#15970: j_invariant_qexp won't allow substitution
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Reporter: katestange | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-6.2
Component: number theory | Resolution:
Keywords: j-invariant, laurent series, | Merged in:
q-expansion, substitution | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: |
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Comment (by fwclarke):
Replying to [comment:2 katestange]:
> But before we close the ticket, can we clarify what way the user should
accomplish the intended calculation? How can one approximate the
j-invariant for various tau in the upper half plane?
For numerical computations, `elliptic_j` will do:
{{{
sage: elliptic_j(I)
1728.00000000000
}}}
and the precision can be increased as in
{{{
sage: elliptic_j(sqrt(-1).n(128))
1728.0000000000000000000000000000000000
}}}
or
{{{
sage: tau = (1 + sqrt(-163))/2
sage: elliptic_j(tau.n(100))
-2.6253741264076799999999999999e17 + 1.3012822400356849057448214481e-12*I
sage: (-elliptic_j(tau.n(100)).real().round())^(1/3)
640320
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/15970#comment:3>
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