d5/df9/groups_8h_source.html

// group_theory.h

//

// Anton Betten

//

// moved here from action.h: July 28, 2018

// based on action.h which was started:  August 13, 2005


#ifndef ORBITER_SRC_LIB_GROUP_ACTIONS_GROUPS_GROUPS_H_

#define ORBITER_SRC_LIB_GROUP_ACTIONS_GROUPS_GROUPS_H_


namespace orbiter {

namespace layer3_group_actions {

namespace groups {


// #############################################################################

// direct_product.cpp

// #############################################################################


class direct_product {


public:

    matrix_group *M1;

    matrix_group *M2;

    field_theory::finite_field *F1;

    field_theory::finite_field *F2;

    int q1;

    int q2;


    std::string label;

    std::string label_tex;


    int degree_of_matrix_group1;

    int dimension_of_matrix_group1;

    int degree_of_matrix_group2;

    int dimension_of_matrix_group2;

    int degree_of_product_action;

    int degree_overall;

    int low_level_point_size;

    int make_element_size;

    int elt_size_int;


    int *perm_offset_i;

    int *tmp_Elt1;


    int bits_per_digit1;

    int bits_per_digit2;


    int bits_per_elt;

    int char_per_elt;


    uchar *elt1;


    int base_len_in_component1;

    long int *base_for_component1;

    int *tl_for_component1;


    int base_len_in_component2;

    long int *base_for_component2;

    int *tl_for_component2;


    int base_length;

    long int *the_base;

    int *the_transversal_length;


    data_structures::page_storage *Elts;


    direct_product();

    ~direct_product();

    void null();

    void freeself();

    void init(matrix_group *M1, matrix_group *M2,

            int verbose_level);

    long int element_image_of(int *Elt, long int a, int verbose_level);

    void element_one(int *Elt);

    int element_is_one(int *Elt);

    void element_mult(int *A, int *B, int *AB, int verbose_level);

    void element_move(int *A, int *B, int verbose_level);

    void element_invert(int *A, int *Av, int verbose_level);

    int offset_i(int i);

    void element_pack(int *Elt, uchar *elt);

    void element_unpack(uchar *elt, int *Elt);

    void put_digit(uchar *elt, int f, int i, int d);

    int get_digit(uchar *elt, int f, int i);

    void make_element(int *Elt, int *data, int verbose_level);

    void element_print_easy(int *Elt, std::ostream &ost);

    void compute_base_and_transversals(int verbose_level);

    void make_strong_generators_data(int *&data,

            int &size, int &nb_gens, int verbose_level);

    void lift_generators(

            strong_generators *SG1,

            strong_generators *SG2,

            actions::action *A, strong_generators *&SG3,

            int verbose_level);

};


// #############################################################################

// exceptional_isomorphism_O4.cpp

// #############################################################################


class exceptional_isomorphism_O4 {

public:

    field_theory::finite_field *Fq;

    actions::action *A2;

    actions::action *A4;

    actions::action *A5;


    int *E5a;

    int *E4a;

    int *E2a;

    int *E2b;


    exceptional_isomorphism_O4();

    ~exceptional_isomorphism_O4();

    void null();

    void freeself();

    void init(field_theory::finite_field *Fq,

            actions::action *A2,

            actions::action *A4,

            actions::action *A5,

            int verbose_level);

    void apply_2to4_embedded(

        int f_switch, int *mtx2x2_T, int *mtx2x2_S, int *Elt,

        int verbose_level);

    void apply_5_to_4(

        int *mtx4x4, int *mtx5x5, int verbose_level);

    void apply_4_to_5(

        int *E4, int *E5, int verbose_level);

    void apply_4_to_2(

        int *E4, int &f_switch, int *E2_a, int *E2_b,

        int verbose_level);

    void apply_2_to_4(

        int &f_switch, int *E2_a, int *E2_b, int *E4,

        int verbose_level);

    void print_as_2x2(int *mtx4x4);

};


// #############################################################################

// linear_group_description.cpp

// #############################################################################


class linear_group_description {

public:

    int f_projective;

    int f_general;

    int f_affine;

    int f_GL_d_q_wr_Sym_n;

    int f_orthogonal;

    int f_orthogonal_p;

    int f_orthogonal_m;

    int GL_wreath_Sym_d;

    int GL_wreath_Sym_n;


    int n;


    // change input_q to string so that we can allow symbols:

    //int input_q;

    std::string input_q;


    int f_override_polynomial;

    std::string override_polynomial;

    field_theory::finite_field *F;

    int f_semilinear;

    int f_special;


    // induced actions and subgroups:


    int f_wedge_action;

    int f_wedge_action_detached;

    int f_PGL2OnConic;

    int f_monomial_group;

    int f_diagonal_group;

    int f_null_polarity_group;

    int f_symplectic_group;

    int f_singer_group;

    int f_singer_group_and_frobenius;

    int singer_power;

    int f_subfield_structure_action;

    int s;

    int f_subgroup_from_file;

    int f_borel_subgroup_upper;

    int f_borel_subgroup_lower;

    int f_identity_group;

    std::string subgroup_fname;

    std::string subgroup_label;

    int f_orthogonal_group;

    int orthogonal_group_epsilon;


    int f_on_k_subspaces;

    int on_k_subspaces_k;


    int f_on_tensors;

    int f_on_rank_one_tensors;


    int f_subgroup_by_generators;

    std::string subgroup_order_text;

    int nb_subgroup_generators;

    std::string subgroup_generators_label;


    int f_Janko1;


    int f_restricted_action;

    std::string restricted_action_text;


    int f_export_magma;


    linear_group_description();

    ~linear_group_description();

    void null();

    void freeself();

    int read_arguments(int argc, std::string *argv,

        int verbose_level);

    void print();


};


// #############################################################################

// linear_group.cpp

// #############################################################################


class linear_group {

public:

    linear_group_description *description;

    int n;

    int input_q;

    field_theory::finite_field *F;

    int f_semilinear;


    std::string label;

    std::string label_tex;


    strong_generators *initial_strong_gens;

    actions::action *A_linear;

    matrix_group *Mtx;


    int f_has_strong_generators;

    strong_generators *Strong_gens;

    actions::action *A2;

    int vector_space_dimension;

    int q;


    int f_has_nice_gens;

    data_structures_groups::vector_ge *nice_gens;


    linear_group();

    ~linear_group();

    void null();

    void freeself();

    void linear_group_init(linear_group_description *description,

        int verbose_level);

    void init_PGL2q_OnConic(int verbose_level);

    void init_wedge_action(int verbose_level);

    void init_wedge_action_detached(int verbose_level);

    void init_monomial_group(int verbose_level);

    void init_diagonal_group(int verbose_level);

    void init_singer_group(int singer_power, int verbose_level);

    void init_singer_group_and_frobenius(int singer_power, int verbose_level);

    void init_null_polarity_group(int verbose_level);

    void init_borel_subgroup_upper(int verbose_level);

    void init_identity_subgroup(int verbose_level);

    void init_symplectic_group(int verbose_level);

    void init_subfield_structure_action(int s, int verbose_level);

    void init_orthogonal_group(int epsilon, int verbose_level);

    void init_subgroup_from_file(

            std::string &subgroup_fname,

            std::string &subgroup_label,

            int verbose_level);

    void init_subgroup_by_generators(

            std::string &subgroup_label,

            std::string &subgroup_order_text,

            int nb_subgroup_generators,

            int *subgroup_generators_data,

            int verbose_level);

    void init_subgroup_Janko1(int verbose_level);

    void report(std::ostream &fp, int f_sylow, int f_group_table,

            int f_conjugacy_classes_and_normalizers,

            graphics::layered_graph_draw_options *LG_Draw_options,

            int verbose_level);

    void create_latex_report(

            graphics::layered_graph_draw_options *O,

            int f_sylow, int f_group_table, int f_classes,

            int verbose_level);


};


// #############################################################################

// matrix_group.cpp

// #############################################################################


class matrix_group {


public:

    int f_projective;

        // n x n matrices (possibly with Frobenius)

        // acting on PG(n - 1, q)

    int f_affine;

        // n x n matrices plus translations

        // (possibly with Frobenius)

        // acting on F_q^n

    int f_general_linear;

        // n x n matrices (possibly with Frobenius)

        // acting on F_q^n


    int n;

        // the size of the matrices


    int degree;

        // the degree of the action:

        // (q^(n-1)-1) / (q - 1) if f_projective

        // q^n if f_affine or f_general_linear


    int f_semilinear;

        // use Frobenius automorphism


    int f_kernel_is_diagonal_matrices;


    int bits_per_digit;

    int bits_per_elt;

    int bits_extension_degree;

    int char_per_elt;

    int elt_size_int;

    int elt_size_int_half;

    int low_level_point_size; // added Jan 26, 2010

        // = n, the size of the vectors on which we act

    int make_element_size;


    std::string label;

    std::string label_tex;


    int f_GFq_is_allocated;

        // if TRUE, GFq will be destroyed in the destructor

        // if FALSE, it is the responsibility

        // of someone else to destroy GFq


    field_theory::finite_field *GFq;

    void *data;


    algebra::gl_classes *C; // added Dec 2, 2013


    // temporary variables, do not use!

    int *Elt1, *Elt2, *Elt3;

        // used for mult, invert

    int *Elt4;

        // used for invert

    int *Elt5;

    int *tmp_M;

        // used for GL_mult_internal

    int *base_cols;

        // used for Gauss during invert

    int *v1, *v2;

        // temporary vectors of length 2n

    int *v3;

        // used in GL_mult_vector_from_the_left_contragredient

    uchar *elt1, *elt2, *elt3;

        // temporary storage, used in element_store()


    data_structures::page_storage *Elts;


    matrix_group();

    ~matrix_group();


    void init_projective_group(int n, field_theory::finite_field *F,

        int f_semilinear, actions::action *A, int verbose_level);

    void init_affine_group(int n, field_theory::finite_field *F,

        int f_semilinear, actions::action *A, int verbose_level);

    void init_general_linear_group(int n, field_theory::finite_field *F,

        int f_semilinear, actions::action *A, int verbose_level);

    void allocate_data(int verbose_level);

    void free_data(int verbose_level);

    void setup_page_storage(int page_length_log, int verbose_level);

    void compute_elt_size(int verbose_level);

    void init_base(actions::action *A, int verbose_level);

    void init_base_projective(actions::action *A, int verbose_level);

        // initializes base, base_len, degree,

        // transversal_length, orbit, orbit_inv

    void init_base_affine(actions::action *A, int verbose_level);

    void init_base_general_linear(actions::action *A, int verbose_level);

    void init_gl_classes(int verbose_level);


    int GL_element_entry_ij(int *Elt, int i, int j);

    int GL_element_entry_frobenius(int *Elt);

    long int image_of_element(int *Elt, long int a, int verbose_level);

    long int GL_image_of_PG_element(int *Elt, long int a, int verbose_level);

    long int GL_image_of_AG_element(int *Elt, long int a, int verbose_level);

    void action_from_the_right_all_types(

        int *v, int *A, int *vA, int verbose_level);

    void projective_action_from_the_right(

        int *v, int *A, int *vA, int verbose_level);

    void general_linear_action_from_the_right(

        int *v, int *A, int *vA, int verbose_level);

    void substitute_surface_equation(int *Elt,

            int *coeff_in, int *coeff_out, algebraic_geometry::surface_domain *Surf,

            int verbose_level);

    void GL_one(int *Elt);

    void GL_one_internal(int *Elt);

    void GL_zero(int *Elt);

    int GL_is_one(int *Elt);

    void GL_mult(int *A, int *B, int *AB, int verbose_level);

    void GL_mult_internal(int *A, int *B, int *AB, int verbose_level);

    void GL_copy(int *A, int *B);

    void GL_copy_internal(int *A, int *B);

    void GL_transpose(int *A, int *At, int verbose_level);

    void GL_transpose_internal(int *A, int *At, int verbose_level);

    void GL_invert(int *A, int *Ainv);

    void GL_invert_internal(int *A, int *Ainv, int verbose_level);

    void GL_unpack(uchar *elt, int *Elt, int verbose_level);

    void GL_pack(int *Elt, uchar *elt);

    void GL_print_easy(int *Elt, std::ostream &ost);

    void GL_code_for_make_element(int *Elt, int *data);

    void GL_print_for_make_element(int *Elt, std::ostream &ost);

    void GL_print_for_make_element_no_commas(int *Elt, std::ostream &ost);

    void GL_print_easy_normalized(int *Elt, std::ostream &ost);

    void GL_print_latex(int *Elt, std::ostream &ost);

    void GL_print_latex_with_print_point_function(int *Elt,

            std::ostream &ost,

            void (*point_label)(std::stringstream &sstr, int pt, void *data),

            void *point_label_data);

    void GL_print_easy_latex(int *Elt, std::ostream &ost);

    void GL_print_easy_latex_with_option_numerical(int *Elt, int f_numerical, std::ostream &ost);

    void decode_matrix(int *Elt, int n, uchar *elt);

    int get_digit(uchar *elt, int i, int j);

    int decode_frobenius(uchar *elt);

    void encode_matrix(int *Elt, int n, uchar *elt);

    void put_digit(uchar *elt, int i, int j, int d);

    void encode_frobenius(uchar *elt, int d);

    void make_element(int *Elt, int *data, int verbose_level);

    void make_GL_element(int *Elt, int *A, int f);

    void orthogonal_group_random_generator(

            actions::action *A,

            orthogonal_geometry::orthogonal *O,

        int f_siegel,

        int f_reflection,

        int f_similarity,

        int f_semisimilarity,

        int *Elt, int verbose_level);

    void matrices_without_eigenvector_one(

        sims *S, int *&Sol, int &cnt,

        int f_path_select, int select_value,

        int verbose_level);

    void matrix_minor(int *Elt, int *Elt1,

        matrix_group *mtx1, int f, int verbose_level);

    int base_len(int verbose_level);

    void base_and_transversal_length(

            int base_len,

            long int *base, int *transversal_length,

            int verbose_level);

    void strong_generators_low_level(int *&data,

            int &size, int &nb_gens, int verbose_level);

    int has_shape_of_singer_cycle(int *Elt);

};


// #############################################################################

// orbits_on_something.cpp

// #############################################################################


class orbits_on_something {


public:


    actions::action *A;

    strong_generators *SG;

    schreier *Sch;


    int f_load_save;

    std::string prefix;

    std::string fname;

    std::string fname_csv;


    data_structures::tally *Classify_orbits_by_length;

    data_structures::set_of_sets *Orbits_classified;


    int *Orbits_classified_length; // [Orbits_classified_nb_types]

    int Orbits_classified_nb_types;


    orbits_on_something();

    ~orbits_on_something();

    void null();

    void freeself();

    void init(

            actions::action *A,

            strong_generators *SG,

            int f_load_save,

            std::string &prefix,

            int verbose_level);

    void stabilizer_of(int orbit_idx, int verbose_level);

    void idx_of_points_in_orbits_of_length_l(

            long int *set, int set_sz, int go, int l,

            std::vector<int> &Idx,

            int verbose_level);

    void orbit_type_of_set(

            long int *set, int set_sz, int go,

            long int *orbit_type,

            int verbose_level);

    // orbit_type[(go + 1) * go] must be allocated beforehand

    void report_type(std::ostream &ost, long int *orbit_type, long int goi);

    void compute_compact_type(long int *orbit_type, long int goi,

            long int *&compact_type, long int *&row_labels, long int *&col_labels, int &m, int &n);

    void report_orbit_lengths(std::ostream &ost);

    void print_orbits_based_on_filtered_orbits(std::ostream &ost, data_structures::set_of_sets *Filtered_orbits);

    void classify_orbits_by_length(int verbose_level);

    void report_classified_orbit_lengths(std::ostream &ost);

    void report_classified_orbits_by_lengths(std::ostream &ost);

    int get_orbit_type_index(int orbit_length);

    int get_orbit_type_index_if_present(int orbit_length);

    void test_all_orbits_by_length(

        int (*test_function)(long int *orbit, int orbit_length, void *data),

        void *test_function_data,

        int verbose_level);

    void test_orbits_of_a_certain_length(

        int orbit_length,

        int &type_idx,

        int &prev_nb,

        int (*test_function)(long int *orbit, int orbit_length, void *data),

        void *test_function_data,

        int verbose_level);

    void print_orbits_of_a_certain_length(int orbit_length);

    int test_pair_of_orbits_of_a_equal_length(

            int orbit_length,

            int type_idx,

            int idx1, int idx2,

            long int *Orbit1,

            long int *Orbit2,

            int (*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data),

            void *test_function_data,

            int verbose_level);

    void report_orbits_of_type(std::ostream &ost, int type_idx);

    void create_graph_on_orbits_of_a_certain_length_after_filtering(

            graph_theory::colored_graph *&CG,

        std::string &fname,

        long int *filter_by_set,

        int filter_by_set_size,

        int orbit_length,

        int &type_idx,

        int f_has_user_data, long int *user_data, int user_data_size,

        int f_has_colors, int number_colors, int *color_table,

        int (*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data),

        void *test_function_data,

        int verbose_level);

    void create_graph_on_orbits_of_a_certain_length(

            graph_theory::colored_graph *&CG,

        std::string &fname,

        int orbit_length,

        int &type_idx,

        int f_has_user_data, long int *user_data, int user_data_size,

        int f_has_colors, int number_colors, int *color_table,

        int (*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data),

        void *test_function_data,

        int verbose_level);

    void extract_orbits(

        int orbit_length,

        int nb_orbits,

        int *orbits,

        long int *extracted_set,

        int verbose_level);

    void extract_orbits_using_classification(

        int orbit_length,

        int nb_orbits,

        long int *orbits_idx,

        long int *extracted_set,

        int verbose_level);

    void create_graph_on_orbits_of_a_certain_length_override_orbits_classified(

            graph_theory::colored_graph *&CG,

        std::string &fname,

        int orbit_length,

        int &type_idx,

        int f_has_user_data, long int *user_data, int user_data_size,

        int (*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data),

        void *test_function_data,

        data_structures::set_of_sets *my_orbits_classified,

        int verbose_level);

    void create_weighted_graph_on_orbits(

            graph_theory::colored_graph *&CG,

        std::string &fname,

        int *Orbit_lengths,

        int nb_orbit_lengths,

        int *&Type_idx,

        int f_has_user_data, long int *user_data, int user_data_size,

        int (*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data),

        void *test_function_data,

        data_structures::set_of_sets *my_orbits_classified,

        int verbose_level);

    void compute_orbit_invariant_after_classification(

            data_structures::set_of_sets *&Orbit_invariant,

            int (*evaluate_orbit_invariant_function)(int a, int i, int j, void *evaluate_data, int verbose_level),

            void *evaluate_data, int verbose_level);

    void get_orbit_number_and_position(long int a, int &orbit_idx, int &orbit_pos, int verbose_level);

    void create_latex_report(int verbose_level);

    void report(std::ostream &ost, int verbose_level);

    void report_quick(std::ostream &ost, int verbose_level);


