,z]` of a generating
point.
EXAMPLES::
sage: E = mwrank_EllipticCurve([0,0,1,-7,6])
sage: EQ = mwrank_MordellWeil(E)
sage: EQ.search(1)
P1 = [0:1:0] is torsion point, order 1
P1 = [-3:0:1] is generator number 1
...
P4 = [12:35:27] = 1*P1 + -1*P2 + -1*P3 (mod torsion)
sage: EQ.points()
[[1, -1, 1], [-2, 3, 1], [-14, 25, 8]]
"""
from sage.misc.all import preparse
from sage.rings.all import Integer
return eval(preparse(self.__mw.getbasis().replace(":", ",")))
def gens(self):
"""
Return a list of the generators for the Mordell-Weil group.
EXAMPLES::
sage: E = mwrank_EllipticCurve([0, 0, 1, -1, 0])
sage: E.gens()
[[0, -1, 1]]
"""
self.saturate()
from sage.misc.all import preparse
from sage.rings.all import Integer
return eval(preparse(self.__two_descent_data().getbasis().replace(":",",")))