#16880: previous_prime, previous_prime_power, next_prime_power
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.7
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16880 | db1e869640dbb20d39e565970aaa8c5d58fa8953
Dependencies: | Stopgaps:
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Comment (by jdemeyer):
1. I don't know if `lesser or equal than` is proper English. How about
`less than or equal to`?
2. `PARI` instead of `Pari`.
3. In `next_prime_power` and `previous_prime_power`, a small optimization
is possible: you can replace
{{{
mpz_set(n.value, self.value)
mpz_add_ui(n.value, n.value, 1)
}}}
by
{{{
mpz_add_ui(n.value, self.value, 1)
}}}
and in `next_prime_power`, replace
{{{
if mpz_cmp_ui(n.value, 2) < 0:
mpz_set_ui(n.value, 2)
return n
}}}
by
{{{
if mpz_cmp_ui(self.value, 2) < 0:
return smallInteger(2)
}}}
4. Another algorithmic comment for `next_prime_power` (an analogous
comment holds for `previous_prime_power`): instead of computing the next
power of 2 and doing
{{{
while mpz_cmp(m.value, n.value) == 1:
}}}
I would instead check if `mpz_sizeinbase(n.value, 2)` increases during the
loop. In that case, we know that we skipped a power of 2.
--
Ticket URL: <http://trac.sagemath.org/ticket/16880#comment:20>
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