};


// #############################################################################

// permutation_group_create.cpp

// #############################################################################


class permutation_group_create {


public:

    permutation_group_description *Descr;


    std::string label;

    std::string label_tex;


    //strong_generators *initial_strong_gens;

    actions::action *A_initial;


    int f_has_strong_generators;

    strong_generators *Strong_gens;

    actions::action *A2;


    int f_has_nice_gens;

    data_structures_groups::vector_ge *nice_gens;


    permutation_group_create();

    ~permutation_group_create();

    void permutation_group_init(

            permutation_group_description *description,

            int verbose_level);

    void init_subgroup_by_generators(

            std::string &subgroup_label,

            std::string &subgroup_order_text,

            int nb_subgroup_generators,

            std::string &subgroup_generators_label,

            int verbose_level);


};


// #############################################################################

// permutation_group_description.cpp

// #############################################################################


class permutation_group_description {


public:

    int degree;

    permutation_group_type type;


    int f_bsgs;

    std::string bsgs_label;

    std::string bsgs_label_tex;

    std::string bsgs_order_text;

    std::string bsgs_base;

    int bsgs_nb_generators;

    std::string bsgs_generators;


    int f_subgroup_by_generators;

    std::string subgroup_label;

    std::string subgroup_order_text;

    int nb_subgroup_generators;

    std::string subgroup_generators_label;


    permutation_group_description();

    ~permutation_group_description();

    int read_arguments(

        int argc, std::string *argv,

        int verbose_level);

    void print();


};


// #############################################################################

// permutation_representation_domain.cpp

// #############################################################################


class permutation_representation_domain {


public:

    int degree;


    int f_induced_action;


    int f_product_action;

    int m;

    int n;

    int mn;

    int offset;


    int char_per_elt;

    int elt_size_int;


    int *Elt1, *Elt2, *Elt3, *Elt4;

    uchar *elt1, *elt2, *elt3;

        // temporary storage, used in element_store()

    int *Eltrk1, *Eltrk2, *Eltrk3;

        // used in store / retrieve


    data_structures::page_storage *Elts;


    permutation_representation_domain();

    ~permutation_representation_domain();

    void null();

    void free();

    void allocate();

    void init_product_action(int m, int n,

        int page_length_log, int verbose_level);

    void init(int degree, int page_length_log, int verbose_level);

    void init_data(int page_length_log, int verbose_level);

    void init_with_base(int degree,

        int base_length, int *base, int page_length_log,

        actions::action &A, int verbose_level);

    void transversal_rep(int i, int j, int *Elt, int verbose_level);

    void one(int *Elt);

    int is_one(int *Elt);

    void mult(int *A, int *B, int *AB);

    void copy(int *A, int *B);

    void invert(int *A, int *Ainv);

    void unpack(uchar *elt, int *Elt);

    void pack(int *Elt, uchar *elt);

    void print(int *Elt, std::ostream &ost);

    void print_with_print_point_function(int *Elt,

            std::ostream &ost,

            void (*point_label)(std::stringstream &sstr, long int pt, void *data),

            void *point_label_data);

    void code_for_make_element(int *Elt, int *data);

    void print_for_make_element(int *Elt, std::ostream &ost);

    void print_for_make_element_no_commas(int *Elt, std::ostream &ost);

    void print_with_action(actions::action *A, int *Elt, std::ostream &ost);

    void make_element(int *Elt, int *data, int verbose_level);


};


// #############################################################################

// permutation_representation.cpp

// #############################################################################


class permutation_representation {


public:

    actions::action *A_original;

    int f_stay_in_the_old_action;

    int nb_gens;

    data_structures_groups::vector_ge *gens; // the original generators in action A_original

    int *Perms; // [nb_gens * degree]

    int degree;

    //longinteger_object target_go;


    permutation_representation_domain *P;

    int perm_offset;

    int elt_size_int;

        // A_original->elt_size_int + P->elt_size_int

    int make_element_size;


    int char_per_elt;

    uchar *elt1; // [char_per_elt]


    std::string label;

    std::string label_tex;


    data_structures::page_storage *PS;


    int *Elts;

        // [nb_gens * elt_size_int], the generators in the induced action


    permutation_representation();

    ~permutation_representation();

    void init(actions::action *A_original,

            int f_stay_in_the_old_action,

            data_structures_groups::vector_ge *gens,

            int *Perms, int degree,

            int verbose_level);

        // Perms is degree x nb_gens

    long int element_image_of(int *Elt, long int a, int verbose_level);

    void element_one(int *Elt);

    int element_is_one(int *Elt);

    void element_mult(int *A, int *B, int *AB, int verbose_level);

    void element_move(int *A, int *B, int verbose_level);

    void element_invert(int *A, int *Av, int verbose_level);

    void element_pack(int *Elt, uchar *elt);

    void element_unpack(uchar *elt, int *Elt);

    void element_print_for_make_element(int *Elt, std::ostream &ost);

    void element_print_easy(int *Elt, std::ostream &ost);

    void element_print_latex(int *Elt, std::ostream &ost);

};


// #############################################################################

// schreier.cpp

// #############################################################################


class schreier {


public:

    actions::action *A;

    int f_images_only;

    long int degree;

    data_structures_groups::vector_ge gens;

    data_structures_groups::vector_ge gens_inv;

    int nb_images;

    int **images;

        // [nb_gens][2 * A->degree],

        // allocated by init_images,

        // called from init_generators

        // for each generator,

        // stores the generator as permutation in 0..A->degree-1 ,

        // then the inverse generator in A->degree..2*A->degree-1


    int *orbit; // [A->degree]

    int *orbit_inv; // [A->degree]


        // prev and label are indexed

        // by the points in the order as listed in orbit.

    int *prev; // [A->degree]

    int *label; // [A->degree]

    //int *orbit_no; // [A->degree]

        // to find out which orbit point a lies in,

        // use orbit_number(pt).

        // It used to be orbit_no[orbit_inv[a]]


    int *orbit_first;  // [A->degree + 1]

    int *orbit_len;  // [A->degree]

    int nb_orbits;


    int *Elt1, *Elt2, *Elt3;

    int *schreier_gen, *schreier_gen1;

        // used in random_schreier_generator

    int *cosetrep, *cosetrep_tmp;

        // used in coset_rep / coset_rep_inv


    int f_print_function;

    void (*print_function)(std::ostream &ost, int pt, void *data);

    void *print_function_data;


    int f_preferred_choice_function;

    void (*preferred_choice_function)(int pt, int &pt_pref, schreier *Sch, void *data, int data2, int verbose_level);

    void *preferred_choice_function_data;

    int preferred_choice_function_data2;


    schreier();

    schreier(actions::action *A, int verbose_level);

    ~schreier();

    void freeself();

    void delete_images();

    void init_preferred_choice_function(

            void (*preferred_choice_function)(int pt, int &pt_pref, schreier *Sch, void *data, int data2, int verbose_level),

            void *preferred_choice_function_data,

            int preferred_choice_function_data2,

            int verbose_level);

    void init_images(int nb_images, int verbose_level);

    void init_images_only(int nb_images,

            long int degree, int *images, int verbose_level);

    void images_append(int verbose_level);

    void init(actions::action *A, int verbose_level);

    void allocate_tables();

    void init2();

    void initialize_tables();

    void init_single_generator(int *elt, int verbose_level);

    void init_generators(data_structures_groups::vector_ge &generators, int verbose_level);

    void init_images_recycle(int nb_images,

            int **old_images,

            int idx_deleted_generator,

            int verbose_level);

    void init_images_recycle(int nb_images,

            int **old_images, int verbose_level);

    void init_generators(int nb, int *elt, int verbose_level);

    void init_generators_recycle_images(

            data_structures_groups::vector_ge &generators, int **old_images,

            int idx_generator_to_delete, int verbose_level);

    void init_generators_recycle_images(

            data_structures_groups::vector_ge &generators, int **old_images, int verbose_level);


        // elt must point to nb * A->elt_size_in_int

        // int's that are

        // group elements in int format

    void init_generators_recycle_images(int nb,

            int *elt, int **old_images,

            int idx_generator_to_delete, int verbose_level);

    void init_generators_recycle_images(int nb,

            int *elt, int **old_images, int verbose_level);

    void init_generators_by_hdl(int nb_gen, int *gen_hdl,

        int verbose_level);

    void init_generators_by_handle(std::vector<int> &gen_hdl, int verbose_level);

    long int get_image(long int i, int gen_idx, int verbose_level);

    void swap_points(int i, int j, int verbose_level);

    void move_point_here(int here, int pt);

    int orbit_representative(int pt);

    int depth_in_tree(int j);

        // j is a coset, not a point

    void transporter_from_orbit_rep_to_point(int pt,

        int &orbit_idx, int *Elt, int verbose_level);

    void transporter_from_point_to_orbit_rep(int pt,

        int &orbit_idx, int *Elt, int verbose_level);

    void coset_rep(int j, int verbose_level);

        // j is a coset, not a point

        // result is in cosetrep

        // determines an element in the group

        // that moves the orbit representative

        // to the j-th point in the orbit.

    void coset_rep_with_verbosity(int j, int verbose_level);

    void coset_rep_inv(int j, int verbose_level);

    void extend_orbit(int *elt, int verbose_level);

    void compute_all_point_orbits(int verbose_level);

    void compute_all_point_orbits_with_prefered_reps(

        int *prefered_reps, int nb_prefered_reps,

        int verbose_level);

    void compute_all_point_orbits_with_preferred_labels(

        long int *preferred_labels, int verbose_level);

    void compute_all_orbits_on_invariant_subset(int len,

        long int *subset, int verbose_level);

    void compute_all_orbits_on_invariant_subset_lint(

        int len, long int *subset, int verbose_level);

    void compute_point_orbit(int pt, int verbose_level);

    void compute_point_orbit_with_limited_depth(

            int pt, int max_depth, int verbose_level);

    int sum_up_orbit_lengths();

    void non_trivial_random_schreier_generator(actions::action *A_original,

            int *Elt, int verbose_level);

        // computes non trivial random Schreier

        // generator into schreier_gen

        // non-trivial is with respect to A_original

    void random_schreier_generator_ith_orbit(

            int *Elt, int orbit_no,

            int verbose_level);

        // computes random Schreier generator for the orbit orbit_no into Elt

    void random_schreier_generator(int *Elt, int verbose_level);

        // computes random Schreier generator for the first orbit into Elt

    void trace_back(int *path, int i, int &j);

    void intersection_vector(int *set, int len,

        int *intersection_cnt);

    void orbits_on_invariant_subset_fast(int len,

        int *subset, int verbose_level);

    void orbits_on_invariant_subset_fast_lint(

        int len, long int *subset, int verbose_level);

    void orbits_on_invariant_subset(int len, int *subset,

        int &nb_orbits_on_subset, int *&orbit_perm, int *&orbit_perm_inv);

    void get_orbit_partition_of_points_and_lines(

            data_structures::partitionstack &S, int verbose_level);

    void get_orbit_partition(data_structures::partitionstack &S,

        int verbose_level);

    void get_orbit_in_order(std::vector<int> &Orb,

        int orbit_idx, int verbose_level);

    strong_generators *stabilizer_any_point_plus_cosets(

            actions::action *default_action,

        ring_theory::longinteger_object &full_group_order,

        int pt, data_structures_groups::vector_ge *&cosets, int verbose_level);

    strong_generators *stabilizer_any_point(

            actions::action *default_action,

        ring_theory::longinteger_object &full_group_order, int pt,

        int verbose_level);

    data_structures_groups::set_and_stabilizer *get_orbit_rep(actions::action *default_action,

            ring_theory::longinteger_object &full_group_order,

            int orbit_idx, int verbose_level);

    void get_orbit_rep_to(actions::action *default_action,

            ring_theory::longinteger_object &full_group_order,

            int orbit_idx,

            data_structures_groups::set_and_stabilizer *Rep,

            int verbose_level);

    strong_generators *stabilizer_orbit_rep(

            actions::action *default_action,

        ring_theory::longinteger_object &full_group_order,

        int orbit_idx, int verbose_level);

    void point_stabilizer(actions::action *default_action,

            ring_theory::longinteger_object &go,

            groups::sims *&Stab, int orbit_no, int verbose_level);

        // this function allocates a sims structure into Stab.

    void get_orbit(int orbit_idx, long int *set, int &len,

        int verbose_level);

    void compute_orbit_statistic(int *set, int set_size,

        int *orbit_count, int verbose_level);

    void compute_orbit_statistic_lint(long int *set, int set_size,

        int *orbit_count, int verbose_level);

    void orbits_as_set_of_sets(data_structures::set_of_sets *&S, int verbose_level);

    void get_orbit_reps(int *&Reps, int &nb_reps, int verbose_level);

    int find_shortest_orbit_if_unique(int &idx);

    void elements_in_orbit_of(int pt, int *orb, int &nb,

        int verbose_level);

    void get_orbit_length(int *&orbit_length, int verbose_level);

    void get_orbit_lengths_once_each(int *&orbit_lengths,

        int &nb_orbit_lengths);

    int orbit_number(int pt);

    void get_orbit_number_and_position(int pt, int &orbit_idx, int &orbit_pos, int verbose_level);

    void get_orbit_decomposition_scheme_of_graph(

        int *Adj, int n, int *&Decomp_scheme, int verbose_level);

    void create_point_list_sorted(

            int *&point_list, int &point_list_length);

    void shallow_tree_generators(int orbit_idx,

            int f_randomized,

            schreier *&shallow_tree,

            int verbose_level);

    data_structures_groups::schreier_vector *get_schreier_vector(

            int gen_hdl_first, int nb_gen,

            enum shallow_schreier_tree_strategy Shallow_schreier_tree_strategy,

            int verbose_level);

    int get_num_points();

        // This function returns the number of points in the

        // schreier forest

    double get_average_word_length();

        // This function returns the average word length of the forest.

    double get_average_word_length(int orbit_idx);

    void compute_orbit_invariant(int *&orbit_invariant,

            int (*compute_orbit_invariant_callback)(schreier *Sch,

                    int orbit_idx, void *data, int verbose_level),

            void *compute_orbit_invariant_data,

            int verbose_level);

    void print_TDA(std::ostream &ost, geometry::object_with_canonical_form *OwCF,

            combinatorics::classification_of_objects_report_options *Report_options,

            int verbose_level);

    void latex_TDA(std::ostream &ost,

            combinatorics::encoded_combinatorial_object *Enc,

            int verbose_level);


