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Commit Graph

4 Commits

Author SHA1 Message Date
Simon Tatham
072d3c665a numbertheory.py: generalise SqrtModP to do other roots.
I'm about to want to solve quartics mod a prime, which means I'll need
to be able to take cube roots mod p as well as square roots.

This commit introduces a more general class which can take rth roots
for any prime r, and moreover, it can do it in a general cyclic group.
(You have to tell it the group's order and give it some primitives for
doing arithmetic, plus a way of iterating over the group elements that
it can use to look for a non-rth-power and roots of unity.)

That system makes it nicely easy to test, because you can give it a
cyclic group represented as the integers under _addition_, and then
you obviously know what all the right answers are. So I've also added
a unit test system checking that.
2020-02-28 20:40:08 +00:00
Simon Tatham
7be2e16023 numbertheory.py: make the ModP class hashable.
That will let me keep them in sets.
2020-02-28 20:40:08 +00:00
Simon Tatham
3ee9b92935 numbertheory.py: factor out invert().
I'm about to want to reuse it.
2020-02-28 20:40:08 +00:00
Simon Tatham
122d785283 eccref.py: move support routines into a new file.
I'm about to want to expand the underlying number-theory code, so I'll
start by moving it into a file where it has room to grow without
swamping the main purpose of eccref.py.
2020-02-28 20:40:08 +00:00