Faster _calc_vacancy_number and phi. Cythonized RiggedPartition.

src/sage/combinat/rigged_configurations/rc_crystal.py

@@ -270,10 +270,13 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
         """
         vac_num = self._wt[self.index_set()[a]]
 
-        for b in range(self._cartan_matrix.ncols()):
+        for b,nu in enumerate(partitions):
             val = self._cartan_matrix[a,b]
             if val:
-                vac_num -= val * partitions[b].get_num_cells_to_column(i)
+                if i == float('inf'):
+                    vac_num -= val * sum(nu)
+                else:
+                    vac_num -= val * nu.get_num_cells_to_column(i)
 
         return vac_num
 
@@ -358,11 +361,15 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
         ia = I[a]
         vac_num = self._wt[ia]
 
+        if i == float('inf'):
+            return vac_num - sum(self._cartan_matrix[a,b] * sum(nu)
+                                 for b,nu in enumerate(partitions))
+
         gamma = self._folded_ct.scaling_factors()
         g = gamma[ia]
-        for b in range(self._cartan_matrix.ncols()):
+        for b, nu in enumerate(partitions):
             ib = I[b]
-            q = partitions[b].get_num_cells_to_column(g*i, gamma[ib])
+            q = nu.get_num_cells_to_column(g*i, gamma[ib])
             vac_num -= self._cartan_matrix[a,b] * q / gamma[ib]
 
         return vac_num

src/sage/combinat/rigged_configurations/rc_infinity.py

@@ -261,12 +261,12 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
             sage: RC._calc_vacancy_number(elt.nu(), 0, 1)
             -1
         """
-        vac_num = 0
+        if i == float('inf'):
+            return -sum(self._cartan_matrix[a,b] * sum(nu)
+                        for b,nu in enumerate(partitions))
 
-        for b in range(self._cartan_matrix.ncols()):
-            vac_num -= self._cartan_matrix[a,b] * partitions[b].get_num_cells_to_column(i)
-
-        return vac_num
+        return -sum(self._cartan_matrix[a,b] * nu.get_num_cells_to_column(i)
+                    for b,nu in enumerate(partitions))
 
     # FIXME: Remove this method!!!
     def weight_lattice_realization(self):
@@ -380,6 +380,10 @@ def _calc_vacancy_number(self, partitions, a, i):
         ia = I[a]
         vac_num = 0
 
+        if i == float('inf'):
+            return -sum(self._cartan_matrix[a,b] * sum(nu)
+                        for b,nu in enumerate(partitions))
+
         gamma = self._folded_ct.scaling_factors()
         g = gamma[ia]
         for b in range(self._cartan_matrix.ncols()):

src/sage/combinat/rigged_configurations/rigged_configurations.py

@@ -810,8 +810,12 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
                 if dim[0] == self._rc_index[a]:
                     vac_num += min(dim[1], i)
 
-        for b in range(self._cartan_matrix.ncols()):
-            vac_num -= self._cartan_matrix[a,b] * partitions[b].get_num_cells_to_column(i)
+        if i == float('inf'):
+            vac_num -= sum(self._cartan_matrix[a,b] * sum(nu)
+                           for b,nu in enumerate(partitions))
+        else:
+            vac_num -= sum(self._cartan_matrix[a,b] * nu.get_num_cells_to_column(i)
+                           for b,nu in enumerate(partitions))
 
         return vac_num
 
@@ -1146,11 +1150,15 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
                 if dim[0] == self._rc_index[a]:
                     vac_num += min(dim[1], i)
 
-        gamma = self._folded_ct.scaling_factors()
-        for b in range(self._cartan_matrix.ncols()):
-            vac_num -= (self._cartan_matrix[a,b]
-                        * partitions[b].get_num_cells_to_column(gamma[a+1]*i, gamma[b+1])
-                        // gamma[b+1])
+        if i == float('inf'):
+            vac_num -= sum(self._cartan_matrix[a,b] * sum(nu)
+                           for b,nu in enumerate(partitions))
+        else:
+            gamma = self._folded_ct.scaling_factors()
+            vac_num -= sum(self._cartan_matrix[a,b]
+                           * nu.get_num_cells_to_column(gamma[a+1]*i, gamma[b+1])
+                           // gamma[b+1]
+                           for b,nu in enumerate(partitions))
 
         return vac_num
 
@@ -1492,8 +1500,12 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
                     vac_num += min(dim[1], i)
 
         gamma = self._folded_ct.scaling_factors()
-        for b in range(self._cartan_matrix.ncols()):
-            vac_num -= self._cartan_matrix[a,b] * partitions[b].get_num_cells_to_column(i) // gamma[b+1]
+        if i == float('inf'):
+            vac_num -= sum(self._cartan_matrix[a,b] * sum(nu) // gamma[b+1]
+                           for b, nu in enumerate(partitions))
+        else:
+            vac_num -= sum(self._cartan_matrix[a,b] * nu.get_num_cells_to_column(i) // gamma[b+1]
+                           for b, nu in enumerate(partitions))
 
         return vac_num
 
@@ -1640,8 +1652,12 @@ def _calc_vacancy_number(self, partitions, a, i, **options):
                 if dim[0] == self._rc_index[a]:
                     vac_num += min(dim[1], i)
 
-        for b in range(self._cartan_matrix.ncols()):
-            vac_num -= self._cartan_matrix[a,b] * partitions[b].get_num_cells_to_column(i) / 2
+        if i == float('inf'):
+            vac_num -= sum(self._cartan_matrix[a,b] * sum(nu) / 2
+                           for b,nu in enumerate(partitions))
+        else:
+            vac_num -= sum(self._cartan_matrix[a,b] * nu.get_num_cells_to_column(i) / 2
+                           for b,nu in enumerate(partitions))
 
         return vac_num
 

src/sage/combinat/rigged_configurations/rigged_partition.pxd

@@ -0,0 +1,15 @@
+from sage.structure.sage_object cimport SageObject
+
+cdef class RiggedPartition(SageObject):
+    cdef public list _list
+    cdef public list vacancy_numbers
+    cdef public list rigging
+    cdef long _hash
+
+    cpdef get_num_cells_to_column(self, int end_column, t=*)
+    cpdef insert_cell(self, int max_width)
+    cpdef remove_cell(self, row, int num_cells=*)
+
+cdef class RiggedPartitionTypeB(RiggedPartition):
+    pass
+