On 07/29/2010 11:10 AM, Simon King wrote:
> On Jul 29, 3:45 pm, eggartmumie <eggartmu...@googlemail.com> wrote:
>>> sage: p>>1
>>> -x + 4/9
>>
>> sorry, in reading reference.pdf I never came across this operation,
>
> Sorry, I don't know if the shift operator for polynomials is explained
> somewhere.
>
>> I just did not know that You can shift a polynomial!
>
> And this can certainly not be detected by tab completion. Sorry again.
It definitely wasn't obvious to me, but
sage: R.<x> = ZZ['t'][]
sage: p = R.random_element(6)
sage: p.shift?
seems to help.
>> This is exactly what I intended to get by calling the function (!)
>> goppapolynomial with parameters ZZ['t'] and var('x'), expecting it to
>> return the polynomial
>> (-3*t^2 - t - 1)*x^2 + (t^2 - t + 1)*x - 3*t - 2
>> over ZZ['t'] in indeterminant x. I was confused by the different
>> result I get on f = goppapolynomial(F,z) when printing
>> type(f)
>> or
>> f.parent()
>
> Yes, the difference between type(f) and f.parent() is quite important,
> though certainly not easy.
>
> I guess a first approximation can be phrased like this: The type tells
> you how an object is implemented. The parent tells you to what
> algebraic structure it belongs. Objects of the same type can have very
> different parents, and theoretically objects of different types can
Could you please give an example? Do you mean that for a given parent
an element could be implemented with FLINT or Singular, say?
> have the same parent.
>
>> Even though I use tab completion quite a lot I did not find the
>> methods coefficient and coeffs because I only tried the tab completion
>> on the rings and not on their elements, the polynomials.
>
> If you want to *get* the coefficients from an existing polynomial, I
> think using tab completion on this polynomial is natural. However,
> from your example c[0]*y^0+c[1]*y^1+c[2]*y^2, it seems that you have a
> list of coefficients and a ring and want to get an element of that
> ring.
>
> Here, the answer *should* be available with "R?", because this will
> also show you the documentation of the call method. Unfortunately, it
> seems that calling a univariate polynomial ring R['x'] on a list, like
> R['x']([1,3,0,1]), is not sufficiently documented.
Thanks for a very informative thread!
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