Ticket #13199: trac_13199_flint_partition_function_v2.patch

module_list.py

@@ -623 +623 @@
     Extension('sage.libs.flint.flint',
               sources = ["sage/libs/flint/flint.pyx"],
               libraries = ["csage", "flint", "gmp", "gmpxx", "m", "stdc++"],
-              extra_compile_args=["-std=c99", "-D_XPG6"],
+              extra_compile_args = ["-std=c99", "-D_XPG6"],
               depends = flint_depends),
 
     Extension('sage.libs.flint.fmpz_poly',
               sources = ["sage/libs/flint/fmpz_poly.pyx"],
               libraries = ["csage", "flint", "gmp", "gmpxx", "m", "stdc++"],
-              extra_compile_args=["-std=c99", "-D_XPG6"],
+              extra_compile_args = ["-std=c99", "-D_XPG6"],
+              depends = flint_depends),
+
+    Extension('sage.libs.flint.arith',
+              sources = ["sage/libs/flint/arith.pyx"],
+              libraries = ["csage", "flint", "gmp", "gmpxx", "m", "stdc++"],
+              include_dirs = [SAGE_INC + 'flint/'],
+              extra_compile_args = ["-std=c99", "-D_XPG6"],
               depends = flint_depends),
     
     Extension('sage.libs.fplll.fplll',

sage/combinat/partition.py

@@ -26 +26 @@
     - If given coordinates of the form ``(r, c)``, then use Python's
       \*-operator.
 
+
     - Throughout this documentation, for a partition `\lambda` we will denote
       its conjugate partition by `\lambda^{\prime}`. For more on conjugate
       partitions, see :meth:`Partition.conjugate()`.
@@ -272 +273 @@
 
 from sage.interfaces.all import gap
 from sage.libs.all import pari
+from sage.libs.flint.arith import number_of_partitions as flint_number_of_partitions
 
 from sage.structure.global_options import GlobalOptions
 from sage.structure.parent import Parent
@@ -4499 +4501 @@
             lst = [self.n-1, 1]
         return self.element_class(self, lst)
 
-    def cardinality(self, algorithm='bober'):
+    def cardinality(self, algorithm='flint'):
         r"""
         Returns the number of partitions of the specified size.
 
@@ -4508 +4510 @@
         - ``algorithm``  - (default: ``'bober'``)
 
           - ``'bober'`` -- Use Jonathan Bober's implementation (*very* fast).
+          - ``'flint'`` -- use FLINT.
           - ``'gap'`` -- use GAP (VERY *slow*)
           - ``'pari'`` -- use PARI. Speed seems the same as GAP until
             `n` is in the thousands, in which case PARI is faster.
@@ -4532 +4535 @@
             7
             sage: Partitions(5).cardinality(algorithm='bober')
             7
+            sage: number_of_partitions(5, algorithm='flint')
+            7
 
         The input must be a nonnegative integer or a ``ValueError`` is raised.
 
@@ -4575 +4580 @@
         if algorithm == 'bober':
             return cached_number_of_partitions(self.n)
 
+        elif algorithm == 'flint':
+            return flint_number_of_partitions(self.n)
+
         elif algorithm == 'gap':
-            return ZZ( gap.eval("NrPartitions(%s)"%(ZZ(self.n))) )
+            return ZZ(gap.eval("NrPartitions(%s)" % (ZZ(self.n))))
 
         elif algorithm == 'pari':
             return ZZ(pari(ZZ(self.n)).numbpart())
 
-        raise ValueError("unknown algorithm '%s'"%algorithm)
+        raise ValueError("unknown algorithm '%s'" % algorithm)
 
     def random_element(self, measure = 'uniform'):
         """
@@ -5913 +5921 @@
     deprecation(13072,'number_of_partitions_set is deprecated. Use SetPartitions().cardinality() instead.')
     return sage.combinat.set_partition.SetPartitions(S,k).cardinality()
 
-def number_of_partitions(n,k=None, algorithm='default'):
+def number_of_partitions(n, k=None, algorithm='default'):
     r"""
     Returns the number of partitions of `n` with, optionally, at most `k`
     parts.
@@ -6064 +6072 @@
 
     if algorithm == 'default':
         if k is None:
-            algorithm = 'bober'
+            algorithm = 'flint'
         else:
             algorithm = 'gap'
 
@@ -6083 +6091 @@
     if algorithm == 'bober':
         return cached_number_of_partitions(n)
 
+    elif algorithm == 'flint':
+        return flint_number_of_partitions(n)
+
     elif algorithm == 'pari':
         deprecation(13072,"sage.combinat.number_of_partitions is deprecated. Use  Partitions().cardinality(algorithm='pari')")
         return ZZ(pari(ZZ(n)).numbpart())

new file sage/libs/flint/arith.pyx

@@ +1 @@
+include "../../ext/interrupt.pxi"
+include "fmpz.pxi"
+
+cdef extern from "flint/arith.h":
+    void arith_number_of_partitions(fmpz_t x, unsigned long n)
+
+from sage.rings.integer cimport Integer
+
+
+def number_of_partitions(unsigned long n):
+    """
+    Returns the number of partitions of the integer n.
+
+    EXAMPLES::
+
+        sage: from sage.libs.flint.arith import number_of_partitions
+        sage: number_of_partitions(10)
+        42
+    """
+    cdef fmpz_t ans_fmpz
+    cdef Integer ans
+
+    fmpz_init(ans_fmpz)
+
+    if n > 1000:
+        sig_on()
+
+    arith_number_of_partitions(ans_fmpz, n)
+
+    if n > 1000:
+        sig_off()
+
+    ans = Integer(0)
+    fmpz_get_mpz(ans.value, ans_fmpz)
+    fmpz_clear(ans_fmpz)
+    return ans
+