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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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#include"typedef.h"

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/**************************************************************************\

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@---------------------------------------------------------------------------

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@---------------------------------------------------------------------------

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@ FILE: hyp_stabilizer.c

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@---------------------------------------------------------------------------

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@---------------------------------------------------------------------------

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@

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\**************************************************************************/

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/**************************************************************************\

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@---------------------------------------------------------------------------

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@ bravais_TYP *hyperbolic_stabilizer(x, S)

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@ matrix_TYP *x, *S;

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@

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@ the functions 'hyperbolic_stabilizer' calculates generators 

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@ for a finite subgroup G of GL_n(Q) with

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@    vg = v   and gSg^{tr} = S for all g in G.

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@ where v denotes the first row of x.

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@ The group H of all integral matrices with this property is

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@ a subgroup of H.

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@---------------------------------------------------------------------------

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@

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\**************************************************************************/

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bravais_TYP *hyperbolic_stabilizer(x, S)

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matrix_TYP *x, *S;

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{

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  matrix_TYP *xS, *xS0, **Sred, *T, *Ti, *W, *W1;

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  bravais_TYP *G1, *G;

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  int i,j,k, n;

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  extern matrix_TYP *mat_mul();

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  extern matrix_TYP *mat_inv();

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  extern bravais_TYP *pr_aut();

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  extern matrix_TYP *solve_mat();

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  extern matrix_TYP *init_mat();

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  extern matrix_TYP *scal_pr();

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  n = x->cols;

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  xS = mat_mul(x, S);

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  xS0 = solve_mat(xS);

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  if((Sred = (matrix_TYP **)malloc(1*sizeof(matrix_TYP *))) == NULL)

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  {

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     printf("malloc of 'Sred' in 'hyperbolic_stabilizer' failed\n");

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     exit(2);

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  }

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  Sred[0] = scal_pr(xS0, S, 1);

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  G1 = pr_aut(Sred, 1, NULL, 0, NULL);

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  if((G = (bravais_TYP *)malloc(sizeof(bravais_TYP))) == NULL)

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  {

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     printf("malloc of 'G' in 'hyperbolic_stabilizer' failed\n");

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     exit(2);

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  }

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  G->gen_no = G1->gen_no;

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  if((G->gen = (matrix_TYP **)malloc(G->gen_no *sizeof(matrix_TYP *))) == NULL)

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  {

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     printf("malloc of 'G->gen' in 'hyperbolic_stabilizer' failed\n");

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     exit(2);

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  }

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  G->zentr_no = G->form_no = G->normal_no = G->cen_no = 0;

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  for(i=0;i<100;i++)

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   G->divisors[i] = G1->divisors[i];

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  G->order = G1->order;

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  G->dim = n;

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  T = init_mat(n,n,"");

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  for(i=0;i<n-1;i++)

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  {

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    for(j=0;j<n;j++)

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     T->array.SZ[i][j] = xS0->array.SZ[i][j];

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  }

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  for(i=0;i<n;i++)

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     T->array.SZ[n-1][i] = x->array.SZ[0][i];

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  Ti = mat_inv(T);

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  W = init_mat(n,n,"");

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  W->array.SZ[n-1][n-1] = 1;

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  for(i=0;i<G->gen_no;i++)

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  {

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    for(j=0;j<n-1;j++)

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      for(k=0;k<n-1;k++)

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        W->array.SZ[j][k] = G1->gen[i]->array.SZ[j][k];

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    W1 = mat_mul(Ti, W);

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    G->gen[i] = mat_mul(W1, T);

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    free_mat(W1); 

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  }

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  free_mat(W); free_mat(T); free_mat(Ti);

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  free_bravais(G1);

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  free_mat(xS); free_mat(xS0); free_mat(Sred[0]); free(Sred);

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  return(G);

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}

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