#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):
The change was made in #3979. Until Sage 5.4, substitution into power
series was incorrectly implemented in many ways. In particular, it was
possible to substitute a non-zero scalar into a series only specified up
to a given precision, but this cannot make sense.
In your case,
{{{
sage: jq = j_invariant_qexp(10)
sage: jq.truncate(10)(exp(-2*pi)).n(100)
1727.9999999999882175423506871
}}}
gives the answer you want. But its meaning depends on assuming
(correctly) that the infinitely many unspecified terms can be ignored (to
within 10^-10^).
In general, writing, say,
{{{
f = x + x^2 + O(x^3)
}}}
tells us nothing about how `f(2)` should be defined, or whether `6` might
be a reasonable approximation.
--
Ticket URL: <http://trac.sagemath.org/ticket/15970#comment:1>
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