#18242: Added algorithm computing special resultants
-------------------------------------+-------------------------------------
Reporter: pernici | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.7
Component: number fields | Resolution:
Keywords: qqbar resultant | Merged in:
exactify minpoly | Reviewers:
Authors: | Work issues:
Report Upstream: N/A | Commit:
Branch: | e0626dcabde6434cedd0c8736df198065b7a01d6
u/pernici/ticket/18242 | Stopgaps:
Dependencies: #17886 |
-------------------------------------+-------------------------------------
Comment (by vdelecroix):
Hello,
This ticket is still in state "new" but here are some remarks.
I would make this ticket independent of #17886 and ignore completely the
potential application to `QQbar` (considering it in another ticket). It
would be more flexible that way.
You implemented functions but I guess some of them would better be methods
over polynomials (that is methods of
`polynomial.polynomial_element.Polynomial`). For example, the
`hadamard_product` or even the `composed_sum`. So move them. For
`_hadamard_exp` it is only well defined in zero characteristic, so I am
not sure what is the most appropriate; what do you think?
Did you do some serious benchmark to see which methods is faster depending
on `p1` and `p2`? I guess it might aslo depends on the sparseness of the
polynomials, the size of the coefficients.
1. `newton_sum`
- I would rather add the power series ring object `R` as an argument.
Building a ring is always costly.
- In
{{{
p2 = R(QQ(1)/p1)
}}}
You would better do
{{{
p2 = ~R(p1)
}}}
you would avoid computing `1/p1` in the fraction field.
- It would be faster to return `p3.truncate()` or `res.truncate()`
instead of adding a truncation argument
- the argument name `typ` is horrible. Be more explicit about what it
is. "a related expression" is not an explanation of the output!
2. In `hadamard_product` there is no need to build the list of
coefficients. You can access the coefficients of a polynomial `p` through
`p[i]`. So just do
{{{
def hadamard_product(p1, p2):
R = p1.parent()
return R([p1[i]*p2[i] for i in range(min(p1.degree(),
p2.degree())+1)])
}}}
(I recall that this function must move as a method of univariate
polynomials)
3. `composed_product`
- you duplicated the code for `BFSS`... moreover if the argument
`algorithm` is neither `"resultant"` nor `"BFSS"` an error should be
raised.
- I guess that the resultant method works in any characteristic?
Sided note: the Bostan-Flajolet-Salvy-Schost deals with any
characteristic. So it would be interesting to have a more general
implementation.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/18242#comment:11>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
