void swap(number* x, number* y) {
    number tmp = *x;
    *x = *y;
    *y = tmp;
}
void string_swap (number* matrix,int dimension, int f_string , int s_string) {
    int i;
    for (i=0; i<dimension;i++) {
        swap(&matrix[f_string*dimension + i],&matrix[s_string*dimension+i]);
    }
}
number determinant (number* matrix, int dimension, Zp field) {
    number res = copy_number(one);
    number* c_matrix = (number*)mlc(sizeof(number)*dimension*dimension);
    int i,j,k,count=0;
    for (i=0;i<dimension*dimension;i++)
        c_matrix[i] = copy_number(matrix[i]);
    number t;
    number deg = Zp_sub(field,field->n, new_number("2"));
    for (i=0;i<dimension;i++) {
         k = i;
         for(j=i+1;j<dimension;j++)
            if (Z_more(c_matrix[j*dimension+i], c_matrix[dimension*k+i]))
                k = j;
        if (Z_equals(c_matrix[k*dimension+i], zero)) {
            free_number(deg);
            for(i=0;i<dimension*dimension;i++)
                free_number(c_matrix[i]);
            fri(c_matrix);
            return zero;
        }
         if(i != k) {
            string_swap(c_matrix,dimension,i,k);
            count++;
         }
            res=Zp_mult_a(field,res, c_matrix[i*dimension+i]);
        for (j= i+1;j<dimension;j++){
            t = fast_pow_in_field(c_matrix[i*dimension+i],deg, field);
            c_matrix[i*dimension+j] = Zp_mult_a(field,c_matrix[i*dimension+j],t);
            free_number(t);
        }
        for (j=0; j<dimension; j++) {
            if (j != i &&  Z_more(c_matrix[j*dimension+i],zero))
                for (k=i+1 ; k<dimension ; k++) {
                    t = Zp_mult(field,c_matrix[i*dimension+k], c_matrix[j*dimension+i]);
                    c_matrix[j*dimension+k] = Zp_sub_a(field,c_matrix[j*dimension+k],t);
                    free_number(t);
                }
        }
    }
    if (count&1) {
        t = copy_number(res);
        free_number(res);
        res=Z_sub(field->n,t);
        free_number(t);
    }
    free_number(deg);
    for(i=0;i<dimension*dimension;i++)
        free_number(c_matrix[i]);
    fri(c_matrix);
    return res;
}