#18356: special resultants ``composed_sum`` and ``composed_product``
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Reporter: pernici | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.7
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pernici/ticket/18356 | 1fe9b052c8f1e49f9b0480f40dfa1937ef9f8dcf
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:31 pernici]:
> Replying to [comment:30 vdelecroix]:
> > Replying to [comment:29 pernici]:
> > > Replying to [comment:28 vdelecroix]:
> > > > Hi,
> > > >
> > > > Did you completely avoid the power series ring? We should provide
more methods to polynomial like:
> > > > - `inverse_series(self, prec, as_polynomial=False)`: return the
inverse series and if `as_polynomial` is true returns it as a polynomial
> > >
> > > Yes, I used `fmpq_poly_inv_series`, `fmpq_poly_exp_series`, so the
power series ring is not used.
> >
> > I think this is bad. This will make your code specific over Q. You
might consider implementing (in an other ticket) an `inverse_series` and
an `exp_series` method on polynoms that handle the option of returning a
polynom. This method would have a default implementation in
`polynomial_element.pyx` and specialized one for the FLINT classes.
>
> I have rewritten `composed_op` using `inverse_series`, `exp_series`,
methods in `polynomial_element.pyx`
> (without default implementation yet), using `_mul_trunc_` in #18420 as a
template.
> It is faster than the "resultant" algorithm in all the cases tested.
>
> I think that `inverse_series`, `exp_series`, etc. in
`polynomial_element.pyx`
> should always return a polynomial.
For a programmer this is clear. But not a user. If you ask
`inverse_series` you expect a series... but I do not have a strong
opinion. A possible alternative is to write:
- one global `def inverse_series(self, prec, as_polynomial=False)` in
`polynomial_element.pyx`
that would use
- several `cpdef Polynomial _inverse_series(self, long prec)` that return
polynomials.
> I could open a ticket on implementing these methods, depending on
#18420.
> Do you think that it is ok?
I think it would be good. Power series are by far too slow to be usable.
Please put me in cc.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18356#comment:32>
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