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implement general Newton's method root finding for power series rings #6397

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ncalexan mannequin opened this issue Jun 24, 2009 · 3 comments
Open

implement general Newton's method root finding for power series rings #6397

ncalexan mannequin opened this issue Jun 24, 2009 · 3 comments
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@malb
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c: commutative algebra p: major / 3 s: needs work t: enhancement t: feature

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ncalexan mannequin commented Jun 24, 2009

Extracting a square root of a power series is implemented in power_series_ring_element.pyx. Could we have the more general "improving a root of a polynomial" Newton's method?

My use case is calculating Puiseaux expansions around points of algebraic curves.

CC: @robertwb @williamstein

Component: commutative algebra

Keywords: power series root newton method

Author: Nick Alexander

Issue created by migration from https://trac.sagemath.org/ticket/6397
@ncalexan ncalexan mannequin assigned malb Jun 24, 2009
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ncalexan mannequin commented Jun 24, 2009

Author: Nick Alexander

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ncalexan mannequin commented Jun 24, 2009

comment:1

Here's a stand-alone implementation that needs to be plugged into the hell that is polynomial.roots().

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ncalexan mannequin commented Jun 24, 2009

Attachment: trac_6397-power-series-newton-ncalexan-1.pyx.gz

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c: commutative algebra p: major / 3 s: needs work t: enhancement t: feature
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