Coverage for local/lib/python2.7/site-packages/sage/libs/symmetrica/sc.pxi : 87%

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 parameter 

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 is 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