#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 | 5f888c83095eab89acbd96ee09e067918a60c258
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:19 pernici]:
> The algorithm for `newton_sum` is slightly changed with respect to the
one written in BFSS, Lemma 1.
> I will change it to the latter form, which is simpler and slightly
faster.
> In either case there is no inversion, there is reversion though.
As far as I understand Lemma 1 is precisely Schoenage formula (but I did
not open the relevant paper). The algorithm of BFSS is Proposition 1. The
inversion is only computed up to the degree of the polynomial. Then there
are some iterations that depends on `prec`. Am I wrong?
> Lemma 1 comes from Schoenage, who used it in a numerical context. Should
I put the reference to
> Schoenage's paper, or is it sufficient to write "See [BFSS] and
references within." ?
I think it would make sense.
About the name, what do you think about `newton_series` instead? It would
make the result clearer. And please, add the mathematical definition in
the function.
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/18356#comment:20>
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