    // schreier_io.cpp:

    void latex(std::string &fname);

    void print_orbit_lengths(std::ostream &ost);

    void print_orbit_lengths_tex(std::ostream &ost);

    void print_fixed_points_tex(std::ostream &ost);

    void print_orbit_length_distribution(std::ostream &ost);

    void print_orbit_reps(std::ostream &ost);

    void print(std::ostream &ost);

    void print_and_list_orbits(std::ostream &ost);

    void print_and_list_orbits_with_original_labels(std::ostream &ost);

    void print_and_list_orbits_tex(std::ostream &ost);

    void print_and_list_all_orbits_and_stabilizers_with_list_of_elements_tex(

            std::ostream &ost, actions::action *default_action, strong_generators *gens,

            int verbose_level);

    void make_orbit_trees(std::ostream &ost,

            std::string &fname_mask,

            graphics::layered_graph_draw_options *Opt,

            int verbose_level);

    void print_and_list_orbits_with_original_labels_tex(std::ostream &ost);

    void print_and_list_orbits_of_given_length(std::ostream &ost,

        int len);

    void print_and_list_orbits_and_stabilizer(std::ostream &ost,

            actions::action *default_action, ring_theory::longinteger_object &go,

        void (*print_point)(std::ostream &ost, int pt, void *data),

            void *data);

    void print_and_list_orbits_using_labels(std::ostream &ost,

        long int *labels);

    void print_tables(std::ostream &ost, int f_with_cosetrep);

    void print_tables_latex(std::ostream &ost, int f_with_cosetrep);

    void print_generators();

    void print_generators_latex(std::ostream &ost);

    void print_generators_with_permutations();

    void print_orbit(int orbit_no);

    void print_orbit_using_labels(int orbit_no, long int *labels);

    void print_orbit(std::ostream &ost, int orbit_no);

    void print_orbit_with_original_labels(std::ostream &ost, int orbit_no);

    void print_orbit_tex(std::ostream &ost, int orbit_no);

    void print_orbit_sorted_tex(std::ostream &ost, int orbit_no, int f_truncate, int max_length);

    void print_and_list_orbit_and_stabilizer_tex(int i,

            actions::action *default_action,

        ring_theory::longinteger_object &full_group_order,

        std::ostream &ost);

    void write_orbit_summary(std::string &fname,

            actions::action *default_action,

            ring_theory::longinteger_object &full_group_order,

            int verbose_level);

    void print_and_list_orbit_and_stabilizer_with_list_of_elements_tex(

        int i, actions::action *default_action,

        strong_generators *gens, std::ostream &ost);

    void print_and_list_orbit_tex(int i, std::ostream &ost);

    void print_and_list_orbits_sorted_by_length_tex(std::ostream &ost);

    void print_and_list_orbits_and_stabilizer_sorted_by_length(

            std::ostream &ost, int f_tex,

            actions::action *default_action,

        ring_theory::longinteger_object &full_group_order);

    void print_fancy(

            std::ostream &ost, int f_tex,

            actions::action *default_action, strong_generators *gens_full_group);

    void print_and_list_orbits_sorted_by_length(std::ostream &ost);

    void print_and_list_orbits_sorted_by_length(std::ostream &ost, int f_tex);

    void print_orbit_sorted_with_original_labels_tex(std::ostream &ost,

            int orbit_no, int f_truncate, int max_length);

    void print_orbit_using_labels(std::ostream &ost, int orbit_no, long int *labels);

    void print_orbit_using_callback(std::ostream &ost, int orbit_no,

        void (*print_point)(std::ostream &ost, int pt, void *data),

        void *data);

    void print_orbit_type(int f_backwards);

    void list_all_orbits_tex(std::ostream &ost);

    void print_orbit_through_labels(std::ostream &ost,

        int orbit_no, long int *point_labels);

    void print_orbit_sorted(std::ostream &ost, int orbit_no);

    void print_orbit(int cur, int last);

    void print_tree(int orbit_no);

    void export_tree_as_layered_graph(int orbit_no,

            std::string &fname_mask,

            int verbose_level);

    void draw_forest(std::string &fname_mask,

            graphics::layered_graph_draw_options *Opt,

            int f_has_point_labels, long int *point_labels,

            int verbose_level);

    void draw_tree(std::string &fname,

            graphics::layered_graph_draw_options *Opt,

            int orbit_no,

            int f_has_point_labels, long int *point_labels,

            int verbose_level);

    void draw_tree2(std::string &fname,

            graphics::layered_graph_draw_options *Opt,

            int *weight, int *placement_x, int max_depth,

            int i, int last,

            int f_has_point_labels, long int *point_labels,

            int verbose_level);

    void subtree_draw_lines(

            graphics::mp_graphics &G,

            graphics::layered_graph_draw_options *Opt,

            int parent_x, int parent_y, int *weight,

            int *placement_x, int max_depth, int i, int last,

            int y_max,

            int verbose_level);

    void subtree_draw_vertices(

            graphics::mp_graphics &G,

            graphics::layered_graph_draw_options *Opt,

            int parent_x, int parent_y, int *weight,

            int *placement_x, int max_depth, int i, int last,

            int f_has_point_labels, long int *point_labels,

            int y_max,

            int verbose_level);

    void subtree_place(int *weight, int *placement_x,

        int left, int right, int i, int last);

    int subtree_calc_weight(int *weight, int &max_depth,

        int i, int last);

    int subtree_depth_first(std::ostream &ost, int *path, int i, int last);

    void print_path(std::ostream &ost, int *path, int l);

    void write_to_file_csv(std::string &fname_csv, int verbose_level);

    void write_to_file_binary(std::ofstream &fp, int verbose_level);

    void read_from_file_binary(std::ifstream &fp, int verbose_level);

    void write_file_binary(std::string &fname, int verbose_level);

    void read_file_binary(std::string &fname, int verbose_level);

    void list_elements_as_permutations_vertically(std::ostream &ost);

};


// #############################################################################

// schreier_sims.cpp

// #############################################################################


class schreier_sims {


public:

    actions::action *GA;

    sims *G;


    int f_interested_in_kernel;

    actions::action *KA;

    sims *K;


    ring_theory::longinteger_object G_order, K_order, KG_order;


    int *Elt1;

    int *Elt2;

    int *Elt3;


    int f_has_target_group_order;

    ring_theory::longinteger_object tgo; // target group order


    int f_from_generators;

    data_structures_groups::vector_ge *external_gens;


    int f_from_random_process;

    void (*callback_choose_random_generator)(int iteration,

        int *Elt, void *data, int verbose_level);

    void *callback_choose_random_generator_data;


    int f_from_old_G;

    sims *old_G;


    int f_has_base_of_choice;

    int base_of_choice_len;

    int *base_of_choice;


    int f_override_choose_next_base_point_method;

    int (*choose_next_base_point_method)(actions::action *A,

        int *Elt, int verbose_level);


    int iteration;


    schreier_sims();

    ~schreier_sims();

    void null();

    void freeself();

    void init(actions::action *A, int verbose_level);

    void interested_in_kernel(actions::action *KA, int verbose_level);

    void init_target_group_order(ring_theory::longinteger_object &tgo,

        int verbose_level);

    void init_generators(data_structures_groups::vector_ge *gens, int verbose_level);

    void init_random_process(

        void (*callback_choose_random_generator)(

        int iteration, int *Elt, void *data,

        int verbose_level),

        void *callback_choose_random_generator_data,

        int verbose_level);

    void init_old_G(sims *old_G, int verbose_level);

    void init_base_of_choice(

        int base_of_choice_len, int *base_of_choice,

        int verbose_level);

    void init_choose_next_base_point_method(

        int (*choose_next_base_point_method)(actions::action *A,

        int *Elt, int verbose_level),

        int verbose_level);

    void compute_group_orders();

    void print_group_orders();

    void get_generator_internal(int *Elt, int verbose_level);

    void get_generator_external(int *Elt, int verbose_level);

    void get_generator_external_from_generators(int *Elt,

        int verbose_level);

    void get_generator_external_random_process(int *Elt,

        int verbose_level);

    void get_generator_external_old_G(int *Elt,

        int verbose_level);

    void get_generator(int *Elt, int verbose_level);

    void closure_group(int verbose_level);

    void create_group(int verbose_level);

};


// #############################################################################

// sims.cpp

// #############################################################################


class sims {


public:

    actions::action *A;


    int my_base_len;


    data_structures_groups::vector_ge gens;

    data_structures_groups::vector_ge gens_inv;


    int *gen_depth; // [nb_gen]

    int *gen_perm; // [nb_gen]


    int *nb_gen; // [my_base_len + 1]

        // nb_gen[i] is the number of generators

        // which stabilize the base points 0,...,i-1,

        // i.e. which belong to G^{(i)}.

        // The actual generator index ("gen_idx") must be obtained

        // from the array gen_perm[].

        // Thus, gen_perm[j] for 0 \le j < nb_gen[i] are the

        // indices of generators which belong to G^{(i)}

        // the generators for G^{(i)} modulo G^{(i+1)}

        // those indexed by nb_gen[i + 1], .., nb_gen[i] - 1 (!!!)

        // Observe that the entries in nb_gen[] are *decreasing*.

        // This is because the generators at the bottom of the

        // stabilizer chain are listed first.

        // (And nb_gen[0] is the total number of generators).


    int transversal_length;

        // an upper bound for the length of every basic orbit


    int *path; // [my_base_len]


    int nb_images;

    int **images;


private:

    // stabilizer chain:


    int *orbit_len; // [my_base_len]

        // orbit_len[i] is the length of the i-th basic orbit.


    int **orbit;

        // [my_base_len][transversal_length]

        // orbit[i][j] is the j-th point in the orbit

        // of the i-th base point.

        // for 0 \le j < orbit_len[i].

        // for orbit_len[i] \le j < A->deg,

        // the points not in the orbit are listed.

    int **orbit_inv;

        // [my_base_len][transversal_length]

        // orbit[i] is the inverse of the permutation orbit[i],

        // i.e. given a point j,

        // orbit_inv[i][j] is the coset (or position in the orbit)

        // which contains j.


    int **prev; // [my_base_len][transversal_length]

    int **label; // [my_base_len][transversal_length]


    // this is wrong, Path and Label describe a path in a schreier tree

    // and hence should be allocated according

    // to the largest degree, not the base length

    //int *Path; // [my_base_len + 1]

    //int *Label; // [my_base_len]


    // storage for temporary data and

    // group elements computed by various routines.

    int *Elt1, *Elt2, *Elt3, *Elt4;

    int *strip1, *strip2;

        // used in strip

    int *eltrk1, *eltrk2, *eltrk3;

        // used in element rank unrank

    int *cosetrep_tmp;

        // used in coset_rep / coset_rep_inv

    int *schreier_gen, *schreier_gen1;

        // used in random_schreier_generator


    int *cosetrep;

public:


    // sims.cpp:

    sims();

    void null();

    sims(actions::action *A, int verbose_level);

    ~sims();

    void freeself();


    void delete_images();

    void init_images(int nb_images);

    void images_append();

    void init(actions::action *A, int verbose_level);

        // initializes the trivial group

        // with the base as given in A

    void init_cyclic_group_from_generator(actions::action *A, int *Elt, int verbose_level);

    // initializes the cyclic group generated by Elt with the base as given in A

    void init_without_base(actions::action *A, int verbose_level);

    void reallocate_base(int old_base_len, int verbose_level);

    void initialize_table(int i, int verbose_level);

    void init_trivial_group(int verbose_level);

        // clears the generators array,

        // and sets the i-th transversal to contain

        // only the i-th base point (for all i).

    void init_trivial_orbit(int i, int verbose_level);

    void init_generators(data_structures_groups::vector_ge &generators, int verbose_level);

    void init_generators(int nb, int *elt, int verbose_level);

        // copies the given elements into the generator array,

        // then computes depth and perm

    void init_generators_by_hdl(int nb_gen, int *gen_hdl, int verbose_level);

    void init_generator_depth_and_perm(int verbose_level);

    void add_generator(int *elt, int verbose_level);

        // adds elt to list of generators,

        // computes the depth of the element,

        // updates the arrays gen_depth and gen_perm accordingly

        // does not change the transversals

    int generator_depth(int gen_idx);

        // returns the index of the first base point

        // which is moved by a given generator.

    int generator_depth(int *elt);

        // returns the index of the first base point

        // which is moved by the given element

    void group_order(ring_theory::longinteger_object &go);

    void group_order_verbose(ring_theory::longinteger_object &go, int verbose_level);

    void subgroup_order_verbose(ring_theory::longinteger_object &go, int level, int verbose_level);

    long int group_order_lint();

    int is_trivial_group();

    int last_moved_base_point();

        // j == -1 means the group is trivial

    int get_image(int i, int gen_idx);

        // get the image of a point i under generator gen_idx,

        // goes through a

        // table of stored images by default.

        // Computes the image only if not yet available.

    int get_image(int i, int *elt);

        // get the image of a point i under a given group element,

        // does not go through a table.

    void swap_points(int lvl, int i, int j);

        // swaps two points given by their cosets

    void path_unrank_lint(long int a);

    long int path_rank_lint();


    void element_from_path(int *elt, int verbose_level);

        // given coset representatives in path[],

        // the corresponding

        // element is multiplied.

        // uses eltrk1, eltrk2

    void element_from_path_inv(int *elt);

    void element_unrank(ring_theory::longinteger_object &a, int *elt,

        int verbose_level);

    void element_unrank(ring_theory::longinteger_object &a, int *elt);

        // Returns group element whose rank is a.

        // the elements represented by the chain are

        // enumerated 0, ... go - 1

        // with the convention that 0 always stands

        // for the identity element.

        // The computed group element will be computed into Elt1

    void element_rank(ring_theory::longinteger_object &a, int *elt);

        // Computes the rank of the element in elt into a.

        // uses eltrk1, eltrk2

    void element_unrank_lint(long int rk, int *Elt, int verbose_level);

    void element_unrank_lint(long int rk, int *Elt);

    long int element_rank_lint(int *Elt);

    int is_element_of(int *elt);

    void test_element_rank_unrank();

    void coset_rep(int *Elt, int i, int j, int verbose_level);

        // computes a coset representative in transversal i

        // which maps

        // the i-th base point to the point which is in

        // coset j of the i-th basic orbit.

        // j is a coset, not a point

        // result is in cosetrep

    int compute_coset_rep_depth(int i, int j, int verbose_level);

    void compute_coset_rep_path(int i, int j, int &depth,

            int *&Path, int *&Label,

        int verbose_level);

    void coset_rep_inv(int *Elt, int i, int j, int verbose_level_le);

        // computes the inverse element of what coset_rep computes,

        // i.e. an element which maps the

        // j-th point in the orbit to the

        // i-th base point.

        // j is a coset, not a point

        // result is in cosetrep

    void extract_strong_generators_in_order(data_structures_groups::vector_ge &SG,

        int *tl, int verbose_level);

    void random_schreier_generator(int *Elt, int verbose_level);

        // computes random Schreier generator

    void element_as_permutation(actions::action *A_special,

        long int elt_rk, int *perm, int verbose_level);

    int least_moved_point_at_level(int lvl, int verbose_level);

    int get_orbit(int i, int j);

    int get_orbit_inv(int i, int j);

    int get_orbit_length(int i);

    void get_orbit(int orbit_idx, std::vector<int> &Orb, int verbose_level);

    void all_elements(data_structures_groups::vector_ge *&vec, int verbose_level);

    void all_elements_save_csv(std::string &fname, int verbose_level);


    // sims_main.cpp:

    void compute_base_orbits(int verbose_level);

    void compute_base_orbits_known_length(int *tl,

        int verbose_level);

    void extend_base_orbit(int new_gen_idx, int lvl,

        int verbose_level);

    void compute_base_orbit(int lvl, int verbose_level);

        // applies all generators at the given level to compute

        // the corresponding basic orbit.

        // the generators are the first nb_gen[lvl]

        // in the generator array

    void compute_base_orbit_known_length(int lvl,

        int target_length, int verbose_level);

    int strip_and_add(int *elt, int *residue, int verbose_level);

        // returns TRUE if something was added,

        // FALSE if element stripped through

    int strip(int *elt, int *residue, int &drop_out_level,

        int &image, int verbose_level);

        // returns TRUE if the element sifts through

    void add_generator_at_level(int *elt, int lvl,

        int verbose_level);

        // add the generator to the array of generators

        // and then extends the

        // basic orbits 0,..,lvl using extend_base_orbit

    void add_generator_at_level_only(int *elt,

        int lvl, int verbose_level);

        // add the generator to the array of generators

        // and then extends the

        // basic orbit lvl using extend_base_orbit

    void build_up_group_random_process_no_kernel(sims *old_G,

        int verbose_level);

    void extend_group_random_process_no_kernel(sims *extending_by_G,

            ring_theory::longinteger_object &target_go,

        int verbose_level);

    void build_up_group_random_process(sims *K, sims *old_G,

            ring_theory::longinteger_object &target_go,

        int f_override_choose_next_base_point,

        int (*choose_next_base_point_method)(actions::action *A,

            int *Elt, int verbose_level),

        int verbose_level);

    void build_up_group_from_generators(sims *K,

            data_structures_groups::vector_ge *gens,

        int f_target_go, ring_theory::longinteger_object *target_go,

        int f_override_choose_next_base_point,

        int (*choose_next_base_point_method)(actions::action *A,

            int *Elt, int verbose_level),

        int verbose_level);

    int closure_group(int nb_times, int verbose_level);


    // sims2.cpp

    void build_up_subgroup_random_process(sims *G,

        void (*choose_random_generator_for_subgroup)(

            sims *G, int *Elt, int verbose_level),

        int verbose_level);


    // sims3.cpp

    void subgroup_make_characteristic_vector(sims *Sub,

        int *C, int verbose_level);

    void normalizer_based_on_characteristic_vector(int *C_sub,

        int *Gen_idx, int nb_gens, int *N, long int &N_go,

        int verbose_level);

    void order_structure_relative_to_subgroup(int *C_sub,

        int *Order, int *Residue, int verbose_level);


    // sims_group_theory.cpp:

    void random_element(int *elt, int verbose_level);

        // compute a random element among the group elements

        // represented by the chain

        // (chooses random cosets along the stabilizer chain)

    void random_element_of_order(int *elt, int order,

        int verbose_level);

    void random_elements_of_order(data_structures_groups::vector_ge *elts,

        int *orders, int nb, int verbose_level);

    void transitive_extension(schreier &O, data_structures_groups::vector_ge &SG,

        int *tl, int verbose_level);

    int transitive_extension_tolerant(schreier &O,

            data_structures_groups::vector_ge &SG, int *tl, int f_tolerant,

        int verbose_level);

    void transitive_extension_using_coset_representatives_extract_generators(

        int *coset_reps, int nb_cosets,

        data_structures_groups::vector_ge &SG, int *tl,

        int verbose_level);

    void transitive_extension_using_coset_representatives(

        int *coset_reps, int nb_cosets,

        int verbose_level);

    void transitive_extension_using_generators(

        int *Elt_gens, int nb_gens, int subgroup_index,

        data_structures_groups::vector_ge &SG, int *tl,

        int verbose_level);

    void point_stabilizer_stabchain_with_action(actions::action *A2,

        sims &S, int pt, int verbose_level);

        // first computes the orbit of the point pt

        // in action A2 under the generators

        // that are stored at present

        // (using a temporary schreier object),

        // then sifts random schreier generators into S

    void point_stabilizer(data_structures_groups::vector_ge &SG, int *tl,

        int pt, int verbose_level);

        // computes strong generating set

        // for the stabilizer of point pt

    void point_stabilizer_with_action(actions::action *A2,

            data_structures_groups::vector_ge &SG, int *tl, int pt, int verbose_level);

        // computes strong generating set for

        // the stabilizer of point pt in action A2

    void conjugate(actions::action *A, sims *old_G, int *Elt,

        int f_overshooting_OK, int verbose_level);

