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Integer.{perfect_power,is_prime_power,is_irreducible}: Handle easy cases without PARI #35847

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merged 5 commits into from
Jul 9, 2023
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Integer.{perfect_power,is_prime_power,is_irreducible}: Handle easy cases without PARI #35847

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94ef4f6
Integer.{perfect_power,is_prime_power}: Check easy cases first before…
mkoeppe Jun 27, 2023
f01b0c2
Integer.{perfect_power,is_prime_power}: Fix up return type
mkoeppe Jun 27, 2023
ab81af0
Integer.is_irreducible: Delegate to is_prime, so that easy cases are …
mkoeppe Jul 1, 2023
053f1a2
Integer.is_irreducible: Delegate to is_prime, so that easy cases are …
mkoeppe Jul 1, 2023
d2c9c5e
src/sage/rings/integer.pyx (is_prime_power, perfect_power): Add docte…
mkoeppe Jul 2, 2023
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53 changes: 47 additions & 6 deletions src/sage/rings/integer.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -4812,23 +4812,44 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):

sage: 144.perfect_power() # optional - sage.libs.pari
(12, 2)
sage: 1.perfect_power() # optional - sage.libs.pari
sage: 1.perfect_power()
(1, 1)
sage: 0.perfect_power() # optional - sage.libs.pari
sage: 0.perfect_power()
(0, 1)
sage: (-1).perfect_power() # optional - sage.libs.pari
sage: (-1).perfect_power()
(-1, 1)
sage: (-8).perfect_power() # optional - sage.libs.pari
(-2, 3)
sage: (-4).perfect_power() # optional - sage.libs.pari
sage: (-4).perfect_power()
(-4, 1)
sage: (101^29).perfect_power() # optional - sage.libs.pari
(101, 29)
sage: (-243).perfect_power() # optional - sage.libs.pari
(-3, 5)
sage: (-64).perfect_power() # optional - sage.libs.pari
(-4, 3)

TESTS::

sage: 4.perfect_power()
(2, 2)
sage: 256.perfect_power()
(2, 8)
"""
cdef long n
# Fast PARI-free path
if mpz_fits_slong_p(self.value):
n = mpz_get_si(self.value)
if -8 < n < 4:
return self, one
if n >= 4:
if not (n & 1):
if mpz_popcount(self.value) == 1:
return smallInteger(2), smallInteger(mpz_sizeinbase(self.value, 2) - 1)
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I would prefer sanity tests for this.
It's so easy to get this wrong by +-1....

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True. Added tests in d2c9c5e

if n < 1000:
if _small_primes_table[n >> 1]:
return self, one

parians = self.__pari__().ispower()
return Integer(parians[1]), Integer(parians[0])

Expand Down Expand Up @@ -5164,11 +5185,32 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
sage: n = 150607571^14
sage: n.is_prime_power() # optional - sage.libs.pari
True

TESTS::

sage: 2.is_prime_power(get_data=True)
(2, 1)
sage: 4.is_prime_power(get_data=True)
(2, 2)
sage: 512.is_prime_power(get_data=True)
(2, 9)
"""
cdef long n

if mpz_sgn(self.value) <= 0:
return (self, zero) if get_data else False

if mpz_fits_slong_p(self.value):
# Fast PARI-free path
n = mpz_get_si(self.value)
if not (n & 1):
if mpz_popcount(self.value) != 1:
return (self, zero) if get_data else False
return (smallInteger(2), smallInteger(mpz_sizeinbase(self.value, 2) - 1)) if get_data else True
if n < 1000:
if _small_primes_table[n >> 1]:
return (self, one) if get_data else True

global pari_is_prime_power
if pari_is_prime_power is None:
try:
Expand All @@ -5178,7 +5220,6 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
if pari_is_prime_power is not None:
return pari_is_prime_power(self, get_data)

cdef long n
if proof is None:
from sage.structure.proof.proof import get_flag
proof = get_flag(proof, "arithmetic")
Expand Down Expand Up @@ -5362,7 +5403,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
True
"""
cdef Integer n = self if self >= 0 else -self
return n.__pari__().isprime()
return n.is_prime(proof=True)

def is_pseudoprime(self):
r"""
Expand Down