#853: Add a pslq implementation to Sage
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Reporter: was | Owner: was
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-wishlist
Component: number theory | Resolution:
Keywords: | Work issues: need advice
on interface
Report Upstream: N/A | Reviewers: David Kirkby
Authors: Paul Zimmermann, Alex Ghitza | Merged in:
Dependencies: | Stopgaps:
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Comment (by AlexGhitza):
This past January, a student of mine and I have run some experiments
comparing fpLLL and the PSLQ implementations from ARPREC (we wanted to
take the best current implementations to get a realistic comparison). In
the examples we ran, we found almost no reason to use PSLQ instead of
fpLLL for finding integer relations. The only situation where PSLQ might
be more appropriate is when it is extremely expensive to generate extra
digits in the input floating point numbers. PSLQ has a slight edge here
because it tends to require fewer digits of precision than fpLLL. Most of
the time this is of no consequence because fpLLL is much faster. We'll
try to write something up describing our experiments and results, but I
don't know how soon I'll find time for that.
In terms of "stability", our experiments indicate that PSLQ tends to stick
with the correct answer once it finds it, as you add more digits of
precision. With fpLLL, you sometimes hit the right answer with, say 190
digits, but then you get different answers for a short while (say, 191 to
197 digits), and then it stabilises on the right answer again. Paul, I
can dig up an explicit example of this if you are interested. Again, I
don't see this as an issue from a practical point of view -- I would run
the algorithm until I get the exact same answer with 3 or 5 different
precisions.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/853#comment:24>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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