        // Elt * g * Elt^{-1} where g is in old_G

    int test_if_in_set_stabilizer(actions::action *A,

        long int *set, int size, int verbose_level);

    int test_if_subgroup(sims *old_G, int verbose_level);

    int find_element_with_exactly_n_fixpoints_in_given_action(

            int *Elt, int nb_fixpoints, actions::action *A_given, int verbose_level);

    void table_of_group_elements_in_data_form(int *&Table,

        int &len, int &sz, int verbose_level);

    void regular_representation(int *Elt, int *perm,

        int verbose_level);

    void center(data_structures_groups::vector_ge &gens, int *center_element_ranks,

        int &nb_elements, int verbose_level);

    void all_cosets(int *subset, int size,

        long int *all_cosets, int verbose_level);

    void element_ranks_subgroup(sims *subgroup,

        int *element_ranks, int verbose_level);

    void find_standard_generators_int(int ord_a, int ord_b,

        int ord_ab, int &a, int &b, int &nb_trials,

        int verbose_level);

    long int find_element_of_given_order_int(int ord,

        int &nb_trials, int verbose_level);

    int find_element_of_given_order_int(int *Elt,

        int ord, int &nb_trials, int max_trials,

        int verbose_level);

    void find_element_of_prime_power_order(int p,

        int *Elt, int &e, int &nb_trials, int verbose_level);

    void evaluate_word_int(int word_len,

        int *word, int *Elt, int verbose_level);

    void sylow_subgroup(int p, sims *P, int verbose_level);

    int is_normalizing(int *Elt, int verbose_level);

    void create_Cayley_graph(data_structures_groups::vector_ge *gens,

            int *&Adj, long int &n,

        int verbose_level);

    void create_group_table(int *&Table, long int &n, int verbose_level);

    void compute_conjugacy_classes(

            actions::action *&Aconj, induced_actions::action_by_conjugation *&ABC, schreier *&Sch,

        strong_generators *&SG, int &nb_classes,

        int *&class_size, int *&class_rep,

        int verbose_level);

    void compute_all_powers(int elt_idx, int n, int *power_elt,

            int verbose_level);

    long int mult_by_rank(long int rk_a, long int rk_b, int verbose_level);

    long int mult_by_rank(long int rk_a, long int rk_b);

    long int invert_by_rank(long int rk_a, int verbose_level);

    long int conjugate_by_rank(long int rk_a, long int rk_b, int verbose_level);

        // comutes b^{-1} * a * b

    long int conjugate_by_rank_b_bv_given(long int rk_a,

        int *Elt_b, int *Elt_bv, int verbose_level);

    void zuppo_list(

            int *Zuppos, int &nb_zuppos, int verbose_level);

    void dimino(

        int *subgroup, int subgroup_sz, int *gens, int &nb_gens,

        int *cosets,

        int new_gen,

        int *group, int &group_sz,

        int verbose_level);

    void Cayley_graph(int *&Adj, int &sz,

            data_structures_groups::vector_ge *gens_S,

        int verbose_level);


    // sims_io.cpp:

    void create_group_tree(const char *fname, int f_full,

        int verbose_level);

    void print_transversals();

    void print_transversals_short();

    void print_transversal_lengths();

    void print_orbit_len();

    void print(int verbose_level);

    void print_generators();

    void print_generators_tex(std::ostream &ost);

    void print_generators_as_permutations();

    void print_generators_as_permutations_override_action(

            actions::action *A);

    void print_basic_orbits();

    void print_basic_orbit(int i);

    void print_generator_depth_and_perm();

    void print_group_order(std::ostream &ost);

    void print_group_order_factored(std::ostream &ost);

    void print_generators_at_level_or_below(int lvl);

    void write_all_group_elements(char *fname, int verbose_level);

    void print_all_group_elements_to_file(char *fname,

        int verbose_level);

    void print_all_group_elements();

    void print_all_group_elements_tex(std::ostream &ost);

    void print_all_group_elements_with_permutations_tex(std::ostream &ost);

    void print_all_group_elements_as_permutations();

    void print_all_group_elements_as_permutations_in_special_action(

            actions::action *A_special);

    void print_all_transversal_elements();

    void save_list_of_elements(char *fname,

        int verbose_level);

    void read_list_of_elements(actions::action *A,

        char *fname, int verbose_level);

    void write_as_magma_permutation_group(std::string &fname_base,

            data_structures_groups::vector_ge *gens, int verbose_level);

    void report(std::ostream &ost,

            std::string &prefix,

            graphics::layered_graph_draw_options *LG_Draw_options,

            int verbose_level);


};


// sims2.cpp

void choose_random_generator_derived_group(sims *G, int *Elt,

    int verbose_level);


// #############################################################################

// strong_generators.cpp

// #############################################################################


class strong_generators {

public:


    actions::action *A;

    int *tl;

    data_structures_groups::vector_ge *gens;


    strong_generators();

    ~strong_generators();

    void null();

    void freeself();

    void swap_with(strong_generators *SG);

    void init(actions::action *A);

    void init(actions::action *A, int verbose_level);

    void init_from_sims(groups::sims *S, int verbose_level);

    void init_from_ascii_coding(actions::action *A,

        char *ascii_coding, int verbose_level);

    strong_generators *create_copy();

    void init_copy(strong_generators *S,

        int verbose_level);

    void init_by_hdl_and_with_tl(actions::action *A,

            std::vector<int> &gen_handle,

            std::vector<int> &tl,

            int verbose_level);

    void init_by_hdl(actions::action *A, int *gen_hdl,

        int nb_gen, int verbose_level);

    void init_from_permutation_representation(actions::action *A,

            sims *parent_group_S, int *data,

            int nb_elements, long int group_order,

            data_structures_groups::vector_ge *&nice_gens,

            int verbose_level);

    void init_from_data(actions::action *A, int *data,

        int nb_elements, int elt_size,

        int *transversal_length,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void init_from_data_with_target_go_ascii(actions::action *A,

        int *data,

        int nb_elements, int elt_size,

        const char *ascii_target_go,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void init_from_data_with_target_go(actions::action *A,

        int *data_gens,

        int data_gens_size, int nb_gens,

        ring_theory::longinteger_object &target_go,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void init_from_data_with_go(

            actions::action *A, std::string &generators_data,

        std::string &go_text,

        int verbose_level);

    void init_point_stabilizer_of_arbitrary_point_through_schreier(

        schreier *Sch,

        int pt, int &orbit_idx,

        ring_theory::longinteger_object &full_group_order,

        int verbose_level);

    void init_point_stabilizer_orbit_rep_schreier(schreier *Sch,

        int orbit_idx, ring_theory::longinteger_object &full_group_order,

        int verbose_level);

    void init_generators_for_the_conjugate_group_avGa(

        strong_generators *SG, int *Elt_a, int verbose_level);

    void init_generators_for_the_conjugate_group_aGav(

        strong_generators *SG, int *Elt_a, int verbose_level);

    void init_transposed_group(strong_generators *SG,

        int verbose_level);

    void init_group_extension(strong_generators *subgroup,

        int *data, int index,

        int verbose_level);

    void init_group_extension(strong_generators *subgroup,

            data_structures_groups::vector_ge *new_gens, int index,

        int verbose_level);

    void switch_to_subgroup(const char *rank_vector_text,

        const char *subgroup_order_text, sims *S,

        int *&subgroup_gens_idx, int &nb_subgroup_gens,

        int verbose_level);

    void init_subgroup(actions::action *A, int *subgroup_gens_idx,

        int nb_subgroup_gens,

        const char *subgroup_order_text,

        sims *S,

        int verbose_level);

    void init_subgroup_by_generators(actions::action *A,

        int nb_subgroup_gens,

        int *subgroup_gens,

        std::string &subgroup_order_text,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    sims *create_sims(int verbose_level);

    sims *create_sims_in_different_action(actions::action *A_given,

        int verbose_level);

    void add_generators(data_structures_groups::vector_ge *coset_reps,

        int group_index, int verbose_level);

    void add_single_generator(int *Elt,

        int group_index, int verbose_level);

    void group_order(ring_theory::longinteger_object &go);

    long int group_order_as_lint();

    void print_group_order(std::ostream &ost);

    void print_generators_in_source_code();

    void print_generators_in_source_code_to_file(

    const char *fname);

    void print_generators_even_odd();

    void print_generators_MAGMA(actions::action *A, std::ostream &ost);

    void export_magma(actions::action *A, std::ostream &ost, int verbose_level);

    void canonical_image_GAP(std::string &input_set_text, std::ostream &ost);

    void print_generators_gap(std::ostream &ost);

    void print_generators_gap_in_different_action(std::ostream &ost, actions::action *A2);

    void print_generators_compact(std::ostream &ost);

    void print_generators(std::ostream &ost);

    void print_generators_in_latex_individually(std::ostream &ost);

    void print_generators_tex();

    void print_generators_tex(std::ostream &ost);

    void print_for_make_element(std::ostream &ost);

    void print_generators_in_different_action_tex(std::ostream &ost, actions::action *A2);

    void print_generators_tex_with_print_point_function(

            actions::action *A,

            std::ostream &ost,

            void (*point_label)(std::stringstream &sstr, long int pt, void *data),

            void *point_label_data);

    void print_generators_for_make_element(std::ostream &ost);

    void print_generators_as_permutations();

    void print_generators_as_permutations_tex(std::ostream &ost, actions::action *A2);

    void print_with_given_action(std::ostream &ost, actions::action *A2);

    void print_elements_ost(std::ostream &ost);

    void print_elements_with_special_orthogonal_action_ost(std::ostream &ost);

    void print_elements_with_given_action(std::ostream &ost, actions::action *A2);

    void print_elements_latex_ost(std::ostream &ost);

    void print_elements_latex_ost_with_print_point_function(

            actions::action *A,

            std::ostream &ost,

            void (*point_label)(std::stringstream &sstr, long int pt, void *data),

            void *point_label_data);

    void create_group_table(int *&Table, long int &go,

        int verbose_level);

    void list_of_elements_of_subgroup(

        strong_generators *gens_subgroup,

        long int *&Subgroup_elements_by_index,

        long int &sz_subgroup, int verbose_level);

    void compute_schreier_with_given_action(actions::action *A_given,

        schreier *&Sch, int verbose_level);

    void compute_schreier_with_given_action_on_a_given_set(

            actions::action *A_given,

        schreier *&Sch, long int *set, int len, int verbose_level);

    void orbits_on_points(int &nb_orbits, int *&orbit_reps,

        int verbose_level);

    void orbits_on_points_with_given_action(actions::action *A_given,

        int &nb_orbits, int *&orbit_reps, int verbose_level);

    schreier *orbits_on_points_schreier(actions::action *A_given,

        int verbose_level);

    schreier *orbit_of_one_point_schreier(actions::action *A_given,

        int pt, int verbose_level);

    void orbits_light(actions::action *A_given,

        int *&Orbit_reps, int *&Orbit_lengths, int &nb_orbits,

        int **&Pts_per_generator, int *&Nb_per_generator,

        int verbose_level);

    void write_to_file_binary(std::ofstream &fp, int verbose_level);

    void read_from_file_binary(actions::action *A, std::ifstream &fp,

        int verbose_level);

    void write_file(std::string &fname, int verbose_level);

    void read_file(actions::action *A, std::string &fname, int verbose_level);

    void compute_ascii_coding(char *&ascii_coding, int verbose_level);

    void decode_ascii_coding(char *ascii_coding, int verbose_level);

    void export_permutation_group_to_magma(std::string &fname,

            actions::action *A2, int verbose_level);

    void export_permutation_group_to_GAP(std::string &fname,

            actions::action *A2, int verbose_level);

    void compute_and_print_orbits_on_a_given_set(actions::action *A_given,

        long int *set, int len, int verbose_level);

    void compute_and_print_orbits(actions::action *A_given,

        int verbose_level);

    int test_if_normalizing(sims *S, int verbose_level);

    void test_if_set_is_invariant_under_given_action(actions::action *A_given,

        long int *set, int set_sz, int verbose_level);

    strong_generators *point_stabilizer(int pt, int verbose_level);

    strong_generators *find_cyclic_subgroup_with_exactly_n_fixpoints(

            int nb_fixpoints, actions::action *A_given, int verbose_level);

    void make_element_which_moves_a_point_from_A_to_B(actions::action *A_given,

        int pt_A, int pt_B, int *Elt, int verbose_level);

    void export_group_to_magma_and_copy_to_latex(

            std::string &label_txt,

            std::ostream &ost,

            actions::action *A2,

            int verbose_level);

    void export_group_to_GAP_and_copy_to_latex(

            std::string &label_txt,

            std::ostream &ost,

            actions::action *A2,

            int verbose_level);

    void export_group_and_copy_to_latex(

            std::string &label_txt,

            std::ostream &ost,

            actions::action *A2,

            int verbose_level);

    void report_fixed_objects_in_P3(

            std::ostream &ost,

            geometry::projective_space *P3,

            int verbose_level);

    void reverse_isomorphism_exterior_square(int verbose_level);

    void get_gens_data(int *&data, int &sz, int verbose_level);

    void get_gens_data_as_string_with_quotes(std::string &str, int verbose_level);

    void export_to_orbiter_as_bsgs(

            actions::action *A2,

            std::string &fname, std::string &label, std::string &label_tex,

            int verbose_level);


    // strong_generators_groups.cpp

    void init_linear_group_from_scratch(actions::action *&A,

            field_theory::finite_field *F, int n,

        linear_group_description *Descr,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void special_subgroup(int verbose_level);

    void projectivity_subgroup(sims *S, int verbose_level);

    void even_subgroup(int verbose_level);

    void Sylow_subgroup(sims *S, int p, int verbose_level);

    void init_single(actions::action *A, int *Elt, int verbose_level);

    void init_single_with_target_go(actions::action *A,

            int *Elt, int target_go, int verbose_level);

    void init_trivial_group(actions::action *A, int verbose_level);

    void generators_for_the_monomial_group(actions::action *A,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_diagonal_group(actions::action *A,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_singer_cycle(actions::action *A,

        matrix_group *Mtx, int power_of_singer,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void generators_for_the_singer_cycle_and_the_Frobenius(

            actions::action *A,

        matrix_group *Mtx, int power_of_singer,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void generators_for_the_null_polarity_group(actions::action *A,

        matrix_group *Mtx, int verbose_level);

    void generators_for_symplectic_group(actions::action *A,

        matrix_group *Mtx, int verbose_level);

    void init_centralizer_of_matrix(actions::action *A, int *Mtx,

        int verbose_level);

    void init_centralizer_of_matrix_general_linear(actions::action *A_projective,

            actions::action *A_general_linear, int *Mtx,

        int verbose_level);

    void field_reduction(actions::action *Aq, int n, int s,

            field_theory::finite_field *Fq, int verbose_level);

    void generators_for_translation_plane_in_andre_model(

            actions::action *A_PGL_n1_q, actions::action *A_PGL_n_q,

        matrix_group *Mtx_n1, matrix_group *Mtx_n,

        data_structures_groups::vector_ge *spread_stab_gens,

        ring_theory::longinteger_object &spread_stab_go,

        int verbose_level);

    void generators_for_the_stabilizer_of_two_components(

            actions::action *A_PGL_n_q,

        matrix_group *Mtx, int verbose_level);

    void regulus_stabilizer(actions::action *A_PGL_n_q,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_borel_subgroup_upper(actions::action *A_linear,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_borel_subgroup_lower(actions::action *A_linear,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_identity_subgroup(actions::action *A_linear,

        matrix_group *Mtx, int verbose_level);

    void generators_for_parabolic_subgroup(actions::action *A_PGL_n_q,

        matrix_group *Mtx, int k, int verbose_level);

    void generators_for_stabilizer_of_three_collinear_points_in_PGL4(

            actions::action *A_PGL_4_q,

        matrix_group *Mtx, int verbose_level);

    void generators_for_stabilizer_of_triangle_in_PGL4(

            actions::action *A_PGL_4_q,

        matrix_group *Mtx, int verbose_level);

    void generators_for_the_orthogonal_group(actions::action *A,

            field_theory::finite_field *F, int n,

        int epsilon,

        int f_semilinear,

        int verbose_level);

    void stabilizer_of_cubic_surface_from_catalogue(

            actions::action *A,

        field_theory::finite_field *F, int iso,

        int verbose_level);

    void stabilizer_of_quartic_curve_from_catalogue(

            actions::action *A,

        field_theory::finite_field *F, int iso,

        int verbose_level);

    void stabilizer_of_Eckardt_surface(

            actions::action *A,

        field_theory::finite_field *F, int f_with_normalizer, int f_semilinear,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void stabilizer_of_G13_surface(

            actions::action *A,

        field_theory::finite_field *F, int a,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void stabilizer_of_F13_surface(

            actions::action *A,

        field_theory::finite_field *F, int a,

        data_structures_groups::vector_ge *&nice_gens,

        int verbose_level);

    void BLT_set_from_catalogue_stabilizer(actions::action *A,

            field_theory::finite_field *F, int iso,

        int verbose_level);

    void stabilizer_of_spread_from_catalogue(actions::action *A,

        int q, int k, int iso,

        int verbose_level);

    void stabilizer_of_pencil_of_conics(

            actions::action *A,

        field_theory::finite_field *F,

        int verbose_level);

    void Janko1(

            actions::action *A,

        field_theory::finite_field *F,

        int verbose_level);

    void Hall_reflection(

        int nb_pairs, int &degree, int verbose_level);

    void normalizer_of_a_Hall_reflection(

        int nb_pairs, int &degree, int verbose_level);

    void hyperplane_lifting_with_two_lines_fixed(

        strong_generators *SG_hyperplane,

        geometry::projective_space *P, int line1, int line2,

        int verbose_level);

    void exterior_square(

            actions::action *A_detached,

            strong_generators *SG_original,

            data_structures_groups::vector_ge *&nice_gens,

            int verbose_level);

    void diagonally_repeat(

            actions::action *An,

            strong_generators *Sn,

            int verbose_level);


