Hi,

this might be related to:

https://trac.sagemath.org/ticket/20752
https://trac.sagemath.org/ticket/20742

(and it is doctested).

Ciao,
Thierry



On Sat, Sep 16, 2017 at 03:17:27PM -0400, Bruno Le Floch wrote:
> Hello,
> 
> In fact, it seems that in Sage 7.2, cos((p/q)*pi) gets reduced mod pi
> instead of 2pi, at least in cases where it does not simplify to square
> roots:
> 
> sage: [cos(pi*(i+13)/13) - cos(pi*i/13)
>        for i in range(0,50) if i%13!=0] == [0]*46
> True
> 
> It would be good to know what fixed that bug.  It might be a Ginac bug.
> Perhaps cos(14*pi/9) should be added as a test of the cos function?
> 
> Bruno
> 
> On 09/16/2017 07:43 AM, John Cremona wrote:
> > You should upgrade to a more recent version:
> > 
> > ┌────────────────────────────────────────────────────────────────────┐
> > │ SageMath version 8.0, Release Date: 2017-07-21                     │
> > │ Type "notebook()" for the browser-based notebook interface.        │
> > │ Type "help()" for help.                                            │
> > └────────────────────────────────────────────────────────────────────┘
> > sage: float(cos(14*pi/9))
> > 0.17364817766693041
> > 
> > 
> > 
> > On 16 September 2017 at 12:27, Mickael Pechaud <mickaelpech...@gmail.com> 
> > wrote:
> >>  Hello,
> >>
> >> I'm running SageMath 7.2, on a 64bits laptop with a Ubuntu 16.04.2 LTS
> >> (xenial). I got a wrong answer from cos :
> >>
> >> sage: float(cos(14*pi/9))
> >> -0.17364817766693041
> >>
> >> It should be positive - and it's inconsistent with the following lines :
> >>
> >> sage: float(cos(14*pi/9-2*pi))
> >> 0.17364817766693041
> >>
> >>
> >> sage: float(14*pi/9)
> >> 4.886921905584122
> >>
> >> sage: float(cos(4.886921905584122))
> >> 0.17364817766692953
> >>
> >> Am I missing something, or is there an actual problem here ?
> >>
> >> Thanks in advance,
> >>
> >> Mickaël
> >>
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