#19738: inconsistency in what simplify() does on trigonometrics expression
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Reporter: thome | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-7.0
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: Reported upstream. Developers | Work issues:
acknowledge bug. | Commit:
Branch: | Stopgaps:
Dependencies: |
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Changes (by rws):
* upstream: N/A => Reported upstream. Developers acknowledge bug.
Old description:
> I stumbled on the following oddity during an exercise class (sage-6.8,
> x86_64-linux, debian 8.2).
> {{{
> sage: simplify(cos(pi/12))
> 1/12*sqrt(6)*(sqrt(3) + 3)
> sage: simplify(sin(pi/12))
> -1/12*sqrt(6)*(sqrt(3) - 3)
> sage: simplify(exp(i*pi/12))
> e^(1/12*I*pi)
> }}}
> Is there any rationale for this ? It looks like an inconsistency.
New description:
I stumbled on the following oddity during an exercise class (sage-6.8,
x86_64-linux, debian 8.2).
{{{
sage: simplify(cos(pi/12))
1/12*sqrt(6)*(sqrt(3) + 3)
sage: simplify(sin(pi/12))
-1/12*sqrt(6)*(sqrt(3) - 3)
sage: simplify(exp(i*pi/12))
e^(1/12*I*pi)
}}}
Is there any rationale for this ? It looks like an inconsistency.
See https://github.com/pynac/pynac/issues/113
--
Comment:
Note expansion is done without the need for simplify.
Certainly the enhancement is within reach. There is a minor catch:
although shortly before we have extended the values `m` for which
`sin/cos/tan(n/m*pi)` is expanded in roots, simply doing `I*sin+cos` can
result in mixed expressions because implementations differed for `sin` vs
`cos`, e.g.
{{{
sage: sin(pi/15)
sin(1/15*pi)
sage: cos(pi/15)
1/8*sqrt(5) + 1/4*sqrt(3/2*sqrt(5) + 15/2) - 1/8
sage: I*sin(pi/15)+cos(pi/15)
1/8*sqrt(5) + 1/4*sqrt(3/2*sqrt(5) + 15/2) + I*sin(1/15*pi) - 1/8
}}}
The reason for the difference was the complexity of results---we stopped
when the roots were nested more than twice.
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Ticket URL: <http://trac.sagemath.org/ticket/19738#comment:2>
Sage <http://www.sagemath.org>
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