2009/5/7 Robert Bradshaw <rober...@math.washington.edu>:
>
> On May 7, 2009, at 2:15 PM, John Cremona wrote:
>
>> It is a documented feature -- look at the docstring which says
>>
>> def coefficient(self, degrees):
>> """
>> Return the coefficient of the variables with the degrees
>> specified in the python dictionary \code{degrees}.
>> Mathematically,
>> this is the coefficient in the base ring adjoined by the
>> variables
>> of this ring not listed in \code{degrees}. However, the
>> result
>> has the same parent as this polynomial.
>>
>> This function contrasts with the function \code
>> {monomial_coefficient}
>> which returns the coefficient in the base ring of a monomial.
>>
>> I do agree that it is a strange design, and would prefer
>> f.coefficient() to return an element of the base ring.
>
> I agree. I think it's to support stuff like
>
> sage: sage: K.<x,y,z>=QQ[]
> sage: f = (x+1)^5*(y+1)^3
> sage: f.coefficient(x^2*y^0)
> 10*y^3 + 30*y^2 + 30*y + 10
>
> which is also an annoying interface to work with.
That's more than an annoying interface -- if you wrote that in an exam
I would give you 0, since the coefficient of x^2*y^0 in that
polynomial is 10 (as reported by monomial_coefficient()). I would
need a lot of convincing that the current behaviour of coefficient()
makes sense -- I can see its use but it should have a different name!
John
>
>> 2009/5/7 Soroosh Yazdani <syazd...@gmail.com>:
>>> Hi,
>>>
>>> this might be a design decision, so I haven't filed a bug report
>>> for it yet.
>>> However, it seems that coefficient is returning the wrong type
>>> when it's
>>> called on multinomials. Here is an example code:
>>>
>>> sage: K.<x,y,z>=QQ[]
>>> sage: f = x^3+y^3+z^3
>>> sage: f.coefficient([3,0,0]).parent()
>>> Multivariate Polynomial Ring in x, y, z over Rational Field
>>>
>>> It makes more sense for the above return value to be the Rational
>>> Field.
>>> Similarly, f.coefficient([3,None,None]).parent(), should probably
>>> return
>>> "Multivariate Polynomial Ring in x, z over Rational Field".
>>>
>>> Should I file a bug for this?
>>> Soroosh
>>>
>>>
>>>>
>>>
>>
>> >
>
>
> >
>
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