poly* Plethysm(entry* lambda,_index l,_index n,poly* p)
{ if (n==0) return poly_one(Lierank(grp)); else if (n==1) return p;
{ _index i,j;
poly* sum= poly_null(Lierank(grp)),**adams=alloc_array(poly*,n+1);
poly* chi_lambda=MN_char(lambda,l);
for (i=1; i<=n; ++i) { adams[i]=Adams(i,p); setshared(adams[i]); }
for (i=0;i<chi_lambda->nrows;i++)
{ entry* mu=chi_lambda->elm[i]; poly* prod=adams[mu[0]],*t;
for (j=1; j<n && mu[j]>0; ++j)
{ t=prod; prod=Tensor(t,adams[mu[j]]); freepol(t); }
sum= Addmul_pol_pol_bin(sum,prod,mult(chi_lambda->coef[i],Classord(mu,n)));
}
freemem(chi_lambda);
setshared(p); /* protect |p|; it coincides with |adams[1]| */
for (i=1; i<=n; ++i)
{ clrshared(adams[i]); freepol(adams[i]); } freearr(adams);
clrshared(p);
{ bigint* fac_n=fac(n); setshared(fac_n); /* used repeatedly */
for (i=0; i<sum->nrows; ++i)
{ bigint** cc= &sum->coef[i]
,* c= (clrshared(*cc),isshared(*cc)) ? copybigint(*cc,NULL) : *cc;
*cc=divq(c,fac_n); setshared(*cc);
if (c->size!=0) error("Internal error (plethysm).\n"); else freemem(c);
}
clrshared(fac_n); freemem(fac_n);
}
return sum;
}
}
local poly* decompose_character(poly* ch)
{ wt_init(ch->ncols); /* for building result */
while (ch->coef[0]->size!=0) /* i.e., |while (ch!=0)| */
{ bigint* c=ch->coef[0];
if (c->size<0)
{ cmpfn=sav_cmpfn;
defaultgrp=sav_dfgrp;
error ("Non-virtual decomposition failed.\n");
}
{ wt_ins(ch->elm[0],c,false); /* contribute weight to result */
c=copybigint(c,NULL);
c->size= -c->size;
ch=Addmul_pol_pol_bin(ch,Domchar_irr(ch->elm[0],NULL),c);
}
}
{ poly* result=wt_collect();
{
cmpfn=sav_cmpfn;
defaultgrp=sav_dfgrp;
clrsorted(result);
}
return result;
}
}
poly* LR_tensor(poly* p,poly* q)
{ _index i,j,n=p->ncols; poly* res=poly_null(n);
for (i=0; i<p->nrows; ++i)
for (j=0; j<q->nrows; ++j)
res=Addmul_pol_pol_bin(res,LR_tensor_irr(p->elm[i],q->elm[j],n)
,mult(p->coef[i],q->coef[j]));
return res;
}
poly* Vdecomp(poly* p)
{ lie_Index i,r=Lierank(grp);
poly* result=poly_null(r);
cur_expon=mkintarray(r); /* large enough */
for (i=0; i<p->nrows; ++i)
result=Addmul_pol_pol_bin(result,vdecomp_irr(p->elm[i]),p->coef[i]);
freearr(cur_expon);
return result;
}