};


// #############################################################################

// subgroup.cpp:

// #############################################################################


class subgroup {

public:

    actions::action *A;

    int *Elements;

    long int group_order;

    int *gens;

    int nb_gens;

    sims *Sub;

    strong_generators *SG;


    subgroup();

    ~subgroup();

    void null();

    void freeself();

    void init_from_sims(sims *S, sims *Sub,

            strong_generators *SG, int verbose_level);

    void init(int *Elements, int group_order, int *gens, int nb_gens);

    void print();

    int contains_this_element(int elt);

    void report(std::ostream &ost);

};


// #############################################################################

// sylow_structure.cpp:

// #############################################################################


class sylow_structure {

public:

    ring_theory::longinteger_object go;

    int *primes;

    int *exponents;

    int nb_primes;


    sims *S; // the group

    subgroup *Sub; // [nb_primes]


    sylow_structure();

    ~sylow_structure();

    void null();

    void freeself();

    void init(sims *S, int verbose_level);

    void report(std::ostream &ost);

};


// #############################################################################

// wreath_product.cpp

// #############################################################################


class wreath_product {


public:

    matrix_group *M;

    actions::action *A_mtx;

    field_theory::finite_field *F;

    int q;

    int nb_factors;


    std::string label;

    std::string label_tex;


    int degree_of_matrix_group;

        // = M->degree;

    int dimension_of_matrix_group;

        // = M->n

    int dimension_of_tensor_action;

        // = i_power_j(dimension_of_matrix_group, nb_factors);

    long int degree_of_tensor_action;

        // = (i_power_j_safe(q, dimension_of_tensor_action) - 1) / (q - 1);

    long int degree_overall;

        // = nb_factors + nb_factors *

        // degree_of_matrix_group + degree_of_tensor_action;

    int low_level_point_size;

        // = dimension_of_tensor_action

    int make_element_size;

        // = nb_factors + nb_factors *

        // dimension_of_matrix_group * dimension_of_matrix_group;

    permutation_representation_domain *P;

    int elt_size_int;

        // = M->elt_size_int * nb_factors + P->elt_size_int;


    int *perm_offset_i; // [nb_factors + 1]

        // perm_offset_i[0] = nb_factors

        // perm_offset_i[nb_factors] = beginning of tensor domain

    int *mtx_size;

    int *index_set1;

    int *index_set2;

    int *u; // [dimension_of_tensor_action]

    int *v; // [dimension_of_tensor_action]

    int *w; // [dimension_of_tensor_action]

    int *A1; // [dimension_of_tensor_action * dimension_of_tensor_action]

    int *A2; // [dimension_of_tensor_action * dimension_of_tensor_action]

    int *A3; // [dimension_of_tensor_action * dimension_of_tensor_action]

    int *tmp_Elt1; // [elt_size_int]

    int *tmp_perm1; // [P->elt_size_int]

    int *tmp_perm2; // [P->elt_size_int]

    int *induced_perm; // [dimension_of_tensor_action]


    int bits_per_digit;

    int bits_per_elt;

    int char_per_elt;


    uchar *elt1;


    int base_len_in_component;

    long int *base_for_component;

    int *tl_for_component;


    int base_length;

    long int *the_base;

    int *the_transversal_length;


    data_structures::page_storage *Elts;


    uint32_t *rank_one_tensors; // [nb_rank_one_tensors]

    long int *rank_one_tensors_in_PG; // [nb_rank_one_tensors]

        // rank_one_tensors_in_PG[i] = affine_rank_to_PG_rank(rank_one_tensors[i]);

    long int *rank_one_tensors_in_PG_sorted; // [nb_rank_one_tensors]

    int nb_rank_one_tensors;


    char *TR; // [degree_of_tensor_action + 1]

    uint32_t *Prev; // [degree_of_tensor_action + 1]


    wreath_product();

    ~wreath_product();

    void null();

    void freeself();

    void init_tensor_wreath_product(matrix_group *M,

            actions::action *A_mtx, int nb_factors,

            int verbose_level);

    void compute_tensor_ranks(int verbose_level);

    void unrank_point(long int a, int *v, int verbose_level);

    long int rank_point(int *v, int verbose_level);

    long int element_image_of(int *Elt, long int a, int verbose_level);

    void element_image_of_low_level(int *Elt,

            int *input, int *output, int verbose_level);

        // we assume that we are in the tensor product domain

    void element_one(int *Elt);

    int element_is_one(int *Elt);

    void element_mult(int *A, int *B, int *AB, int verbose_level);

    void element_move(int *A, int *B, int verbose_level);

    void element_invert(int *A, int *Av, int verbose_level);

    void compute_induced_permutation(int *Elt, int *perm);

    void apply_permutation(int *Elt,

            int *v_in, int *v_out, int verbose_level);

    int offset_i(int i);

    void create_matrix(int *Elt, int *A, int verbose_level);

        // uses A1, A2

    void element_pack(int *Elt, uchar *elt);

    void element_unpack(uchar *elt, int *Elt);

    void put_digit(uchar *elt, int f, int i, int j, int d);

    int get_digit(uchar *elt, int f, int i, int j);

    void make_element_from_one_component(int *Elt,

            int f, int *Elt_component);

    void make_element_from_permutation(int *Elt, int *perm);

    void make_element(int *Elt, int *data, int verbose_level);

    void element_print_for_make_element(int *Elt, std::ostream &ost);

    void element_print_easy(int *Elt, std::ostream &ost);

    void element_print_latex(int *Elt, std::ostream &ost);

    void compute_base_and_transversals(int verbose_level);

    void make_strong_generators_data(int *&data,

            int &size, int &nb_gens, int verbose_level);

    void report_rank_one_tensors(

            std::ostream &ost, int verbose_level);

    void create_all_rank_one_tensors(

            uint32_t *&rank_one_tensors,

            int &nb_rank_one_tensors, int verbose_level);

    uint32_t tensor_affine_rank(int *tensor);

    void tensor_affine_unrank(int *tensor, uint32_t rk);

    long int tensor_PG_rank(int *tensor);

    void tensor_PG_unrank(int *tensor, long int PG_rk);

    long int affine_rank_to_PG_rank(uint32_t affine_rk);

    uint32_t PG_rank_to_affine_rank(long int PG_rk);

    void save_rank_one_tensors(int verbose_level);

    void compute_tensor_ranks(char *&TR, uint32_t *&Prev, int verbose_level);

    void report(std::ostream &ost, int verbose_level);

    void compute_permutations_and_write_to_file(

            strong_generators* SG,

            actions::action* A,

            int*& result,

            int &nb_gens, int &degree,

            int nb_factors,

            int verbose_level);

    void make_fname(char *fname, int nb_factors, int h, int b);

    int test_if_file_exists(int nb_factors, int h, int b);

    void orbits_using_files_and_union_find(

            strong_generators* SG,

            actions::action* A,

            int*& result,

            int &nb_gens, int &degree,

            int nb_factors,

            int verbosity);

    void orbits_restricted(

            strong_generators* SG,

            actions::action* A,

            int*& result,

            int &nb_gens, int &degree,

            int nb_factors,

            std::string &orbits_restricted_fname,

            int verbose_level);

    void orbits_restricted_compute(

            strong_generators* SG,

            actions::action* A,

            int*& result,

            int &nb_gens, int &degree,

            int nb_factors,

            std::string &orbits_restricted_fname,

            int verbose_level);

};


}}}


#endif /* ORBITER_SRC_LIB_GROUP_ACTIONS_GROUPS_GROUPS_H_ */


orbiter::layer3_group_actions::actions::action
a permutation group in a fixed action.
Definition: actions.h:99

orbiter::layer3_group_actions::data_structures_groups::schreier_vector
compact storage of schreier vectors
Definition: data_structures.h:359

orbiter::layer3_group_actions::data_structures_groups::set_and_stabilizer
a set and its known set stabilizer
Definition: data_structures.h:431

orbiter::layer3_group_actions::data_structures_groups::vector_ge
to hold a vector of group elements
Definition: data_structures.h:558

orbiter::layer3_group_actions::groups::direct_product
the direct product of two matrix groups in product action
Definition: groups.h:26

orbiter::layer3_group_actions::groups::direct_product::Elts
data_structures::page_storage * Elts
Definition: groups.h:73

orbiter::layer3_group_actions::groups::direct_product::base_len_in_component1
int base_len_in_component1
Definition: groups.h:61

orbiter::layer3_group_actions::groups::direct_product::init
void init(matrix_group *M1, matrix_group *M2, int verbose_level)
Definition: direct_product.cpp:95

orbiter::layer3_group_actions::groups::direct_product::F2
field_theory::finite_field * F2
Definition: groups.h:32

orbiter::layer3_group_actions::groups::direct_product::low_level_point_size
int low_level_point_size
Definition: groups.h:46

orbiter::layer3_group_actions::groups::direct_product::element_pack
void element_pack(int *Elt, uchar *elt)
Definition: direct_product.cpp:405

orbiter::layer3_group_actions::groups::direct_product::M2
matrix_group * M2
Definition: groups.h:30

orbiter::layer3_group_actions::groups::direct_product::compute_base_and_transversals
void compute_base_and_transversals(int verbose_level)
Definition: direct_product.cpp:549

orbiter::layer3_group_actions::groups::direct_product::make_strong_generators_data
void make_strong_generators_data(int *&data, int &size, int &nb_gens, int verbose_level)
Definition: direct_product.cpp:592

orbiter::layer3_group_actions::groups::direct_product::put_digit
void put_digit(uchar *elt, int f, int i, int d)
Definition: direct_product.cpp:439

orbiter::layer3_group_actions::groups::direct_product::null
void null()
Definition: direct_product.cpp:31

orbiter::layer3_group_actions::groups::direct_product::element_unpack
void element_unpack(uchar *elt, int *Elt)
Definition: direct_product.cpp:417

orbiter::layer3_group_actions::groups::direct_product::lift_generators
void lift_generators(strong_generators *SG1, strong_generators *SG2, actions::action *A, strong_generators *&SG3, int verbose_level)
Definition: direct_product.cpp:665

orbiter::layer3_group_actions::groups::direct_product::label_tex
std::string label_tex
Definition: groups.h:37

orbiter::layer3_group_actions::groups::direct_product::elt_size_int
int elt_size_int
Definition: groups.h:48

orbiter::layer3_group_actions::groups::direct_product::M1
matrix_group * M1
Definition: groups.h:29

orbiter::layer3_group_actions::groups::direct_product::label
std::string label
Definition: groups.h:36

orbiter::layer3_group_actions::groups::direct_product::base_len_in_component2
int base_len_in_component2
Definition: groups.h:65

orbiter::layer3_group_actions::groups::direct_product::F1
field_theory::finite_field * F1
Definition: groups.h:31

orbiter::layer3_group_actions::groups::direct_product::base_length
int base_length
Definition: groups.h:69

orbiter::layer3_group_actions::groups::direct_product::element_print_easy
void element_print_easy(int *Elt, std::ostream &ost)
Definition: direct_product.cpp:524

orbiter::layer3_group_actions::groups::direct_product::the_transversal_length
int * the_transversal_length
Definition: groups.h:71

orbiter::layer3_group_actions::groups::direct_product::base_for_component2
long int * base_for_component2
Definition: groups.h:66

orbiter::layer3_group_actions::groups::direct_product::freeself
void freeself()
Definition: direct_product.cpp:51

orbiter::layer3_group_actions::groups::direct_product::bits_per_elt
int bits_per_elt
Definition: groups.h:56

orbiter::layer3_group_actions::groups::direct_product::offset_i
int offset_i(int i)
Definition: direct_product.cpp:391

orbiter::layer3_group_actions::groups::direct_product::make_element
void make_element(int *Elt, int *data, int verbose_level)
Definition: direct_product.cpp:496

orbiter::layer3_group_actions::groups::direct_product::direct_product
direct_product()
Definition: direct_product.cpp:21

orbiter::layer3_group_actions::groups::direct_product::degree_of_matrix_group2
int degree_of_matrix_group2
Definition: groups.h:42

orbiter::layer3_group_actions::groups::direct_product::element_invert
void element_invert(int *A, int *Av, int verbose_level)
Definition: direct_product.cpp:376

orbiter::layer3_group_actions::groups::direct_product::degree_overall
int degree_overall
Definition: groups.h:45

orbiter::layer3_group_actions::groups::direct_product::dimension_of_matrix_group1
int dimension_of_matrix_group1
Definition: groups.h:41

orbiter::layer3_group_actions::groups::direct_product::~direct_product
~direct_product()
Definition: direct_product.cpp:26

orbiter::layer3_group_actions::groups::direct_product::element_mult
void element_mult(int *A, int *B, int *AB, int verbose_level)
Definition: direct_product.cpp:341

orbiter::layer3_group_actions::groups::direct_product::the_base
long int * the_base
Definition: groups.h:70

orbiter::layer3_group_actions::groups::direct_product::bits_per_digit1
int bits_per_digit1
Definition: groups.h:53

orbiter::layer3_group_actions::groups::direct_product::element_move
void element_move(int *A, int *B, int verbose_level)
Definition: direct_product.cpp:363

orbiter::layer3_group_actions::groups::direct_product::get_digit
int get_digit(uchar *elt, int f, int i)
Definition: direct_product.cpp:468

orbiter::layer3_group_actions::groups::direct_product::degree_of_product_action
int degree_of_product_action
Definition: groups.h:44

orbiter::layer3_group_actions::groups::direct_product::tl_for_component1
int * tl_for_component1
Definition: groups.h:63

orbiter::layer3_group_actions::groups::direct_product::q1
int q1
Definition: groups.h:33

orbiter::layer3_group_actions::groups::direct_product::element_is_one
int element_is_one(int *Elt)
Definition: direct_product.cpp:330

orbiter::layer3_group_actions::groups::direct_product::degree_of_matrix_group1
int degree_of_matrix_group1
Definition: groups.h:40

orbiter::layer3_group_actions::groups::direct_product::q2
int q2
Definition: groups.h:34

orbiter::layer3_group_actions::groups::direct_product::element_image_of
long int element_image_of(int *Elt, long int a, int verbose_level)
Definition: direct_product.cpp:248

orbiter::layer3_group_actions::groups::direct_product::dimension_of_matrix_group2
int dimension_of_matrix_group2
Definition: groups.h:43

orbiter::layer3_group_actions::groups::direct_product::element_one
void element_one(int *Elt)
Definition: direct_product.cpp:324

orbiter::layer3_group_actions::groups::direct_product::bits_per_digit2
int bits_per_digit2
Definition: groups.h:54

orbiter::layer3_group_actions::groups::direct_product::elt1
uchar * elt1
Definition: groups.h:59

orbiter::layer3_group_actions::groups::direct_product::base_for_component1
long int * base_for_component1
Definition: groups.h:62

orbiter::layer3_group_actions::groups::direct_product::make_element_size
int make_element_size
Definition: groups.h:47

orbiter::layer3_group_actions::groups::direct_product::char_per_elt
int char_per_elt
Definition: groups.h:57

orbiter::layer3_group_actions::groups::direct_product::perm_offset_i
int * perm_offset_i
Definition: groups.h:50

orbiter::layer3_group_actions::groups::direct_product::tl_for_component2
int * tl_for_component2
Definition: groups.h:67

orbiter::layer3_group_actions::groups::direct_product::tmp_Elt1
int * tmp_Elt1
Definition: groups.h:51

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4
exceptional isomorphism between orthogonal groups: O4, O5 and GL(2,q)
Definition: groups.h:111

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::apply_4_to_2
void apply_4_to_2(int *E4, int &f_switch, int *E2_a, int *E2_b, int verbose_level)
Definition: exceptional_isomorphism_O4.cpp:347

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::Fq
field_theory::finite_field * Fq
Definition: groups.h:113

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::E2b
int * E2b
Definition: groups.h:121

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::~exceptional_isomorphism_O4
~exceptional_isomorphism_O4()
Definition: exceptional_isomorphism_O4.cpp:34

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::null
void null()
Definition: exceptional_isomorphism_O4.cpp:39

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::E5a
int * E5a
Definition: groups.h:118

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::A2
actions::action * A2
Definition: groups.h:114

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::apply_4_to_5
void apply_4_to_5(int *E4, int *E5, int verbose_level)
Definition: exceptional_isomorphism_O4.cpp:167

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::print_as_2x2
void print_as_2x2(int *mtx4x4)
Definition: exceptional_isomorphism_O4.cpp:421

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::init
void init(field_theory::finite_field *Fq, actions::action *A2, actions::action *A4, actions::action *A5, int verbose_level)
Definition: exceptional_isomorphism_O4.cpp:63

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::freeself
void freeself()
Definition: exceptional_isomorphism_O4.cpp:52

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::exceptional_isomorphism_O4
exceptional_isomorphism_O4()
Definition: exceptional_isomorphism_O4.cpp:20

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::apply_2to4_embedded
void apply_2to4_embedded(int f_switch, int *mtx2x2_T, int *mtx2x2_S, int *Elt, int verbose_level)
Definition: exceptional_isomorphism_O4.cpp:89

orbiter::layer3_group_actions::groups::exceptional_isomorphism_O4::apply_2_to_4
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Definition: exceptional_isomorphism_O4.cpp:387

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Definition: groups.h:119

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Definition: exceptional_isomorphism_O4.cpp:136

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Definition: groups.h:115

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Definition: groups.h:120

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Definition: groups.h:116

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Definition: groups.h:158

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Definition: groups.h:221

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Definition: linear_group_description.cpp:17

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Definition: groups.h:188

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Definition: groups.h:186

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Definition: linear_group_description.cpp:528

