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#include "lie.h"
poly* LR_tensor_irr(entry* lambda,entry * mu, index n)
{ index i,j;
entry* nu; entry** T;
if (n==0) return poly_one(0);
{ nu=&mkintarray(n+1)[1]; copyrow(lambda,nu,n); nu[-1]=lambda[0]+mu[0];
T=alloc_array(entry*,n+1);
for (i=0;i<=n;++i) /* allocate row |T[i]| and place sentinel before it */
{ T[i]= &mkintarray(mu[i==0?0:i-1]+1)[1]; T[i][-1]=n-1-i; }
for (i=0,j=mu[0]-1; j>=0; --j)
{ while (i<n && mu[i]>j) ++i; /* find first |i| with |mu[i]<=j| */
T[i][j]=-1; /* place sentinel at bottom of column |j| */
}
}
wt_init(n); /* prepare to collect terms with exponents of size~|n| */
{ j=-1; for (i=n-1; i>0 && mu[i]==0; --i) {} /* move to initial position */
recurse: /* recursive starting point; */
if (++j>=mu[i] &&(j=0,--i<0)) /* move to next empty position, if any */
wt_ins(nu,one,false); /* if not, |T| is full; contribute |nu| once */
else
{ index k= T[i+1][j]; entry prev= nu[k];
do
{ while (nu[++k]==prev) {} /* find next |k| with |nu[k]<nu[@t$k'$@>]| */
++nu[T[i][j]=k]; goto recurse;
/* insert |k| into |T| and extend partition |nu|; recurse */
resume: prev= --nu[k=T[i][j]];
/* restore |k| and |nu|; set |prev=nu[k]| */
} while (prev>nu[T[i][j-1]]);
/* if so, there are still corners of |nu| to try */
}
if (j==0) j= ++i<n?mu[i]:0; /* return to end of row below if necessary */
if (--j>=0) goto resume; /* do return jump unless empty row is reached */
}
{ --nu; freearr(nu);
for (i=0;i<=n;i++) { entry* t=&T[i][-1]; freearr(t); }
freearr(T);
}
return wt_collect(); /* return sum of all contributed terms */
}
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;
}
vector* From_Part_v (entry* lambda, index n)
{ index i; vector* result=mkvector(n-1); entry* res=result->compon;
for (i=0; i<n-1; ++i) res[i]=lambda[i]-lambda[i+1];
return result;
}
matrix* From_Part_m (entry** lambda, index n_rows, index n)
{ index i,j; matrix* result=mkmatrix(n_rows,n-1); entry** res=result->elm;
for (i=0; i<n_rows; ++i)
for (j=0; j<n-1; ++j) res[i][j]=lambda[i][j]-lambda[i][j+1];
return result;
}
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);
}
vector* To_Part_v (entry* wt,index n)
{ index i=n; vector* result=mkvector(n+1); entry* lambda=result->compon;
entry sum=0;
while (lambda[i]=sum, --i>=0) sum+=wt[i];
return result;
}
matrix* To_Part_m (entry** wt, index n_rows, index n)
{ index i; matrix* result=mkmatrix(n_rows,n+1); entry** lambda=result->elm;
for (i=0; i<n_rows; ++i)
{ index j=n; entry sum=0;
while (lambda[i][j]=sum, --j>=0) sum+=wt[i][j];
}
return 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);
}
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