[GAP Forum] Re: Coefficients of constant polynomials

[Alexander Hulpke]

Dear Gap Forum,

Someone called `Anvita' wrote:

>
>>> If the function  "CoefficientsOfUnivariatePolynomial" is applied  
>>> to the
>>> unit polynomial, the result is [ 1 ], as expected:
>>> ...
>>> For the zero polynomial, however, it returns an empty set:
>>
>> Yes. the zero polynomial is stored by an empty coefficient list, as
>> there are no nonzero coefficients.
>>
>
> If the zero polynomial is stored as an empty list then why does the  
> function
> "UnivariatePolynomial" return an error with an empty list as the  
> second
> argument?

That is an oversight. (The conditions on coefficients is to be a list  
of ring elements, the empty list does not qualify and needs to be  
treated specially.) Thank you for spotting this. It will be corrected  
in a future release.

As a workaround you can issue the command:
InstallOtherMethod( UnivariatePolynomial, "ring,empty cof",true,
     [ IsRing, IsEmpty ], 0,
function( ring, cofs )
     return LaurentPolynomialByCoefficients( ElementsFamily(FamilyObj 
(ring)),cofs, 0, 1 );
end );

Best wishes,

     Alexander Hulpke