[seqfan] Re: how to simplify sin(3*Pi/10) etc in Maple

[Simon Plouffe]

Hello,

Yes, this does work but in addition you may get all the roots
even when <RootOf> is displayed of course when it is possible.

for that use the command : allvalues();

here explained : 
https://www.maplesoft.com/support/help/maple/view.aspx?path=allvalues


Best regards,
  Simon Plouffe


Le 2023-05-25 à 07:18, israel at math.ubc.ca a écrit :
> For other values of sin(a*Pi/b) or cos(a*Pi/b), convert(..., radical) 
> might not work, but you can try convert(...,RootOf).  For example:
>
>>  convert(sin(3*Pi/13), RootOf);
>
> RootOf(4096*_Z^12 - 13312*_Z^10 + 16640*_Z^8 - 9984*_Z^6 + 2912*_Z^4 - 
> 364*_Z^2 + 13, 0.6631226582)
>
> Note btw that the polynomial 4096*Z^12 - 13312*Z^10 + 16640*Z^8 - 
> 9984*Z^6 + 2912*Z^4 - 364*Z^2 + 13 is one of the irreducible factors 
> of T_26(Z) + 1 where T_26 is a Chebyshev polynomial of the first kind. 
> In general we have T_b(cos(a*Pi/b)) = cos(a*Pi) = (-1)^a.
>
> Cheers,
> Robert
>
>
> On May 24 2023, W. Edwin Clark wrote:
>
>> convert(sin(3*Pi/10),radical);
>>
>> On Wed, May 24, 2023 at 8:34PM Neil Sloane <njasloane at gmail.com> wrote:
>>
>>> How do I get Maple to evaluate expressions like sin(3*Pi/10) ?
>>>
>>> That one is easy, it is (1+sqrt(5))/4, just look up the decimal 
>>> expansion
>>> in the OEIS and you get the answer, A019863.
>>>
>>> But in general? I can't find an answer in any of the help pages.
>>>
>>> If you know the answer please post it here, to avoid duplication of 
>>> effort.
>>>
>>> -- 
>>> Seqfan Mailing list - http://list.seqfan.eu/
>>>
>>
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>
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