#18954: special values of trig. functions with arguments n*pi/5
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: Fixed upstream, but not in a | Work issues:
stable release. | Commit:
Branch: | Stopgaps:
Dependencies: pynac-0.4.3 |
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Changes (by rws):
* dependencies: => pynac-0.4.3
* upstream: N/A => Fixed upstream, but not in a stable release.
Comment:
New code in Pynac does the following:
{{{
sage: sin(pi/5)
1/4*sqrt(-2*sqrt(5) + 10)
sage: sin(pi/8)
1/2*sqrt(-sqrt(2) + 2)
sage: sin(pi/24)
1/4*sqrt(-2*sqrt(6) - 2*sqrt(2) + 8)
sage: sin(pi/30)
-1/8*sqrt(5) + 1/4*sqrt(-3/2*sqrt(5) + 15/2) - 1/8
sage: cos(pi/8)
1/2*sqrt(sqrt(2) + 2)
sage: cos(pi/10)
1/2*sqrt(1/2*sqrt(5) + 5/2)
sage: cos(pi/12)
1/12*sqrt(6)*(sqrt(3) + 3)
sage: cos(pi/15)
1/8*sqrt(5) + 1/4*sqrt(3/2*sqrt(5) + 15/2) - 1/8
sage: cos(pi/24)
1/4*sqrt(2*sqrt(6) + 2*sqrt(2) + 8)
sage: tan(pi/5)
sqrt(-2*sqrt(5) + 5)
sage: tan(pi/8)
sqrt(2) - 1
sage: tan(pi/10)
sqrt(-2/5*sqrt(5) + 1)
sage: tan(pi/16)
-sqrt(2) + sqrt(2*sqrt(2) + 4) - 1
sage: tan(pi/20)
sqrt(5) - 1/2*sqrt(8*sqrt(5) + 20) + 1
sage: tan(pi/24)
sqrt(6) - sqrt(-2*sqrt(6) + 5) - 2
sage: all(sin(rat*pi).n(200)-sin(rat*pi,hold=True).n(200) < 1e-30 for rat
in [1/5,2/5,1/30,7/30,11/30,13/30,1/8,3/8,1/24,5/24,7/24,11/24])
True
sage: all(cos(rat*pi).n(200)-cos(rat*pi,hold=True).n(200) < 1e-30 for rat
in [1/10,3/10,1/12,5/12,1/15,2/15,4/15,7/15,1/8,3/8,1/24,5/24,11/24])
True
sage: all(tan(rat*pi).n(200)-tan(rat*pi,hold=True).n(200) < 1e-30 for rat
in
[1/5,2/5,1/10,3/10,1/20,3/20,7/20,9/20,1/8,3/8,1/16,3/16,5/16,7/16,1/24,5/24,7/24,11/24])
True
}}}
This ticket should merge them as doctests.
--
Ticket URL: <http://trac.sagemath.org/ticket/18954#comment:2>
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