cdef extern from 'symmetrica/def.h':
INT chartafel(OP degree, OP result)
INT charvalue(OP irred, OP cls, OP result, OP table)
INT kranztafel(OP a, OP b, OP res, OP co, OP cl)
INT c_ijk_sn(OP i, OP j, OP k, OP res)
def chartafel_symmetrica(n):
"""
you enter the degree of the symmetric group, as INTEGER
object and the result is a MATRIX object: the charactertable
of the symmetric group of the given degree.
EXAMPLES:
sage: symmetrica.chartafel(3)
[ 1 1 1]
[-1 0 2]
[ 1 -1 1]
sage: symmetrica.chartafel(4)
[ 1 1 1 1 1]
[-1 0 -1 1 3]
[ 0 -1 2 0 2]
[ 1 0 -1 -1 3]
[-1 1 1 -1 1]
"""
cdef OP cn, cres
cn = callocobject()
cres = callocobject()
_op_integer(n, cn)
chartafel(cn, cres)
res = _py(cres)
freeall(cn)
freeall(cres)
return res
def charvalue_symmetrica(irred, cls, table=None):
"""
you enter a PARTITION object part, labelling the irreducible
character, you enter a PARTITION object class, labeling the class
or class may be a PERMUTATION object, then result becomes the value
of that character on that class or permutation. Note that the
table may be NULL, in which case the value is computed, or it may be
taken from a precalculated charactertable.
FIXME: add table paramter
EXAMPLES:
sage: n = 3
sage: m = matrix([[symmetrica.charvalue(irred, cls) for cls in Partitions(n)] for irred in Partitions(n)]); m
[ 1 1 1]
[-1 0 2]
[ 1 -1 1]
sage: m == symmetrica.chartafel(n)
True
sage: n = 4
sage: m = matrix([[symmetrica.charvalue(irred, cls) for cls in Partitions(n)] for irred in Partitions(n)])
sage: m == symmetrica.chartafel(n)
True
"""
cdef OP cirred, cclass, ctable, cresult
cirred = callocobject()
cclass = callocobject()
cresult = callocobject()
if table == None:
ctable = NULL
else:
ctable = callocobject()
_op_matrix(table, ctable)
#FIXME: assume that class is a partition
_op_partition(cls, cclass)
_op_partition(irred, cirred)
charvalue(cirred, cclass, cresult, ctable)
res = _py(cresult)
freeall(cirred)
freeall(cclass)
freeall(cresult)
if ctable != NULL:
freeall(ctable)
return res
def kranztafel_symmetrica(a, b):
"""
you enter the INTEGER objects, say a and b, and res becomes a
MATRIX object, the charactertable of S_b \wr S_a, co becomes a
VECTOR object of classorders and cl becomes a VECTOR object of
the classlabels.
EXAMPLES:
sage: (a,b,c) = symmetrica.kranztafel(2,2)
sage: a
[ 1 -1 1 -1 1]
[ 1 1 1 1 1]
[-1 1 1 -1 1]
[ 0 0 2 0 -2]
[-1 -1 1 1 1]
sage: b
[2, 2, 1, 2, 1]
sage: for m in c: print m
...
[0 0]
[0 1]
[0 0]
[1 0]
[0 2]
[0 0]
[1 1]
[0 0]
[2 0]
[0 0]
"""
cdef OP ca, cb, cres, cco, ccl
ca = callocobject()
cb = callocobject()
cres = callocobject()
cco = callocobject()
ccl = callocobject()
_op_integer(a, ca)
_op_integer(b, cb)
kranztafel(ca,cb,cres,cco,ccl)
res = _py(cres)
co = _py(cco)
cl = _py(ccl)
freeall(ca)
freeall(cb)
freeall(cres)
freeall(cco)
freeall(ccl)
return (res, co, cl)
## def c_ijk_sn_symmetrica(i, j, k):
## """
## computes the coefficients of the class multiplication in the
## group algebra of the S_n. It uses the method described in
## Curtis/Reiner: Methods of representation theory I p. 216
## EXAMPLES:
## """
## cdef OP ci, cj, ck, cresult
## ci = callocobject()
## cj = callocobject()
## cresult = callocobject()
## ck = callocobject()
## _op_partition(i, ci)
## _op_partition(j, cj)
## _op_partition(k, ck)
## c_ijk_sn(ci, cj, ck, cresult)
## res = _py(cresult)
## freeall(ci)
## freeall(cj)
## freeall(cresult)
## freeall(ck)
## return res
