#4388: elliptic curves: basis_matrix command totally broken
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Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.2
Component: number theory | Resolution:
Keywords: |
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Comment (by cremona):
Replying to [comment:2 was]:
> But I really wanted basis_matrix(), since I wanted to compute the
determinant of the basis matrix in order to find the volume of the period
lattice.
>
> There is no volume method. That would also be nice.
It _is_ there: complex_area() (not my choice of name)!
>
> I think at least mathematically the idea of "basis matrix" makes sense,
and I was happy it was there (except that it is broken).
You'll have to explain it to me. Do you want the 2x2 matrix of reals
consisting of the real and imaginary parts of the period basis? That
would be easy to add, like this:
{{{
sage: E = EllipticCurve('389a1')
sage: L = E.period_lattice()
sage: M = Matrix([[CC(w).real(), CC(w).imag()] for w in L.basis()]); M
[ 2.49021256085505 0.000000000000000]
[0.000000000000000 1.97173770155165]
sage: M.det()
4.91004599111539
sage: L.complex_area()
4.91004599111539
}}}
and
{{{
sage: E = EllipticCurve('11a1')
sage: L = E.period_lattice()
sage: M = Matrix([[CC(w).real(), CC(w).imag()] for w in L.basis()]); M
[ 1.26920930427955 0.000000000000000]
[0.634604652139777 1.45881661693850]
sage: M.det()
1.85154362345596
sage: L.complex_area()
1.85154362345596
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4388#comment:3>
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