sagemathgh-35019: add limit= argument to Integer.prime_divisors()

`Integer.factor()` has an optional `limit=` argument to restrict the
search to prime factors up to a certain size. This patch adds a similar
argument to the `.prime_divisors()` method.

URL: sagemath#35019
Reported by: Lorenz Panny
Reviewer(s): Edgar Costa, Lorenz Panny

build/pkgs/configure/checksums.ini

@@ -1,4 +1,4 @@
 tarball=configure-VERSION.tar.gz
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-md5=a1f271e5ffcf558d054028839296a072
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+sha1=b26cd9a17917ab6dd2f601e7448929fc9c09767d
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build/pkgs/configure/package-version.txt

@@ -1 +1 @@
-08185d786047228caff879eba88a1f8148a49020
+0ce2ea5d3d899264aef63cea22b27b209b60bec8

src/sage/rings/integer.pyx

@@ -2951,13 +2951,21 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
 
  return n
 
- def prime_divisors(self):
+ def prime_divisors(self, *args, **kwds):
  """
  Return the prime divisors of this integer, sorted in increasing order.
 
  If this integer is negative, we do *not* include -1 among
  its prime divisors, since -1 is not a prime number.
 
+ INPUT:
+
+ - ``limit`` -- (integer, optional keyword argument)
+ Return only prime divisors up to this bound, and the factorization
+ is done by checking primes up to ``limit`` using trial division.
+
+ Any additional arguments are passed on to the :meth:`factor` method.
+
  EXAMPLES::
 
  sage: a = 1; a.prime_divisors()
@@ -2968,8 +2976,23 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
  [2, 5]
  sage: a = 2004; a.prime_divisors()
  [2, 3, 167]
+
+ Setting the optional ``limit`` argument works as expected::
+
+ sage: a = 10^100 + 1
+ sage: a.prime_divisors()
+ [73, 137, 401, 1201, 1601, 1676321, 5964848081,
+ 129694419029057750551385771184564274499075700947656757821537291527196801]
+ sage: a.prime_divisors(limit=10^3)
+ [73, 137, 401]
+ sage: a.prime_divisors(limit=10^7)
+ [73, 137, 401, 1201, 1601, 1676321]
  """
- return [r[0] for r in self.factor()]
+ res = [r[0] for r in self.factor(*args, **kwds)]
+ limit = kwds.get('limit')
+ if limit is not None:
+ res = [r for r in res if r <= limit]
+ return res
 
  prime_factors = prime_divisors