#14551: Tuning nth root for finite fields
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Reporter: roed | Owner: AlexGhitza
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.10
Component: basic arithmetic | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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As of #7931, Sage uses an algorithm due to Johnston for computing the
`n`th root of finite field elements and elements modulo `n`. In `GF(p)`
for very large `p` and small `n` this algorithm is inferior to just
factoring `x^n-a`, since it requires a primitive root modulo `p`.
Preliminary timings indicate that Johnston's algorithm is sometimes faster
even in the range of `80` decimal digits, but it sometimes fails
spectacularly with runtime 300 times slower than factoring the polynomial.
We should add the polynomial option as an algorithm to `n`th root and have
a reasonable default based on the size of `n` and `p`.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14551>
Sage <http://www.sagemath.org>
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