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- Use 'r' instead of 'n' as variable name for radix
- Use 'ln' instead of 'Ln'
Both of these are for consistency.
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because it's not public API!
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These radices are large enough that:
- there is no reason to use them as actual radices
- calculating them takes a lot of time!
Therefore, the exact MTC and radix type shouldn't be calculated by
default. If you want to take the time, you still can with -l. I am
keeping the original 2^32 limit even with -l, because the problem with
that is not performance, it is that the resulting MTC could overflow a
uint64 (also the CAN list only goes up to this range).
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This can easily be estimated from existing information, so it's useful
to have, even in the compact view.
This estimate is more accurate (narrows the range down further) the
higher the radix's totative ratio. It also should be closer to the
actual value than the upper bound.
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This value can easily be calculated as φ(r)/r. There is no need to have
this now that I have a function φ(r) (renamed to its mathematical name,
Totient).
I removed totative ratio instead of totient because, while it is more
important, totient is an integer while totative ratio is a float. This
means that the totative ratio can be calculated exactly from the
totient, but not the other way round.
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Full digit maps will show every digit from 0 to 35, regardless of the
radix. This allows you to see extra fractions for small radices and to
get a digit map for radices above 36.
This isn't enabled by default because the extra "digits" added for small
radices aren't actually digits - so it may be unintuitive. There are
also some situations where only a radix's actual digits matter, such as
multiplication tables.
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In general, components go in the order Factors → Totatives → Size. 2345
Score was moved to fit this order, since it concerns both factors (2-5)
and totatives (5). The compact view was rearranged to have a consistent
order with the normal view.
Also I added the MTC estimate for very large radices into the compact
view, because it can be there.
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The compact output attempts to maximize the power-to-weight ratio of
this program, and the 2345 Score does not do this:
- It can already be easily determined from the prime factorization and
decimal radix, or trivially determined from the digit map.
- It does not take mixed radices (the radices you'll need to use bases
large enough to not show a digit map) into account.
- Although a big part of the 2345 Rank is strict improvements, some of
the decisions made in its design were necessarily arbitrary. The
alternatives give a more objective view.
The normal output is about showing everything worth showing, and the
2345 score is still useful there (especially for making sense of the
resulting complexity), so it is not removed from there.
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This is done for a few reasons:
- Allow the user to easily determine the exact value of the totative
ratio
- This information is important when the digit map isn't accessible (for
radices >36)
- More consistency with factors
I don't show the exact values of totatives like I do with factors
because they're far more common - the superior highly composite (i.e.
one of the numbers with the highest factor count) number 720720 has
240 factors and 138240 totatives, for example.
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The non-compact display is intended as a "full info" display, so it
makes sense to have more precision in these numbers. The compact
display is unchanged.
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This achieves two things:
- Decouples my code by putting the printing code into its own file
- Makes it easier to make alternate ways of printing (e.g. a compact
mode)
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