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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_isom.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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@ matrix_TYP *hyperbolic_isometry(x1, x2, S)

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@ matrix_TYP *x1, *x2, *S;

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@

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@ The first row in the matrix x1 (resp. x2) is interpreted as a vector

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@ v1 (resp. v2) in Z^n.

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@ The function calculates a matrix A in GL_n(Q) (if exists) with

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@          v1A = v2 and ASA^{tr} = S

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@ Any integral matrix with this property must be of the form BA where

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@ B is a matrix of the group that can be caluclated with

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@    B = hyperbolic_stabilizer(x1, S)

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

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@

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

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matrix_TYP *hyperbolic_isometry(x1, x2, S)

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matrix_TYP *x1, *x2, *S;

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{

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  matrix_TYP *x1S, *x2S, *x1SO, *x2SO, **S1red, **S2red, *T1,*T1i, *T2;

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  matrix_TYP *Y1, *Y1i, *Y2, *Y;

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  int i,j,k, n;

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  extern matrix_TYP *solve_mat();

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  extern matrix_TYP *mat_mul();

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  extern matrix_TYP *mat_inv();

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  extern matrix_TYP *scal_pr();

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  extern matrix_TYP *pr_isom();

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  extern matrix_TYP *init_mat();

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  n = x1->cols;

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  if((S1red = (matrix_TYP **)malloc(1 *sizeof(matrix_TYP *))) == NULL)

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  {

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    printf("malloc of 'S1red' in 'hyperbolic_isometry' failed\n");

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    exit(2);

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  }

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  if((S2red = (matrix_TYP **)malloc(1 *sizeof(matrix_TYP *))) == NULL)

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  {

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    printf("malloc of 'S2red' in 'hyperbolic_isometry' failed\n");

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    exit(2);

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  }

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  x1S = mat_mul(x1, S);

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  x1SO = solve_mat(x1S);

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  S1red[0] = scal_pr(x1SO, S, 1);

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  x2S = mat_mul(x2, S);

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  x2SO = solve_mat(x2S);

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  S2red[0] = scal_pr(x2SO, S, 1);

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  Y1 = pr_isom(S1red, S2red, 1, NULL, 0, NULL);

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  free_mat(S1red[0]); free(S1red);

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  free_mat(S2red[0]); free(S2red);

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  free_mat(x1S); free_mat(x2S);

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  if(Y1 == NULL)

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  {

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    free_mat(x1SO); free_mat(x2SO);

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    return(NULL);

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  }

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  T1 = init_mat(n,n,"");

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

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

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     T1->array.SZ[i][j] = x1SO->array.SZ[i][j];

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

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   T1->array.SZ[n-1][i] = x1->array.SZ[0][i];

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  T1i = mat_inv(T1);

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  free_mat(T1);

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  free_mat(x1SO);

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  T2 = init_mat(n,n,"");

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  Y1i = mat_inv(Y1);

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  Y2 = mat_mul(Y1i, x2SO);

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

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

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      T2->array.SZ[i][j] = Y2->array.SZ[i][j];

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

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    T2->array.SZ[n-1][i] = x2->array.SZ[0][i];

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  free_mat(x2SO);

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  free_mat(Y2);

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  free_mat(Y1);

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  free_mat(Y1i);

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  Y = mat_mul(T1i, T2);

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  free_mat(T1i); free_mat(T2);

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  return(Y);

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}

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