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Definition: groups.h:165

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Definition: linear_group_description.cpp:80

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Definition: linear_group_description.cpp:89

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Definition: groups.h:203

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Definition: groups.h:164

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Definition: groups.h:215

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Definition: groups.h:168

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Definition: groups.h:162

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Definition: groups.h:189

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Definition: groups.h:193

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Definition: groups.h:160

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Definition: groups.h:204

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Definition: groups.h:191

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Definition: groups.h:201

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Definition: linear_group_description.cpp:85

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Definition: groups.h:210

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Definition: groups.h:181

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Definition: groups.h:213

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Definition: groups.h:161

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Definition: groups.h:196

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Definition: groups.h:199

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Definition: groups.h:180

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Definition: groups.h:175

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Definition: linear_group_description.cpp:94

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Definition: groups.h:223

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Definition: groups.h:205

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Definition: groups.h:214

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Definition: groups.h:190

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Definition: groups.h:200

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Definition: groups.h:171

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Definition: groups.h:202

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Definition: groups.h:166

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Definition: groups.h:198

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Definition: groups.h:197

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int f_singer_group_and_frobenius
Definition: groups.h:194

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Definition: groups.h:208

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Definition: groups.h:187

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Definition: groups.h:179

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int f_on_rank_one_tensors
Definition: groups.h:211

orbiter::layer3_group_actions::groups::linear_group_description::override_polynomial
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Definition: groups.h:178

orbiter::layer3_group_actions::groups::linear_group_description::subgroup_generators_label
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Definition: groups.h:216

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Definition: groups.h:195

orbiter::layer3_group_actions::groups::linear_group_description::f_restricted_action
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Definition: groups.h:220

orbiter::layer3_group_actions::groups::linear_group_description::f_override_polynomial
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Definition: groups.h:177

orbiter::layer3_group_actions::groups::linear_group_description::f_on_k_subspaces
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Definition: groups.h:207

orbiter::layer3_group_actions::groups::linear_group_description::f_Janko1
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Definition: groups.h:218

orbiter::layer3_group_actions::groups::linear_group_description::GL_wreath_Sym_d
int GL_wreath_Sym_d
Definition: groups.h:167

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Definition: groups.h:192

orbiter::layer3_group_actions::groups::linear_group_description::f_GL_d_q_wr_Sym_n
int f_GL_d_q_wr_Sym_n
Definition: groups.h:163

orbiter::layer3_group_actions::groups::linear_group
creates a linear group from command line arguments using linear_group_description
Definition: groups.h:244

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Definition: linear_group.cpp:58

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void create_latex_report(graphics::layered_graph_draw_options *O, int f_sylow, int f_group_table, int f_classes, int verbose_level)
Definition: linear_group.cpp:1612

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Definition: linear_group.cpp:783

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void report(std::ostream &fp, int f_sylow, int f_group_table, int f_conjugacy_classes_and_normalizers, graphics::layered_graph_draw_options *LG_Draw_options, int verbose_level)
Definition: linear_group.cpp:1345

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Definition: linear_group.cpp:44

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Definition: linear_group.cpp:889

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strong_generators * Strong_gens
Definition: groups.h:260

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void init_diagonal_group(int verbose_level)
Definition: linear_group.cpp:818

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Definition: linear_group.cpp:1296

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int vector_space_dimension
Definition: groups.h:262

orbiter::layer3_group_actions::groups::linear_group::Mtx
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Definition: groups.h:257

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Definition: groups.h:247

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data_structures_groups::vector_ge * nice_gens
Definition: groups.h:266

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Definition: linear_group.cpp:573

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Definition: groups.h:246

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Definition: groups.h:250

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Definition: groups.h:248

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Definition: linear_group.cpp:852

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Definition: groups.h:263

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Definition: linear_group.cpp:998

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Definition: groups.h:253

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Definition: linear_group.cpp:1168

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Definition: groups.h:261

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Definition: linear_group.cpp:962

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Definition: linear_group.cpp:53

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Definition: linear_group.cpp:1032

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Definition: linear_group.cpp:927

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Definition: groups.h:255

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Definition: groups.h:259

orbiter::layer3_group_actions::groups::linear_group::label
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Definition: groups.h:252

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Definition: groups.h:249

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Definition: groups.h:265

orbiter::layer3_group_actions::groups::linear_group::linear_group
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Definition: linear_group.cpp:19

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Definition: linear_group.cpp:49

orbiter::layer3_group_actions::groups::linear_group::init_subgroup_by_generators
void init_subgroup_by_generators(std::string &subgroup_label, std::string &subgroup_order_text, int nb_subgroup_generators, int *subgroup_generators_data, int verbose_level)
Definition: linear_group.cpp:1219

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Definition: linear_group.cpp:624

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Definition: linear_group.cpp:692

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Definition: groups.h:256

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Definition: linear_group.cpp:1114

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Definition: linear_group.cpp:1068

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Definition: groups.h:318

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Definition: groups.h:380

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Definition: matrix_group.cpp:1965

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Definition: matrix_group.cpp:1614

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Definition: matrix_group.cpp:807

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Definition: matrix_group.cpp:1500

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Definition: matrix_group.cpp:1335

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Definition: matrix_group.cpp:1527

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Definition: groups.h:349

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Definition: groups.h:351

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Definition: groups.h:347

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Definition: groups.h:343

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Definition: matrix_group.cpp:204

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Definition: matrix_group.cpp:1469

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Definition: matrix_group.cpp:1543

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Definition: groups.h:380

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Definition: matrix_group.cpp:387

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Definition: groups.h:324

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Definition: matrix_group.cpp:853

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Definition: matrix_group.cpp:2299

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Definition: matrix_group.cpp:629

orbiter::layer3_group_actions::groups::matrix_group::init_base_general_linear
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Definition: matrix_group.cpp:750

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Definition: matrix_group.cpp:68

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Definition: groups.h:353

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Definition: groups.h:356

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Definition: matrix_group.cpp:1904

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Definition: groups.h:384

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Definition: matrix_group.cpp:1211

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Definition: matrix_group.cpp:356

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Definition: matrix_group.cpp:2334

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Definition: groups.h:375

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Definition: matrix_group.cpp:1940

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Definition: matrix_group.cpp:1341

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Definition: matrix_group.cpp:578

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Definition: matrix_group.cpp:1180

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Definition: matrix_group.cpp:1874

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Definition: groups.h:365

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Definition: matrix_group.cpp:1885

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Definition: matrix_group.cpp:1585

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Definition: matrix_group.cpp:512

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Definition: matrix_group.cpp:2033

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Definition: matrix_group.cpp:927

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Definition: matrix_group.cpp:1290

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Definition: groups.h:382

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Definition: matrix_group.cpp:1993

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Definition: matrix_group.cpp:468

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Definition: matrix_group.cpp:1124

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Definition: matrix_group.cpp:2274

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Definition: matrix_group.cpp:1311

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Definition: matrix_group.cpp:2380

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Definition: matrix_group.cpp:1765

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Definition: groups.h:348

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void orthogonal_group_random_generator(actions::action *A, orthogonal_geometry::orthogonal *O, int f_siegel, int f_reflection, int f_similarity, int f_semisimilarity, int *Elt, int verbose_level)
Definition: matrix_group.cpp:2061

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Definition: groups.h:328

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Definition: matrix_group.cpp:1673

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Definition: matrix_group.cpp:1772

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Definition: matrix_group.cpp:1285

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Definition: groups.h:371

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Definition: matrix_group.cpp:1058

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Definition: matrix_group.cpp:1413

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Definition: groups.h:384

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Definition: matrix_group.cpp:2423

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Definition: matrix_group.cpp:1295

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Definition: matrix_group.cpp:1929

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int f_GFq_is_allocated
Definition: groups.h:359

orbiter::layer3_group_actions::groups::matrix_group::Elt1
int * Elt1
Definition: groups.h:371

orbiter::layer3_group_actions::groups::matrix_group::elt2
uchar * elt2
Definition: groups.h:384

orbiter::layer3_group_actions::groups::matrix_group::Elt3
int * Elt3
Definition: groups.h:371

orbiter::layer3_group_actions::groups::matrix_group::label_tex
std::string label_tex
Definition: groups.h:357

orbiter::layer3_group_actions::groups::matrix_group::action_from_the_right_all_types
void action_from_the_right_all_types(int *v, int *A, int *vA, int verbose_level)
Definition: matrix_group.cpp:950

orbiter::layer3_group_actions::groups::matrix_group::n
int n
Definition: groups.h:332

orbiter::layer3_group_actions::groups::matrix_group::projective_action_from_the_right
void projective_action_from_the_right(int *v, int *A, int *vA, int verbose_level)
Definition: matrix_group.cpp:982

orbiter::layer3_group_actions::groups::matrix_group::init_projective_group
void init_projective_group(int n, field_theory::finite_field *F, int f_semilinear, actions::action *A, int verbose_level)
Definition: matrix_group.cpp:99

orbiter::layer3_group_actions::groups::matrix_group::Elts
data_structures::page_storage * Elts
Definition: groups.h:387

orbiter::layer3_group_actions::groups::matrix_group::f_projective
int f_projective
Definition: groups.h:321

orbiter::layer3_group_actions::groups::matrix_group::GL_print_latex_with_print_point_function
void GL_print_latex_with_print_point_function(int *Elt, std::ostream &ost, void(*point_label)(std::stringstream &sstr, int pt, void *data), void *point_label_data)
Definition: matrix_group.cpp:1703

orbiter::layer3_group_actions::groups::matrix_group::elt_size_int_half
int elt_size_int_half
Definition: groups.h:350

orbiter::layer3_group_actions::groups::matrix_group::GFq
field_theory::finite_field * GFq
Definition: groups.h:364

orbiter::layer3_group_actions::groups::matrix_group::general_linear_action_from_the_right
void general_linear_action_from_the_right(int *v, int *A, int *vA, int verbose_level)
Definition: matrix_group.cpp:999

orbiter::layer3_group_actions::groups::matrix_group::GL_one_internal
void GL_one_internal(int *Elt)
Definition: matrix_group.cpp:1064

orbiter::layer3_group_actions::groups::matrix_group::f_semilinear
int f_semilinear
Definition: groups.h:340

orbiter::layer3_group_actions::groups::matrix_group::C
algebra::gl_classes * C
Definition: groups.h:367

orbiter::layer3_group_actions::groups::matrix_group::matrices_without_eigenvector_one
void matrices_without_eigenvector_one(sims *S, int *&Sol, int &cnt, int f_path_select, int select_value, int verbose_level)
Definition: matrix_group.cpp:2122

orbiter::layer3_group_actions::groups::matrix_group::GL_zero
void GL_zero(int *Elt)
Definition: matrix_group.cpp:1091

orbiter::layer3_group_actions::groups::matrix_group::tmp_M
int * tmp_M
Definition: groups.h:376

orbiter::layer3_group_actions::groups::matrix_group::matrix_group
matrix_group()
Definition: matrix_group.cpp:22

orbiter::layer3_group_actions::groups::matrix_group::init_general_linear_group
void init_general_linear_group(int n, field_theory::finite_field *F, int f_semilinear, actions::action *A, int verbose_level)
Definition: matrix_group.cpp:280

orbiter::layer3_group_actions::groups::matrix_group::bits_per_digit
int bits_per_digit
Definition: groups.h:345

orbiter::layer3_group_actions::groups::matrix_group::GL_image_of_PG_element
long int GL_image_of_PG_element(int *Elt, long int a, int verbose_level)
Definition: matrix_group.cpp:906

orbiter::layer3_group_actions::groups::matrix_group::image_of_element
long int image_of_element(int *Elt, long int a, int verbose_level)
Definition: matrix_group.cpp:876

orbiter::layer3_group_actions::groups::matrix_group::bits_per_elt
int bits_per_elt
Definition: groups.h:346

orbiter::layer3_group_actions::groups::matrix_group::base_cols
int * base_cols
Definition: groups.h:378

orbiter::layer3_group_actions::groups::matrix_group::substitute_surface_equation
void substitute_surface_equation(int *Elt, int *coeff_in, int *coeff_out, algebraic_geometry::surface_domain *Surf, int verbose_level)
Definition: matrix_group.cpp:1016

orbiter::layer3_group_actions::groups::matrix_group::degree
int degree
Definition: groups.h:335

orbiter::layer3_group_actions::groups::matrix_group::GL_element_entry_ij
int GL_element_entry_ij(int *Elt, int i, int j)
Definition: matrix_group.cpp:848

orbiter::layer3_group_actions::groups::matrix_group::init_base_affine
void init_base_affine(actions::action *A, int verbose_level)
Definition: matrix_group.cpp:695

orbiter::layer3_group_actions::groups::matrix_group::Elt4
int * Elt4
Definition: groups.h:373

orbiter::layer3_group_actions::groups::orbits_on_something
compute orbits of a group in a given action; allows file io
Definition: groups.h:492

orbiter::layer3_group_actions::groups::orbits_on_something::get_orbit_number_and_position
void get_orbit_number_and_position(long int a, int &orbit_idx, int &orbit_pos, int verbose_level)
Definition: orbits_on_something.cpp:1807

orbiter::layer3_group_actions::groups::orbits_on_something::~orbits_on_something
~orbits_on_something()
Definition: orbits_on_something.cpp:41

orbiter::layer3_group_actions::groups::orbits_on_something::SG
strong_generators * SG
Definition: groups.h:497

orbiter::layer3_group_actions::groups::orbits_on_something::extract_orbits_using_classification
void extract_orbits_using_classification(int orbit_length, int nb_orbits, long int *orbits_idx, long int *extracted_set, int verbose_level)
Definition: orbits_on_something.cpp:1337

orbiter::layer3_group_actions::groups::orbits_on_something::extract_orbits
void extract_orbits(int orbit_length, int nb_orbits, int *orbits, long int *extracted_set, int verbose_level)
Definition: orbits_on_something.cpp:1299

orbiter::layer3_group_actions::groups::orbits_on_something::prefix
std::string prefix
Definition: groups.h:501

orbiter::layer3_group_actions::groups::orbits_on_something::compute_orbit_invariant_after_classification
void compute_orbit_invariant_after_classification(data_structures::set_of_sets *&Orbit_invariant, int(*evaluate_orbit_invariant_function)(int a, int i, int j, void *evaluate_data, int verbose_level), void *evaluate_data, int verbose_level)
Definition: orbits_on_something.cpp:1777

orbiter::layer3_group_actions::groups::orbits_on_something::orbits_on_something
orbits_on_something()
Definition: orbits_on_something.cpp:24

orbiter::layer3_group_actions::groups::orbits_on_something::create_graph_on_orbits_of_a_certain_length
void create_graph_on_orbits_of_a_certain_length(graph_theory::colored_graph *&CG, std::string &fname, int orbit_length, int &type_idx, int f_has_user_data, long int *user_data, int user_data_size, int f_has_colors, int number_colors, int *color_table, int(*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data), void *test_function_data, int verbose_level)
Definition: orbits_on_something.cpp:1090

orbiter::layer3_group_actions::groups::orbits_on_something::freeself
void freeself()
Definition: orbits_on_something.cpp:57

orbiter::layer3_group_actions::groups::orbits_on_something::compute_compact_type
void compute_compact_type(long int *orbit_type, long int goi, long int *&compact_type, long int *&row_labels, long int *&col_labels, int &m, int &n)
Definition: orbits_on_something.cpp:392

orbiter::layer3_group_actions::groups::orbits_on_something::create_latex_report
void create_latex_report(int verbose_level)
Definition: orbits_on_something.cpp:1824

orbiter::layer3_group_actions::groups::orbits_on_something::report_type
void report_type(std::ostream &ost, long int *orbit_type, long int goi)
Definition: orbits_on_something.cpp:352

orbiter::layer3_group_actions::groups::orbits_on_something::idx_of_points_in_orbits_of_length_l
void idx_of_points_in_orbits_of_length_l(long int *set, int set_sz, int go, int l, std::vector< int > &Idx, int verbose_level)
Definition: orbits_on_something.cpp:273

orbiter::layer3_group_actions::groups::orbits_on_something::f_load_save
int f_load_save
Definition: groups.h:500

orbiter::layer3_group_actions::groups::orbits_on_something::fname_csv
std::string fname_csv
Definition: groups.h:503

orbiter::layer3_group_actions::groups::orbits_on_something::create_graph_on_orbits_of_a_certain_length_override_orbits_classified
void create_graph_on_orbits_of_a_certain_length_override_orbits_classified(graph_theory::colored_graph *&CG, std::string &fname, int orbit_length, int &type_idx, int f_has_user_data, long int *user_data, int user_data_size, int(*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data), void *test_function_data, data_structures::set_of_sets *my_orbits_classified, int verbose_level)
Definition: orbits_on_something.cpp:1376

orbiter::layer3_group_actions::groups::orbits_on_something::create_weighted_graph_on_orbits
void create_weighted_graph_on_orbits(graph_theory::colored_graph *&CG, std::string &fname, int *Orbit_lengths, int nb_orbit_lengths, int *&Type_idx, int f_has_user_data, long int *user_data, int user_data_size, int(*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data), void *test_function_data, data_structures::set_of_sets *my_orbits_classified, int verbose_level)
Definition: orbits_on_something.cpp:1538

orbiter::layer3_group_actions::groups::orbits_on_something::print_orbits_based_on_filtered_orbits
void print_orbits_based_on_filtered_orbits(std::ostream &ost, data_structures::set_of_sets *Filtered_orbits)
Definition: orbits_on_something.cpp:467

orbiter::layer3_group_actions::groups::orbits_on_something::Orbits_classified_nb_types
int Orbits_classified_nb_types
Definition: groups.h:509

orbiter::layer3_group_actions::groups::orbits_on_something::report_quick
void report_quick(std::ostream &ost, int verbose_level)
Definition: orbits_on_something.cpp:2050

