include '../../ext/python_object.pxi'
cdef extern from 'symmetrica/def.h':
INT kostka_number(OP shape, OP content, OP result)
INT kostka_tab(OP shape, OP content, OP result)
INT kostka_tafel(OP n, OP result)
def kostka_number_symmetrica(shape, content):
"""
computes the kostkanumber, i.e. the number of
tableaux of given shape, which is a PARTITION object, and
of given content, which also is a PARTITION object, or a VECTOR
object with INTEGER entries. The
result is an INTEGER object, which is freed to an empty
object at the beginning. The shape could also be a
SKEWPARTITION object, then we compute the number of
skewtableaux of the given shape.
EXAMPLES:
sage: symmetrica.kostka_number([2,1],[1,1,1])
2
sage: symmetrica.kostka_number([1,1,1],[1,1,1])
1
sage: symmetrica.kostka_number([3],[1,1,1])
1
"""
cdef OP cshape = callocobject(), ccontent = callocobject(), result = callocobject()
if PyObject_TypeCheck(shape, builtinlist):
if PyObject_TypeCheck(shape[0], builtinlist):
shape = SkewPartition(shape)
else:
shape = Partition(shape)
if PyObject_TypeCheck(shape, SkewPartition):
_op_skew_partition(shape, cshape)
else:
_op_partition(shape, cshape)
_op_partition(content, ccontent)
kostka_number(ccontent, cshape, result)
res = _py(result)
freeall(cshape)
freeall(ccontent)
freeall(result)
return res
def kostka_tab_symmetrica(shape, content):
"""
computes the list of tableaux of given shape
and content. shape is a PARTITION object or a
SKEWPARTITION object and
content is a PARTITION object or a VECTOR object with
INTEGER entries, the result becomes a
LIST object whose entries are the computed TABLEAUX
object.
EXAMPLES:
sage: symmetrica.kostka_tab([3],[1,1,1])
[[[1, 2, 3]]]
sage: symmetrica.kostka_tab([2,1],[1,1,1])
[[[1, 2], [3]], [[1, 3], [2]]]
sage: symmetrica.kostka_tab([1,1,1],[1,1,1])
[[[1], [2], [3]]]
sage: symmetrica.kostka_tab([[2,2,1],[1,1]],[1,1,1])
[[[None, 1], [None, 2], [3]],
[[None, 1], [None, 3], [2]],
[[None, 2], [None, 3], [1]]]
sage: symmetrica.kostka_tab([[2,2],[1]],[1,1,1])
[[[None, 1], [2, 3]], [[None, 2], [1, 3]]]
"""
late_import()
cdef OP cshape = callocobject(), ccontent = callocobject(), result = callocobject()
cdef INT err
if PyObject_TypeCheck(shape, builtinlist):
if PyObject_TypeCheck(shape[0], builtinlist):
shape = SkewPartition(shape)
else:
shape = Partition(shape)
if PyObject_TypeCheck(shape, SkewPartition_class):
_op_skew_partition(shape, cshape)
else:
_op_partition(shape, cshape)
#Check to make sure the content is compatible with the shape.
_op_il_vector(content, ccontent)
err = kostka_tab(cshape, ccontent, result)
res = _py(result)
freeall(cshape)
freeall(ccontent)
freeall(result)
return res
def kostka_tafel_symmetrica(n):
"""
Returns the table of Kostka numbers of weight n.
EXAMPLES:
sage: symmetrica.kostka_tafel(1)
[1]
sage: symmetrica.kostka_tafel(2)
[1 0]
[1 1]
sage: symmetrica.kostka_tafel(3)
[1 0 0]
[1 1 0]
[1 2 1]
sage: symmetrica.kostka_tafel(4)
[1 0 0 0 0]
[1 1 0 0 0]
[1 1 1 0 0]
[1 2 1 1 0]
[1 3 2 3 1]
sage: symmetrica.kostka_tafel(5)
[1 0 0 0 0 0 0]
[1 1 0 0 0 0 0]
[1 1 1 0 0 0 0]
[1 2 1 1 0 0 0]
[1 2 2 1 1 0 0]
[1 3 3 3 2 1 0]
[1 4 5 6 5 4 1]
"""
cdef OP cn = callocobject(), cresult = callocobject()
_op_integer(n, cn)
sig_on()
kostka_tafel(cn, cresult)
sig_off()
res = _py(cresult)
freeall(cn)
freeall(cresult)
return res
