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; } }
poly* SAtensor(boolean alt,_index m,poly* p) { _index n,r=Lierank(grp); poly** adams,** q,* result; if (m==0) return poly_one(r); else if (m==1) return p; adams=alloc_array(poly*,m+1); for (n=1; n<=m; ++n) adams[n]=Adams(n,p); q=alloc_array(poly*,m+1); q[0]=poly_one(r); for (n=1; n<=m; ++n) { { _index i; q[n]=Tensor(p,q[n-1]); /* the initial term of the summation */ for (i=2; i<=n; ++i) q[n] = Add_pol_pol(q[n],Tensor(adams[i],q[n-i]),alt&&i%2==0); } { _index i; bigint* big_n=entry2bigint(n); setshared(big_n); for (i=0; i<q[n]->nrows; ++i) { bigint** cc= &q[n]->coef[i] ,* c= (clrshared(*cc),isshared(*cc)) ? copybigint(*cc,NULL) : *cc; *cc=divq(c,big_n); setshared(*cc); { if (c->size != 0) error("Internal error (SAtensor): remainder from %ld.\n" ,(long)n); freemem(c); } } clrshared(big_n); freemem(big_n); } } result=q[m]; { for (n=1; n<=m; ++n) freepol(adams[n]); } freearr(adams); { for (n=0; n<m; ++n) freepol(q[n]); } freearr(q); return result; }
void freep(poly* addr) { index j; for (j=0; j<addr->nrows; j++) { object c=(object) addr->coef[j]; assert(isshared(c)); clrshared(c); freemem(c); } freemem(addr); }