void w_refl(entry* lambda, lie_Index wi)
{ if (type_of(grp)==SIMPGRP) simp_w_refl(lambda,wi,&grp->s);
else if (simpgroup(grp)) simp_w_refl(lambda,wi,Liecomp(grp,0));
else
{ lie_Index i,d,offset=0;
for (i=0; wi>=(d=Liecomp(grp,i)->lierank); ++i) { offset+=d; wi-=d; }
simp_w_refl(lambda+offset,wi,Liecomp(grp,i));
}
}
void Wrtaction(entry* alpha, vector* word)
{ lie_Index i; entry* w=word->compon;
for (i=0; i<word->ncomp; ++i) if(w[i]!=0)
{ lie_Index wi=w[i]-1;
if (type_of(grp)==SIMPGRP) simp_rt_refl(alpha,wi,&grp->s);
else if (simpgroup(grp)) simp_rt_refl(alpha,wi,Liecomp(grp,0));
else
{ lie_Index j,d,offset=0;
for (j=0; wi>=(d=Liecomp(grp,j)->lierank); ++j)
{ offset+=d; wi-=d; }
simp_rt_refl(alpha+offset,wi,Liecomp(grp,j));
}
}
}
matrix* Cartan(void)
{ if (type_of(grp)==SIMPGRP) return simp_Cartan(&grp->s);
if (simpgroup(grp)) return simp_Cartan(Liecomp(grp,0));
{ _index i,j, t=0;
matrix* cartan=mat_null(Ssrank(grp),Lierank(grp));
for (i=0; i<grp->g.ncomp; ++i)
{ _index r=Liecomp(grp,i)->lierank;
entry** c=simp_Cartan(Liecomp(grp,i))->elm;
for (j=0; j<r; ++j) copyrow(c[j],&cartan->elm[t+j][t],r);
t+=r;
}
return cartan;
}
}
matrix* Posroots(object grp)
{ if (type_of(grp)==SIMPGRP) return simp_proots(&grp->s);
if (simpgroup(grp)) return simp_proots(Liecomp(grp,0));
{ _index i,j,t1=0,t2=0;
matrix* result=mat_null(Numproots(grp),Ssrank(grp));
entry** m=result->elm;
for (i=0; i<grp->g.ncomp; ++i)
{ matrix* posr=simp_proots(Liecomp(grp,i));
_index r=Liecomp(grp,i)->lierank;
for (j=0; j<posr->nrows; ++j) copyrow(posr->elm[j],&m[t1+j][t2],r);
t1+=posr->nrows; t2+=r;
}
return result;
}
}
vector* Exponents(object grp)
{ if (type_of(grp)==SIMPGRP)
{ simp_exponents(&grp->s); return grp->s.exponents; }
if (simpgroup(grp))
{ simp_exponents(Liecomp(grp,0)); return Liecomp(grp,0)->exponents; }
{ _index i,t=0; vector* v=mkvector(Lierank(grp)); entry* e=v->compon;
{ for (i=0; i<grp->g.ncomp; ++i)
{ simpgrp* g=Liecomp(grp,i); _index r=g->lierank;
copyrow(simp_exponents(g),&e[t],r); t+=r;
}
for (i=0; i<grp->g.toraldim; ++i) e[t+i]=0;
}
return v;
}
}
matrix* Icartan(void)
{ if (simpgroup(grp)) return simp_icart(Liecomp(grp,0));
{ matrix* result=mat_null(Lierank(grp),Ssrank(grp)); entry** m=result->elm;
_index k,t=0;
entry det=Detcartan(); /* product of determinants of simple factors */
for (k=0; k<grp->g.ncomp; ++k)
{ simpgrp* g=Liecomp(grp,k);
_index i,j,r=g->lierank;
entry** a=simp_icart(g)->elm;
entry f=det/simp_detcart(g); /* multiplication factor */
for (i=0; i<r; ++i) for (j=0; j<r; ++j) m[t+i][t+j]=f*a[i][j];
t+=r;
}
return result;
}
}
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;
}
}