orbiter::layer3_group_actions::groups::orbits_on_something::report_classified_orbits_by_lengths
void report_classified_orbits_by_lengths(std::ostream &ost)
Definition: orbits_on_something.cpp:560

orbiter::layer3_group_actions::groups::orbits_on_something::null
void null()
Definition: orbits_on_something.cpp:46

orbiter::layer3_group_actions::groups::orbits_on_something::report_orbits_of_type
void report_orbits_of_type(std::ostream &ost, int type_idx)
Definition: orbits_on_something.cpp:771

orbiter::layer3_group_actions::groups::orbits_on_something::init
void init(actions::action *A, strong_generators *SG, int f_load_save, std::string &prefix, int verbose_level)
Definition: orbits_on_something.cpp:81

orbiter::layer3_group_actions::groups::orbits_on_something::classify_orbits_by_length
void classify_orbits_by_length(int verbose_level)
Definition: orbits_on_something.cpp:499

orbiter::layer3_group_actions::groups::orbits_on_something::get_orbit_type_index
int get_orbit_type_index(int orbit_length)
Definition: orbits_on_something.cpp:580

orbiter::layer3_group_actions::groups::orbits_on_something::Classify_orbits_by_length
data_structures::tally * Classify_orbits_by_length
Definition: groups.h:505

orbiter::layer3_group_actions::groups::orbits_on_something::print_orbits_of_a_certain_length
void print_orbits_of_a_certain_length(int orbit_length)
Definition: orbits_on_something.cpp:702

orbiter::layer3_group_actions::groups::orbits_on_something::Sch
schreier * Sch
Definition: groups.h:498

orbiter::layer3_group_actions::groups::orbits_on_something::get_orbit_type_index_if_present
int get_orbit_type_index_if_present(int orbit_length)
Definition: orbits_on_something.cpp:593

orbiter::layer3_group_actions::groups::orbits_on_something::test_all_orbits_by_length
void test_all_orbits_by_length(int(*test_function)(long int *orbit, int orbit_length, void *data), void *test_function_data, int verbose_level)
Definition: orbits_on_something.cpp:605

orbiter::layer3_group_actions::groups::orbits_on_something::create_graph_on_orbits_of_a_certain_length_after_filtering
void create_graph_on_orbits_of_a_certain_length_after_filtering(graph_theory::colored_graph *&CG, std::string &fname, long int *filter_by_set, int filter_by_set_size, int orbit_length, int &type_idx, int f_has_user_data, long int *user_data, int user_data_size, int f_has_colors, int number_colors, int *color_table, int(*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data), void *test_function_data, int verbose_level)
Definition: orbits_on_something.cpp:798

orbiter::layer3_group_actions::groups::orbits_on_something::test_pair_of_orbits_of_a_equal_length
int test_pair_of_orbits_of_a_equal_length(int orbit_length, int type_idx, int idx1, int idx2, long int *Orbit1, long int *Orbit2, int(*test_function)(long int *orbit1, int orbit_length1, long int *orbit2, int orbit_length2, void *data), void *test_function_data, int verbose_level)
Definition: orbits_on_something.cpp:729

orbiter::layer3_group_actions::groups::orbits_on_something::orbit_type_of_set
void orbit_type_of_set(long int *set, int set_sz, int go, long int *orbit_type, int verbose_level)
Definition: orbits_on_something.cpp:290

orbiter::layer3_group_actions::groups::orbits_on_something::Orbits_classified_length
int * Orbits_classified_length
Definition: groups.h:508

orbiter::layer3_group_actions::groups::orbits_on_something::stabilizer_of
void stabilizer_of(int orbit_idx, int verbose_level)
Definition: orbits_on_something.cpp:202

orbiter::layer3_group_actions::groups::orbits_on_something::A
actions::action * A
Definition: groups.h:496

orbiter::layer3_group_actions::groups::orbits_on_something::test_orbits_of_a_certain_length
void test_orbits_of_a_certain_length(int orbit_length, int &type_idx, int &prev_nb, int(*test_function)(long int *orbit, int orbit_length, void *data), void *test_function_data, int verbose_level)
Definition: orbits_on_something.cpp:637

orbiter::layer3_group_actions::groups::orbits_on_something::report_orbit_lengths
void report_orbit_lengths(std::ostream &ost)
Definition: orbits_on_something.cpp:462

orbiter::layer3_group_actions::groups::orbits_on_something::fname
std::string fname
Definition: groups.h:502

orbiter::layer3_group_actions::groups::orbits_on_something::report
void report(std::ostream &ost, int verbose_level)
Definition: orbits_on_something.cpp:1883

orbiter::layer3_group_actions::groups::orbits_on_something::report_classified_orbit_lengths
void report_classified_orbit_lengths(std::ostream &ost)
Definition: orbits_on_something.cpp:548

orbiter::layer3_group_actions::groups::orbits_on_something::Orbits_classified
data_structures::set_of_sets * Orbits_classified
Definition: groups.h:506

orbiter::layer3_group_actions::groups::permutation_group_create
a domain for permutation groups whose elements are given in the permutation representation
Definition: groups.h:636

orbiter::layer3_group_actions::groups::permutation_group_create::f_has_strong_generators
int f_has_strong_generators
Definition: groups.h:647

orbiter::layer3_group_actions::groups::permutation_group_create::Strong_gens
strong_generators * Strong_gens
Definition: groups.h:648

orbiter::layer3_group_actions::groups::permutation_group_create::label
std::string label
Definition: groups.h:641

orbiter::layer3_group_actions::groups::permutation_group_create::label_tex
std::string label_tex
Definition: groups.h:642

orbiter::layer3_group_actions::groups::permutation_group_create::permutation_group_init
void permutation_group_init(permutation_group_description *description, int verbose_level)
Definition: permutation_group_create.cpp:47

orbiter::layer3_group_actions::groups::permutation_group_create::A_initial
actions::action * A_initial
Definition: groups.h:645

orbiter::layer3_group_actions::groups::permutation_group_create::~permutation_group_create
~permutation_group_create()
Definition: permutation_group_create.cpp:41

orbiter::layer3_group_actions::groups::permutation_group_create::init_subgroup_by_generators
void init_subgroup_by_generators(std::string &subgroup_label, std::string &subgroup_order_text, int nb_subgroup_generators, std::string &subgroup_generators_label, int verbose_level)
Definition: permutation_group_create.cpp:192

orbiter::layer3_group_actions::groups::permutation_group_create::f_has_nice_gens
int f_has_nice_gens
Definition: groups.h:651

orbiter::layer3_group_actions::groups::permutation_group_create::A2
actions::action * A2
Definition: groups.h:649

orbiter::layer3_group_actions::groups::permutation_group_create::Descr
permutation_group_description * Descr
Definition: groups.h:639

orbiter::layer3_group_actions::groups::permutation_group_create::nice_gens
data_structures_groups::vector_ge * nice_gens
Definition: groups.h:652

orbiter::layer3_group_actions::groups::permutation_group_create::permutation_group_create
permutation_group_create()
Definition: permutation_group_create.cpp:23

orbiter::layer3_group_actions::groups::permutation_group_description
a domain for permutation groups whose elements are given in the permutation representation
Definition: groups.h:677

orbiter::layer3_group_actions::groups::permutation_group_description::subgroup_order_text
std::string subgroup_order_text
Definition: groups.h:694

orbiter::layer3_group_actions::groups::permutation_group_description::read_arguments
int read_arguments(int argc, std::string *argv, int verbose_level)
Definition: permutation_group_description.cpp:51

orbiter::layer3_group_actions::groups::permutation_group_description::f_subgroup_by_generators
int f_subgroup_by_generators
Definition: groups.h:692

orbiter::layer3_group_actions::groups::permutation_group_description::degree
int degree
Definition: groups.h:680

orbiter::layer3_group_actions::groups::permutation_group_description::f_bsgs
int f_bsgs
Definition: groups.h:683

orbiter::layer3_group_actions::groups::permutation_group_description::~permutation_group_description
~permutation_group_description()
Definition: permutation_group_description.cpp:46

orbiter::layer3_group_actions::groups::permutation_group_description::subgroup_generators_label
std::string subgroup_generators_label
Definition: groups.h:696

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_base
std::string bsgs_base
Definition: groups.h:687

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_label_tex
std::string bsgs_label_tex
Definition: groups.h:685

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_nb_generators
int bsgs_nb_generators
Definition: groups.h:688

orbiter::layer3_group_actions::groups::permutation_group_description::print
void print()
Definition: permutation_group_description.cpp:127

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_label
std::string bsgs_label
Definition: groups.h:684

orbiter::layer3_group_actions::groups::permutation_group_description::permutation_group_description
permutation_group_description()
Definition: permutation_group_description.cpp:24

orbiter::layer3_group_actions::groups::permutation_group_description::subgroup_label
std::string subgroup_label
Definition: groups.h:693

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_order_text
std::string bsgs_order_text
Definition: groups.h:686

orbiter::layer3_group_actions::groups::permutation_group_description::nb_subgroup_generators
int nb_subgroup_generators
Definition: groups.h:695

orbiter::layer3_group_actions::groups::permutation_group_description::type
permutation_group_type type
Definition: groups.h:681

orbiter::layer3_group_actions::groups::permutation_group_description::bsgs_generators
std::string bsgs_generators
Definition: groups.h:689

orbiter::layer3_group_actions::groups::permutation_representation_domain
a domain for permutation groups whose elements are given in the permutation representation
Definition: groups.h:715

orbiter::layer3_group_actions::groups::permutation_representation_domain::elt3
uchar * elt3
Definition: groups.h:733

orbiter::layer3_group_actions::groups::permutation_representation_domain::permutation_representation_domain
permutation_representation_domain()
Definition: permutation_representation_domain.cpp:22

orbiter::layer3_group_actions::groups::permutation_representation_domain::offset
int offset
Definition: groups.h:727

orbiter::layer3_group_actions::groups::permutation_representation_domain::unpack
void unpack(uchar *elt, int *Elt)
Definition: permutation_representation_domain.cpp:370

orbiter::layer3_group_actions::groups::permutation_representation_domain::Elt3
int * Elt3
Definition: groups.h:732

orbiter::layer3_group_actions::groups::permutation_representation_domain::Elt2
int * Elt2
Definition: groups.h:732

orbiter::layer3_group_actions::groups::permutation_representation_domain::elt1
uchar * elt1
Definition: groups.h:733

orbiter::layer3_group_actions::groups::permutation_representation_domain::null
void null()
Definition: permutation_representation_domain.cpp:32

orbiter::layer3_group_actions::groups::permutation_representation_domain::make_element
void make_element(int *Elt, int *data, int verbose_level)
Definition: permutation_representation_domain.cpp:498

orbiter::layer3_group_actions::groups::permutation_representation_domain::Eltrk1
int * Eltrk1
Definition: groups.h:735

orbiter::layer3_group_actions::groups::permutation_representation_domain::m
int m
Definition: groups.h:724

orbiter::layer3_group_actions::groups::permutation_representation_domain::print
void print(int *Elt, std::ostream &ost)
Definition: permutation_representation_domain.cpp:398

orbiter::layer3_group_actions::groups::permutation_representation_domain::Elt4
int * Elt4
Definition: groups.h:732

orbiter::layer3_group_actions::groups::permutation_representation_domain::code_for_make_element
void code_for_make_element(int *Elt, int *data)
Definition: permutation_representation_domain.cpp:421

orbiter::layer3_group_actions::groups::permutation_representation_domain::mn
int mn
Definition: groups.h:726

orbiter::layer3_group_actions::groups::permutation_representation_domain::Eltrk3
int * Eltrk3
Definition: groups.h:735

orbiter::layer3_group_actions::groups::permutation_representation_domain::allocate
void allocate()
Definition: permutation_representation_domain.cpp:79

orbiter::layer3_group_actions::groups::permutation_representation_domain::degree
int degree
Definition: groups.h:718

orbiter::layer3_group_actions::groups::permutation_representation_domain::print_for_make_element
void print_for_make_element(int *Elt, std::ostream &ost)
Definition: permutation_representation_domain.cpp:426

orbiter::layer3_group_actions::groups::permutation_representation_domain::f_induced_action
int f_induced_action
Definition: groups.h:720

orbiter::layer3_group_actions::groups::permutation_representation_domain::init_product_action
void init_product_action(int m, int n, int page_length_log, int verbose_level)
Definition: permutation_representation_domain.cpp:95

orbiter::layer3_group_actions::groups::permutation_representation_domain::init_data
void init_data(int page_length_log, int verbose_level)
Definition: permutation_representation_domain.cpp:143

orbiter::layer3_group_actions::groups::permutation_representation_domain::elt2
uchar * elt2
Definition: groups.h:733

orbiter::layer3_group_actions::groups::permutation_representation_domain::invert
void invert(int *A, int *Ainv)
Definition: permutation_representation_domain.cpp:363

orbiter::layer3_group_actions::groups::permutation_representation_domain::f_product_action
int f_product_action
Definition: groups.h:723

orbiter::layer3_group_actions::groups::permutation_representation_domain::mult
void mult(int *A, int *B, int *AB)
Definition: permutation_representation_domain.cpp:344

orbiter::layer3_group_actions::groups::permutation_representation_domain::init
void init(int degree, int page_length_log, int verbose_level)
Definition: permutation_representation_domain.cpp:122

orbiter::layer3_group_actions::groups::permutation_representation_domain::free
void free()
Definition: permutation_representation_domain.cpp:47

orbiter::layer3_group_actions::groups::permutation_representation_domain::transversal_rep
void transversal_rep(int i, int j, int *Elt, int verbose_level)
Definition: permutation_representation_domain.cpp:311

orbiter::layer3_group_actions::groups::permutation_representation_domain::copy
void copy(int *A, int *B)
Definition: permutation_representation_domain.cpp:354

orbiter::layer3_group_actions::groups::permutation_representation_domain::print_for_make_element_no_commas
void print_for_make_element_no_commas(int *Elt, std::ostream &ost)
Definition: permutation_representation_domain.cpp:435

orbiter::layer3_group_actions::groups::permutation_representation_domain::Eltrk2
int * Eltrk2
Definition: groups.h:735

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void init_with_base(int degree, int base_length, int *base, int page_length_log, actions::action &A, int verbose_level)
Definition: permutation_representation_domain.cpp:202

orbiter::layer3_group_actions::groups::permutation_representation_domain::~permutation_representation_domain
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Definition: permutation_representation_domain.cpp:27

orbiter::layer3_group_actions::groups::permutation_representation_domain::print_with_action
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Definition: permutation_representation_domain.cpp:445

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int n
Definition: groups.h:725

orbiter::layer3_group_actions::groups::permutation_representation_domain::char_per_elt
int char_per_elt
Definition: groups.h:729

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Definition: groups.h:738

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Definition: groups.h:730

orbiter::layer3_group_actions::groups::permutation_representation_domain::print_with_print_point_function
void print_with_print_point_function(int *Elt, std::ostream &ost, void(*point_label)(std::stringstream &sstr, long int pt, void *data), void *point_label_data)
Definition: permutation_representation_domain.cpp:408

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Definition: permutation_representation_domain.cpp:384

orbiter::layer3_group_actions::groups::permutation_representation_domain::one
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Definition: permutation_representation_domain.cpp:323

orbiter::layer3_group_actions::groups::permutation_representation_domain::Elt1
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Definition: groups.h:732

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Definition: permutation_representation_domain.cpp:332

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homomorphism to a permutation group
Definition: groups.h:780

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Definition: groups.h:786

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Definition: groups.h:795

orbiter::layer3_group_actions::groups::permutation_representation::init
void init(actions::action *A_original, int f_stay_in_the_old_action, data_structures_groups::vector_ge *gens, int *Perms, int degree, int verbose_level)
Definition: permutation_representation.cpp:63

orbiter::layer3_group_actions::groups::permutation_representation::element_print_latex
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Definition: permutation_representation.cpp:230

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Definition: permutation_representation.cpp:182

orbiter::layer3_group_actions::groups::permutation_representation::element_one
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Definition: permutation_representation.cpp:150

orbiter::layer3_group_actions::groups::permutation_representation::element_print_for_make_element
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Definition: permutation_representation.cpp:220

orbiter::layer3_group_actions::groups::permutation_representation::~permutation_representation
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Definition: permutation_representation.cpp:46

orbiter::layer3_group_actions::groups::permutation_representation::permutation_representation
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Definition: permutation_representation.cpp:24

orbiter::layer3_group_actions::groups::permutation_representation::Perms
int * Perms
Definition: groups.h:787

orbiter::layer3_group_actions::groups::permutation_representation::element_print_easy
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Definition: permutation_representation.cpp:225

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Definition: groups.h:785

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Definition: groups.h:802

orbiter::layer3_group_actions::groups::permutation_representation::Elts
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Definition: groups.h:806

orbiter::layer3_group_actions::groups::permutation_representation::element_unpack
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Definition: permutation_representation.cpp:215

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Definition: permutation_representation.cpp:195

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actions::action * A_original
Definition: groups.h:783

orbiter::layer3_group_actions::groups::permutation_representation::f_stay_in_the_old_action
int f_stay_in_the_old_action
Definition: groups.h:784

