sage.groups.perm_gps.partn_ref*: Remove dependency of everything on GAP

Author: Matthias Koeppe

src/sage/groups/perm_gps/partn_ref/data_structures.pxd

@@ -13,7 +13,6 @@ from sage.data_structures.bitset_base cimport *
 from libc.string cimport memcpy
 from libc.stdlib cimport rand
 from sage.libs.gmp.mpz cimport *
-from sage.groups.perm_gps.partn_ref2.refinement_generic cimport PartitionRefinement_generic
 
 
 cdef enum:
@@ -260,8 +259,7 @@ cdef PS_print(PartitionStack *PS)
 
 cdef void PS_unit_partition(PartitionStack *PS)
 
-cdef int PS_first_smallest(PartitionStack *PS, bitset_t b, int *second_pos=?,
-        PartitionRefinement_generic partn_ref_alg=?)
+cdef int PS_first_smallest(PartitionStack *PS, bitset_t b, int *second_pos=?)
 
 cdef PartitionStack *PS_from_list(list L)
 

src/sage/groups/perm_gps/partn_ref/data_structures.pyx

@@ -284,8 +284,7 @@ cdef PS_print_partition(PartitionStack *PS, int k):
     s = s[:-1] + ')'
     print(s)
 
-cdef int PS_first_smallest(PartitionStack *PS, bitset_t b, int *second_pos=NULL,
-                           PartitionRefinement_generic partn_ref_alg=None):
+cdef int PS_first_smallest(PartitionStack *PS, bitset_t b, int *second_pos=NULL):
     """
     Find the first occurrence of the smallest cell of size greater than one,
     which is admissible (checked by the function ``test_allowance``).
@@ -295,8 +294,7 @@ cdef int PS_first_smallest(PartitionStack *PS, bitset_t b, int *second_pos=NULL,
     bitset_zero(b)
     while 1:
         if PS.levels[i] <= PS.depth:
-            if i != j and n > i - j + 1 and (partn_ref_alg is None or
-                                partn_ref_alg._minimization_allowed_on_col(PS.entries[j])):
+            if i != j and n > i - j + 1:
                 n = i - j + 1
                 location = j
             j = i + 1

src/sage/groups/perm_gps/partn_ref2/refinement_generic.pxd

@@ -82,3 +82,7 @@ cdef class PartitionRefinement_generic:
                               bint* inner_group_changed, bint* changed_partition,
                               str refine_name)
     cdef int len(self)
+
+
+cdef int PS_first_smallest_PR(PartitionStack *PS, bitset_t b, int *second_pos=?,
+        PartitionRefinement_generic partn_ref_alg=?)

src/sage/groups/perm_gps/partn_ref2/refinement_generic.pyx

@@ -941,3 +941,40 @@ cdef class PartitionRefinement_generic:
         """
         if BACKTRACK_WITHLATEX_DEBUG:
             self._latex_debug_string += "]\n"
+
+
+cdef int PS_first_smallest_PR(PartitionStack *PS, bitset_t b, int *second_pos=NULL,
+                              PartitionRefinement_generic partn_ref_alg=None):
+    """
+    Find the first occurrence of the smallest cell of size greater than one,
+    which is admissible (checked by the function ``test_allowance``).
+    Its entries are stored to b and its minimum element is returned.
+
+    This generalizes :func:`sage.groups.perm_gps.partn_ref.data_structures.PS_first_smallest`.
+    """
+    cdef int i = 0, j = 0, location = 0, n = PS.degree
+    bitset_zero(b)
+    while 1:
+        if PS.levels[i] <= PS.depth:
+            if i != j and n > i - j + 1 and (partn_ref_alg is None or
+                                partn_ref_alg._minimization_allowed_on_col(PS.entries[j])):
+                n = i - j + 1
+                location = j
+            j = i + 1
+        if PS.levels[i] == -1: break
+        i += 1
+    # location now points to the beginning of the first, smallest,
+    # nontrivial cell
+    i = location
+    while 1:
+        bitset_flip(b, PS.entries[i])
+        if PS.levels[i] <= PS.depth: break
+        i += 1
+
+    if second_pos != NULL:
+        if n==2:
+            second_pos[0] = PS.entries[location+1]
+        else:
+            second_pos[0] = -1
+
+    return PS.entries[location]