Thanks William and Nils!
So now I can write better code than yesterday and, as John says, the only
remaining question is how someone with no sage experience is supposed to
work out for themselves that if R is a polynomial ring then R([1,2,3]) is
the way to create 3x^2+2x+1.
Let me stress that I am not ruling out that there is a sensible algorithmic
way to do this from the docs! I'm just saying I couldn't figure out how to
use the docs to answer this sort of question yesterday, whereas my
experience with other programming languages is that in the end I find a
resource (possibly via google) which, whenever you want to know about how
to know about foobars, will offer you a page titled "foobars" with an
essentially complete list of how to create foobars, coerce them to and from
other data structures, and manipulate them. I'm not talking about a
tutorial with examples, I'm talking about a resource giving essentially
complete documentation about certain common objects.
Of course it could well be just a matter of experience. For all I know, it
might be a general thing in sage that if the parent of f is R, and if S is
a bunch of data that can be used to build an f, then R(S) will pretty much
always work. If this is the case then I should just do some more coding
until I get the hang of it.
Kevin
On Wednesday, 9 April 2014 08:59:11 UTC+1, John Cremona wrote:
>
> These clever hacks do not take away from Kevin's main points: that
> getting field automorphisms to act on objects like polynomials over
> the field, with related functionality (norms etc); and that basic
> functions related to polynomials (extracting coefficients and creating
> a poly from a list of coeffs) should not be hard to find in the
> documentation.
>
> John
>
> On 9 April 2014 00:05, Nils Bruin <nbr...@sfu.ca <javascript:>> wrote:
> > On Tuesday, April 8, 2014 1:55:49 PM UTC-7, Nils Bruin wrote:
> >>
> >> F=Qxz(f) #this conveniently lifts z to a
> >> transcendental in Q[x,z]
> >
> >
> > Oops, that only works because of the last-resort attempt of converting f
> to
> > a string and then feeding the string to Qxz. One probably shouldn't rely
> on
> > such code in production situations. You'd be better off using
> >
> > F=Qxz({ (degx,degz) :cfz for degx,cfx in enumerate(f.list()) for
> degz,cfz in
> > enumerate(cfx.list())})
> >
> > which won't win any prizes for legibility and only qualifies as a
> one-liner
> > in the technical sense, but it is much faster than the string-based
> > conversion.
> >
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