void wt_init(lie_Index r)
{ sorted=copypoly(poly_null(r));
pos_acc=mkpoly(ACCMIN,r);
neg_acc=mkpoly(ACCMIN,r);
pos_acc->nrows=0;
neg_acc->nrows=0;
}
void wt_ins(entry* wt, bigint* c, boolean neg)
{ if (c->size==0) {
freemem(c);
return;
}
{ lie_Index i=searchterm(sorted,wt);
if (i>=0)
{ clrshared(sorted->coef[i]);
sorted->coef[i]= (neg ? sub : add)(sorted->coef[i],c);
setshared(sorted->coef[i]);
}
else
{ poly** acc= neg ? &neg_acc : &pos_acc;
lie_Index i=(*acc)->nrows;
if (i==(*acc)->rowsize)
{ sorted=Add_pol_pol(sorted,*acc,neg);
*acc=mkpoly(Max(sorted->nrows,ACCMIN),sorted->ncols);
i=0;
}
copyrow(wt,(*acc)->elm[i],sorted->ncols);
(*acc)->coef[i++]=c;
setshared(c);
(*acc)->nrows=i;
}
}
}
poly* From_Part_p (poly* p)
{ _index i,j,n_rows=p->nrows,n=p->ncols; poly* result=mkpoly(n_rows,n-1);
entry** lambda=p->elm; entry** res=result->elm;
for (i=0; i<n_rows; ++i)
{ result->coef[i]=p->coef[i]; setshared(p->coef[i]); /* copy coefficient */
for (j=0; j<n-1; ++j) res[i][j]=lambda[i][j]-lambda[i][j+1];
}
return Reduce_pol(result);
}
poly* To_Part_p (poly* p)
{ _index i,n_rows=p->nrows,n=p->ncols; entry** wt=p->elm;
poly* result=mkpoly(n_rows,n+1); entry** lambda=result->elm;
for (i=0; i<n_rows; ++i)
{ _index j=n; entry sum=0;
result->coef[i]=p->coef[i]; setshared(p->coef[i]);
while (lambda[i][j]=sum, --j>=0) sum+=wt[i][j];
}
return Reduce_pol(result);
}
poly *pol_mul_pol_mat(poly *a, matrix *b) {
poly *m;
int i;
if (a->ncols != b->nrows)
error("Number variables arg1 unequal number of rows arg2 .\n");
m = mkpoly(a->nrows,b->ncols);
mulmatmatelm(a->elm,b->elm,m->elm,a->nrows,a->ncols,b->ncols);
for (i=0;i<m->nrows;i++) {
m->coef[i] = a->coef[i];
setshared(m->coef[i]);
}
return m;
}
poly* alt_Wsum(poly* p)
{ lie_Index i,k=0,r=p->ncols; poly* result; entry** res,*rho=mkintarray(r);
p=Alt_dom(p); for (i=0; i<r; ++i) rho[i]=1;
for (i=0; i<p->nrows; ++i) add_xrow_to(p->elm[i],1,rho,r);
result=mkpoly(p->nrows*bigint2entry(Worder(grp)),r); res=result->elm;
for (i=0; i<p->nrows; ++i)
{ lie_Index j,l; matrix* orbit=Weyl_orbit(p->elm[i],NULL); entry** x=orbit->elm;
bigint* c=p->coef[i],* min_c=sub(null,c);
for (j=0; j<orbit->nrows; ++j)
{ subrow(*x,rho,res[k],r); l=make_dominant(*x++)%2;
result->coef[k]= l ? min_c : c; setshared(result->coef[k]); ++k;
}
freemem(orbit);
}
freearr(rho);
assert(k==result->nrows);
return result; /* not sorted, but rows are unique */
}
poly* Adjoint(object grp)
{ _index i,j,r=Lierank(grp)
,n=type_of(grp)==SIMPGRP ? 1: grp->g.ncomp+(grp->g.toraldim!=0);
poly* adj= mkpoly(n,r);
for (i=0; i<n; ++i)
{ adj->coef[i]=one; for (j=0; j<r; ++j) adj->elm[i][j]=0; }
if (type_of(grp)==SIMPGRP) set_simp_adjoint(adj->elm[0],&grp->s);
else
{ _index offs=0; simpgrp* g;
for (i=0; i<grp->g.ncomp; offs+=g->lierank,++i)
set_simp_adjoint(&adj->elm[i][offs],g=Liecomp(grp,i));
if (grp->g.toraldim!=0)
{ adj->coef[i]=entry2bigint(grp->g.toraldim);
setshared(adj->coef[i]);
}
}
return adj;
}
poly* Worbit_p(poly* p)
{ lie_Index i,k=0,l=0,r=p->ncols; poly* result; entry** res;
p=copypoly(p); for (i=0; i<p->nrows; ++i) make_dominant(p->elm[i]);
Reduce_pol(p);
for (i=0; i<p->nrows; ++i)
if ((l += bigint2entry(Orbitsize(p->elm[i])))<0)
error ("That's too large an orbit");
result=mkpoly(l,p->ncols); res=result->elm;
for (i=0; i<p->nrows; ++i)
{ lie_Index j; matrix* orbit=Weyl_orbit(p->elm[i],NULL); entry** x=orbit->elm;
for (j=0; j<orbit->nrows; ++j)
{ result->coef[k]=p->coef[i]; setshared(p->coef[i]);
copyrow(*x++,res[k++],r);
}
freemem(orbit);
}
assert(k==result->nrows);
return result; /* not sorted, but rows are unique */
}
local poly* vdecomp_irr(entry* lambda)
{ if (type_of(grp)==SIMPGRP) return simp_vdecomp_irr(lambda,&grp->s);
if (simpgroup(grp)) return simp_vdecomp_irr(lambda,Liecomp(grp,0));
{ poly* result;
lie_Index i;
{ lie_Index td=grp->g.toraldim;
lambda+=Ssrank(grp);
result=mkpoly(1,td);
copyrow(lambda,*result->elm,td);
*result->coef=one;
}
for (i=grp->g.ncomp-1; i>=0; --i)
/* traverse simple components in reverse order */
{ simpgrp* g=Liecomp(grp,i);
lambda-=g->lierank;
result= Disjunct_mul_pol_pol(simp_vdecomp_irr(lambda,g),result);
}
return result;
}
}
