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fixing a bug in perfect_power #40850

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Merged
merged 2 commits into from
Sep 21, 2025
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fixing a bug in perfect_power #40850

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8e6bb50
fixing a bug
fchapoton Sep 18, 2025
5649932
add comment in doc
fchapoton Sep 19, 2025
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4 changes: 3 additions & 1 deletion src/sage/rings/integer.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -4963,6 +4963,8 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
(2, 2)
sage: 256.perfect_power()
(2, 8)
sage: (26**2).perfect_power()
(26, 2)
"""
cdef long n
# Fast PARI-free path
Expand All @@ -4974,7 +4976,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
if not (n & 1):
if mpz_popcount(self.value) == 1:
return smallInteger(2), smallInteger(mpz_sizeinbase(self.value, 2) - 1)
if n < 1000:
elif n < 1000:
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@mantepse mantepse Sep 18, 2025

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wouldn't it be better to test against len(_small_primes_table) (or store this in a constant)?

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@vincentmacri vincentmacri Sep 18, 2025 •
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wouldn't it be better to test against len(_small_primes_table) (or store this in a constant)?

_small_primes_table is kind of weird. It's not a list or table of primes themselves. Rather, _small_primes_table[n] is 1 if $2n + 1$ is prime, and 0 if $2n + 1$ is not prime (so _small_primes_table[0] = 0 because 1 is not prime, and _small_primes_table[1] = 1 because 3 is prime).

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@whoami730 whoami730 Sep 19, 2025

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This and similar logic is being employed in three different places in the code, ie, check if value < 1000 and is odd and if so, invoke _small_primes_table[value >> 1]. We should store this 1000 value in a constant.

if _small_primes_table[n >> 1]:
return self, one

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