cdef extern from 'symmetrica/def.h':
INT dimension_symmetrization(OP n, OP part, OP a)
INT bdg(OP part, OP perm, OP D)
INT sdg(OP part, OP perm, OP D)
INT odg(OP part, OP perm, OP D)
INT ndg(OP part, OP perm, OP D)
INT specht_dg(OP part, OP perm, OP D)
INT glmndg(OP m, OP n, OP M, INT VAR)
def dimension_symmetrization_symmetrica(n, part):
"""
computes the dimension of the degree of a irreducible
representation of the GL_n, n is a INTEGER object, labeled
by the PARTITION object a.
"""
cdef OP cn, cpart, cres
cn = callocobject()
cpart = callocobject()
cres = callocobject()
_op_partition(part, cpart)
_op_integer(n, cn)
dimension_symmetrization(cn, cpart, cres)
res = _py(cres)
freeall(cn)
freeall(cpart)
freeall(cres)
return res
def bdg_symmetrica(part, perm):
"""
Calculates the irreduzible matrix representation
D^part(perm), whose entries are of integral numbers.
REFERENCE: H. Boerner:
Darstellungen von Gruppen, Springer 1955.
pp. 104-107.
"""
cdef OP cpart, cperm, cD
cpart = callocobject()
cperm = callocobject()
cD = callocobject()
_op_partition(part, cpart)
_op_permutation(perm, cperm)
bdg(cpart, cperm, cD)
res = _py_matrix(cD)
freeall(cpart)
freeall(cperm)
freeall(cD)
def sdg_symmetrica(part, perm):
"""
Calculates the irreduzible matrix representation
D^part(perm), which consists of rational numbers.
REFERENCE: G. James/ A. Kerber:
Representation Theory of the Symmetric Group.
Addison/Wesley 1981.
pp. 124-126.
"""
cdef OP cpart, cperm, cD
cpart = callocobject()
cperm = callocobject()
cD = callocobject()
_op_partition(part, cpart)
_op_permutation(perm, cperm)
sdg(cpart, cperm, cD)
res = _py_matrix(cD)
freeall(cpart)
freeall(cperm)
freeall(cD)
return res
def odg_symmetrica(part, perm):
"""
Calculates the irreduzible matrix representation
D^part(perm), which consists of real numbers.
REFERENCE: G. James/ A. Kerber:
Representation Theory of the Symmetric Group.
Addison/Wesley 1981.
pp. 127-129.
"""
cdef OP cpart, cperm, cD
cpart = callocobject()
cperm = callocobject()
cD = callocobject()
_op_partition(part, cpart)
_op_permutation(perm, cperm)
odg(cpart, cperm, cD)
res = _py_matrix(cD)
freeall(cpart)
freeall(cperm)
freeall(cD)
return res
def ndg_symmetrica(part, perm):
"""
"""
cdef OP cpart, cperm, cD
cpart = callocobject()
cperm = callocobject()
cD = callocobject()
_op_partition(part, cpart)
_op_permutation(perm, cperm)
ndg(cpart, cperm, cD)
res = _py_matrix(cD)
freeall(cpart)
freeall(cperm)
freeall(cD)
return res
def specht_dg_symmetrica(part, perm):
"""
"""
cdef OP cpart, cperm, cD
cpart = callocobject()
cperm = callocobject()
cD = callocobject()
_op_partition(part, cpart)
_op_permutation(perm, cperm)
specht_dg(cpart, cperm, cD)
res = _py_matrix(cD)
freeall(cpart)
freeall(cperm)
freeall(cD)
return res
## def glmndg_symmetrica(m, n, VAR=0):
## """
## If VAR is equal to 0 the orthogonal representation
## is used for the decomposition, otherwise, if VAR
## equals 1, the natural representation is considered.
## The result is the VECTOR-Object M, consisting of
## components of type MATRIX, representing the several
## irreducible matrix representations of GLm(C) with
## part_1' <= m, where part is a partition of n.
## """
## cdef OP cm, cn, cM
##
## cm = callocobject()
## _op_integer(m, cm)
## cn = callocobject()
## _op_integer(n, cn)
## cM = callocobject()
## glmndg(cm, cn, cM, VAR)
## res = _py(cM)
## freeall(cm)
## freeall(cn)
## freeall(cM)
##
## return res