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permutation_representation_domain * P
Definition: groups.h:791

orbiter::layer3_group_actions::groups::permutation_representation::PS
data_structures::page_storage * PS
Definition: groups.h:804

orbiter::layer3_group_actions::groups::permutation_representation::element_mult
void element_mult(int *A, int *B, int *AB, int verbose_level)
Definition: permutation_representation.cpp:166

orbiter::layer3_group_actions::groups::permutation_representation::element_is_one
int element_is_one(int *Elt)
Definition: permutation_representation.cpp:158

orbiter::layer3_group_actions::groups::permutation_representation::element_image_of
long int element_image_of(int *Elt, long int a, int verbose_level)
Definition: permutation_representation.cpp:120

orbiter::layer3_group_actions::groups::permutation_representation::char_per_elt
int char_per_elt
Definition: groups.h:797

orbiter::layer3_group_actions::groups::permutation_representation::degree
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Definition: groups.h:788

orbiter::layer3_group_actions::groups::permutation_representation::perm_offset
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Definition: groups.h:792

orbiter::layer3_group_actions::groups::permutation_representation::label
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Definition: groups.h:801

orbiter::layer3_group_actions::groups::permutation_representation::element_pack
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Definition: permutation_representation.cpp:210

orbiter::layer3_group_actions::groups::permutation_representation::elt1
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Definition: groups.h:798

orbiter::layer3_group_actions::groups::permutation_representation::elt_size_int
int elt_size_int
Definition: groups.h:793

orbiter::layer3_group_actions::groups::schreier_sims
Schreier Sims algorithm to create the stabilizer chain of a permutation group.
Definition: groups.h:1188

orbiter::layer3_group_actions::groups::schreier_sims::get_generator_external_from_generators
void get_generator_external_from_generators(int *Elt, int verbose_level)
Definition: schreier_sims.cpp:329

orbiter::layer3_group_actions::groups::schreier_sims::get_generator_internal
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Definition: schreier_sims.cpp:268

orbiter::layer3_group_actions::groups::schreier_sims::callback_choose_random_generator_data
void * callback_choose_random_generator_data
Definition: groups.h:1214

orbiter::layer3_group_actions::groups::schreier_sims::get_generator
void get_generator(int *Elt, int verbose_level)
Definition: schreier_sims.cpp:394

orbiter::layer3_group_actions::groups::schreier_sims::~schreier_sims
~schreier_sims()
Definition: schreier_sims.cpp:58

orbiter::layer3_group_actions::groups::schreier_sims::old_G
sims * old_G
Definition: groups.h:1217

orbiter::layer3_group_actions::groups::schreier_sims::f_from_old_G
int f_from_old_G
Definition: groups.h:1216

orbiter::layer3_group_actions::groups::schreier_sims::KA
actions::action * KA
Definition: groups.h:1195

orbiter::layer3_group_actions::groups::schreier_sims::null
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Definition: schreier_sims.cpp:63

orbiter::layer3_group_actions::groups::schreier_sims::f_override_choose_next_base_point_method
int f_override_choose_next_base_point_method
Definition: groups.h:1223

orbiter::layer3_group_actions::groups::schreier_sims::iteration
int iteration
Definition: groups.h:1227

orbiter::layer3_group_actions::groups::schreier_sims::init_base_of_choice
void init_base_of_choice(int base_of_choice_len, int *base_of_choice, int verbose_level)
Definition: schreier_sims.cpp:217

orbiter::layer3_group_actions::groups::schreier_sims::init
void init(actions::action *A, int verbose_level)
Definition: schreier_sims.cpp:95

orbiter::layer3_group_actions::groups::schreier_sims::f_has_base_of_choice
int f_has_base_of_choice
Definition: groups.h:1219

orbiter::layer3_group_actions::groups::schreier_sims::f_from_generators
int f_from_generators
Definition: groups.h:1208

orbiter::layer3_group_actions::groups::schreier_sims::Elt3
int * Elt3
Definition: groups.h:1202

orbiter::layer3_group_actions::groups::schreier_sims::init_choose_next_base_point_method
void init_choose_next_base_point_method(int(*choose_next_base_point_method)(actions::action *A, int *Elt, int verbose_level), int verbose_level)
Definition: schreier_sims.cpp:231

orbiter::layer3_group_actions::groups::schreier_sims::choose_next_base_point_method
int(* choose_next_base_point_method)(actions::action *A, int *Elt, int verbose_level)
Definition: groups.h:1224

orbiter::layer3_group_actions::groups::schreier_sims::get_generator_external_old_G
void get_generator_external_old_G(int *Elt, int verbose_level)
Definition: schreier_sims.cpp:376

orbiter::layer3_group_actions::groups::schreier_sims::get_generator_external
void get_generator_external(int *Elt, int verbose_level)
Definition: schreier_sims.cpp:290

orbiter::layer3_group_actions::groups::schreier_sims::f_has_target_group_order
int f_has_target_group_order
Definition: groups.h:1204

orbiter::layer3_group_actions::groups::schreier_sims::Elt1
int * Elt1
Definition: groups.h:1200

orbiter::layer3_group_actions::groups::schreier_sims::init_old_G
void init_old_G(sims *old_G, int verbose_level)
Definition: schreier_sims.cpp:206

orbiter::layer3_group_actions::groups::schreier_sims::f_from_random_process
int f_from_random_process
Definition: groups.h:1211

orbiter::layer3_group_actions::groups::schreier_sims::Elt2
int * Elt2
Definition: groups.h:1201

orbiter::layer3_group_actions::groups::schreier_sims::K
sims * K
Definition: groups.h:1196

orbiter::layer3_group_actions::groups::schreier_sims::GA
actions::action * GA
Definition: groups.h:1191

orbiter::layer3_group_actions::groups::schreier_sims::f_interested_in_kernel
int f_interested_in_kernel
Definition: groups.h:1194

orbiter::layer3_group_actions::groups::schreier_sims::init_generators
void init_generators(data_structures_groups::vector_ge *gens, int verbose_level)
Definition: schreier_sims.cpp:164

orbiter::layer3_group_actions::groups::schreier_sims::closure_group
void closure_group(int verbose_level)
Definition: schreier_sims.cpp:424

orbiter::layer3_group_actions::groups::schreier_sims::print_group_orders
void print_group_orders()
Definition: schreier_sims.cpp:259

orbiter::layer3_group_actions::groups::schreier_sims::compute_group_orders
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Definition: schreier_sims.cpp:246

orbiter::layer3_group_actions::groups::schreier_sims::schreier_sims
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Definition: schreier_sims.cpp:19

orbiter::layer3_group_actions::groups::schreier_sims::K_order
ring_theory::longinteger_object K_order
Definition: groups.h:1198

orbiter::layer3_group_actions::groups::schreier_sims::get_generator_external_random_process
void get_generator_external_random_process(int *Elt, int verbose_level)
Definition: schreier_sims.cpp:363

orbiter::layer3_group_actions::groups::schreier_sims::external_gens
data_structures_groups::vector_ge * external_gens
Definition: groups.h:1209

orbiter::layer3_group_actions::groups::schreier_sims::callback_choose_random_generator
void(* callback_choose_random_generator)(int iteration, int *Elt, void *data, int verbose_level)
Definition: groups.h:1212

orbiter::layer3_group_actions::groups::schreier_sims::interested_in_kernel
void interested_in_kernel(actions::action *KA, int verbose_level)
Definition: schreier_sims.cpp:134

orbiter::layer3_group_actions::groups::schreier_sims::tgo
ring_theory::longinteger_object tgo
Definition: groups.h:1205

orbiter::layer3_group_actions::groups::schreier_sims::create_group
void create_group(int verbose_level)
Definition: schreier_sims.cpp:471

orbiter::layer3_group_actions::groups::schreier_sims::freeself
void freeself()
Definition: schreier_sims.cpp:67

orbiter::layer3_group_actions::groups::schreier_sims::KG_order
ring_theory::longinteger_object KG_order
Definition: groups.h:1198

orbiter::layer3_group_actions::groups::schreier_sims::init_random_process
void init_random_process(void(*callback_choose_random_generator)(int iteration, int *Elt, void *data, int verbose_level), void *callback_choose_random_generator_data, int verbose_level)
Definition: schreier_sims.cpp:188

orbiter::layer3_group_actions::groups::schreier_sims::init_target_group_order
void init_target_group_order(ring_theory::longinteger_object &tgo, int verbose_level)
Definition: schreier_sims.cpp:152

orbiter::layer3_group_actions::groups::schreier_sims::base_of_choice_len
int base_of_choice_len
Definition: groups.h:1220

orbiter::layer3_group_actions::groups::schreier_sims::G_order
ring_theory::longinteger_object G_order
Definition: groups.h:1198

orbiter::layer3_group_actions::groups::schreier_sims::base_of_choice
int * base_of_choice
Definition: groups.h:1221

orbiter::layer3_group_actions::groups::schreier_sims::G
sims * G
Definition: groups.h:1192

orbiter::layer3_group_actions::groups::schreier
Schreier trees for orbits of groups on points.
Definition: groups.h:839

orbiter::layer3_group_actions::groups::schreier::init_generators_recycle_images
void init_generators_recycle_images(data_structures_groups::vector_ge &generators, int **old_images, int idx_generator_to_delete, int verbose_level)
Definition: schreier.cpp:393

orbiter::layer3_group_actions::groups::schreier::draw_forest
void draw_forest(std::string &fname_mask, graphics::layered_graph_draw_options *Opt, int f_has_point_labels, long int *point_labels, int verbose_level)
Definition: schreier_io.cpp:1222

orbiter::layer3_group_actions::groups::schreier::get_orbit_decomposition_scheme_of_graph
void get_orbit_decomposition_scheme_of_graph(int *Adj, int n, int *&Decomp_scheme, int verbose_level)
Definition: schreier.cpp:2858

orbiter::layer3_group_actions::groups::schreier::compute_orbit_invariant
void compute_orbit_invariant(int *&orbit_invariant, int(*compute_orbit_invariant_callback)(schreier *Sch, int orbit_idx, void *data, int verbose_level), void *compute_orbit_invariant_data, int verbose_level)
Definition: schreier.cpp:3320

orbiter::layer3_group_actions::groups::schreier::shallow_tree_generators
void shallow_tree_generators(int orbit_idx, int f_randomized, schreier *&shallow_tree, int verbose_level)
Definition: schreier.cpp:2962

orbiter::layer3_group_actions::groups::schreier::print_tree
void print_tree(int orbit_no)
Definition: schreier_io.cpp:1198

orbiter::layer3_group_actions::groups::schreier::degree
long int degree
Definition: groups.h:844

orbiter::layer3_group_actions::groups::schreier::print_function_data
void * print_function_data
Definition: groups.h:880

orbiter::layer3_group_actions::groups::schreier::freeself
void freeself()
Definition: schreier.cpp:64

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits
void print_and_list_orbits(std::ostream &ost)
Definition: schreier_io.cpp:250

orbiter::layer3_group_actions::groups::schreier::preferred_choice_function_data2
int preferred_choice_function_data2
Definition: groups.h:885

orbiter::layer3_group_actions::groups::schreier::compute_point_orbit_with_limited_depth
void compute_point_orbit_with_limited_depth(int pt, int max_depth, int verbose_level)
Definition: schreier.cpp:1395

orbiter::layer3_group_actions::groups::schreier::compute_all_point_orbits
void compute_all_point_orbits(int verbose_level)
Definition: schreier.cpp:988

orbiter::layer3_group_actions::groups::schreier::init_images_only
void init_images_only(int nb_images, long int degree, int *images, int verbose_level)
Definition: schreier.cpp:167

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_and_stabilizer_sorted_by_length
void print_and_list_orbits_and_stabilizer_sorted_by_length(std::ostream &ost, int f_tex, actions::action *default_action, ring_theory::longinteger_object &full_group_order)
Definition: schreier_io.cpp:587

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_and_stabilizer
void print_and_list_orbits_and_stabilizer(std::ostream &ost, actions::action *default_action, ring_theory::longinteger_object &go, void(*print_point)(std::ostream &ost, int pt, void *data), void *data)
Definition: schreier_io.cpp:213

orbiter::layer3_group_actions::groups::schreier::print_and_list_all_orbits_and_stabilizers_with_list_of_elements_tex
void print_and_list_all_orbits_and_stabilizers_with_list_of_elements_tex(std::ostream &ost, actions::action *default_action, strong_generators *gens, int verbose_level)
Definition: schreier_io.cpp:301

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbit_tex
void print_and_list_orbit_tex(int i, std::ostream &ost)
Definition: schreier_io.cpp:385

orbiter::layer3_group_actions::groups::schreier::cosetrep
int * cosetrep
Definition: groups.h:875

orbiter::layer3_group_actions::groups::schreier::elements_in_orbit_of
void elements_in_orbit_of(int pt, int *orb, int &nb, int verbose_level)
Definition: schreier.cpp:2733

orbiter::layer3_group_actions::groups::schreier::orbits_as_set_of_sets
void orbits_as_set_of_sets(data_structures::set_of_sets *&S, int verbose_level)
Definition: schreier.cpp:2653

orbiter::layer3_group_actions::groups::schreier::write_orbit_summary
void write_orbit_summary(std::string &fname, actions::action *default_action, ring_theory::longinteger_object &full_group_order, int verbose_level)
Definition: schreier_io.cpp:411

orbiter::layer3_group_actions::groups::schreier::orbits_on_invariant_subset_fast
void orbits_on_invariant_subset_fast(int len, int *subset, int verbose_level)
Definition: schreier.cpp:1931

orbiter::layer3_group_actions::groups::schreier::compute_all_orbits_on_invariant_subset_lint
void compute_all_orbits_on_invariant_subset_lint(int len, long int *subset, int verbose_level)
Definition: schreier.cpp:1221

orbiter::layer3_group_actions::groups::schreier::get_num_points
int get_num_points()
Definition: schreier.cpp:3276

orbiter::layer3_group_actions::groups::schreier::get_orbit_number_and_position
void get_orbit_number_and_position(int pt, int &orbit_idx, int &orbit_pos, int verbose_level)
Definition: schreier.cpp:2822

orbiter::layer3_group_actions::groups::schreier::subtree_calc_weight
int subtree_calc_weight(int *weight, int &max_depth, int i, int last)
Definition: schreier_io.cpp:1780

orbiter::layer3_group_actions::groups::schreier::coset_rep_with_verbosity
void coset_rep_with_verbosity(int j, int verbose_level)
Definition: schreier.cpp:824

orbiter::layer3_group_actions::groups::schreier::list_elements_as_permutations_vertically
void list_elements_as_permutations_vertically(std::ostream &ost)
Definition: schreier_io.cpp:2027

orbiter::layer3_group_actions::groups::schreier::orbits_on_invariant_subset
void orbits_on_invariant_subset(int len, int *subset, int &nb_orbits_on_subset, int *&orbit_perm, int *&orbit_perm_inv)
Definition: schreier.cpp:2035

orbiter::layer3_group_actions::groups::schreier::orbit_first
int * orbit_first
Definition: groups.h:868

orbiter::layer3_group_actions::groups::schreier::get_orbit_partition_of_points_and_lines
void get_orbit_partition_of_points_and_lines(data_structures::partitionstack &S, int verbose_level)
Definition: schreier.cpp:2070

orbiter::layer3_group_actions::groups::schreier::print_orbit
void print_orbit(int orbit_no)
Definition: schreier_io.cpp:929

orbiter::layer3_group_actions::groups::schreier::write_to_file_binary
void write_to_file_binary(std::ofstream &fp, int verbose_level)
Definition: schreier_io.cpp:1900

orbiter::layer3_group_actions::groups::schreier::print_TDA
void print_TDA(std::ostream &ost, geometry::object_with_canonical_form *OwCF, combinatorics::classification_of_objects_report_options *Report_options, int verbose_level)
Definition: schreier.cpp:3342

orbiter::layer3_group_actions::groups::schreier::random_schreier_generator
void random_schreier_generator(int *Elt, int verbose_level)
Definition: schreier.cpp:1709

orbiter::layer3_group_actions::groups::schreier::orbit_len
int * orbit_len
Definition: groups.h:869

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_sorted_by_length
void print_and_list_orbits_sorted_by_length(std::ostream &ost)
Definition: schreier_io.cpp:525

orbiter::layer3_group_actions::groups::schreier::compute_orbit_statistic_lint
void compute_orbit_statistic_lint(long int *set, int set_size, int *orbit_count, int verbose_level)
Definition: schreier.cpp:2631

orbiter::layer3_group_actions::groups::schreier::random_schreier_generator_ith_orbit
void random_schreier_generator_ith_orbit(int *Elt, int orbit_no, int verbose_level)
Definition: schreier.cpp:1574

orbiter::layer3_group_actions::groups::schreier::A
actions::action * A
Definition: groups.h:842

orbiter::layer3_group_actions::groups::schreier::allocate_tables
void allocate_tables()
Definition: schreier.cpp:324

orbiter::layer3_group_actions::groups::schreier::swap_points
void swap_points(int i, int j, int verbose_level)
Definition: schreier.cpp:678

orbiter::layer3_group_actions::groups::schreier::read_from_file_binary
void read_from_file_binary(std::ifstream &fp, int verbose_level)
Definition: schreier_io.cpp:1929

orbiter::layer3_group_actions::groups::schreier::Elt2
int * Elt2
Definition: groups.h:872

orbiter::layer3_group_actions::groups::schreier::prev
int * prev
Definition: groups.h:861

orbiter::layer3_group_actions::groups::schreier::print_generators
void print_generators()
Definition: schreier_io.cpp:873

orbiter::layer3_group_actions::groups::schreier::init2
void init2()
Definition: schreier.cpp:334

orbiter::layer3_group_actions::groups::schreier::init_generators_by_handle
void init_generators_by_handle(std::vector< int > &gen_hdl, int verbose_level)
Definition: schreier.cpp:571

orbiter::layer3_group_actions::groups::schreier::extend_orbit
void extend_orbit(int *elt, int verbose_level)
Definition: schreier.cpp:901

orbiter::layer3_group_actions::groups::schreier::compute_all_point_orbits_with_preferred_labels
void compute_all_point_orbits_with_preferred_labels(long int *preferred_labels, int verbose_level)
Definition: schreier.cpp:1104

orbiter::layer3_group_actions::groups::schreier::print_orbit_lengths_tex
void print_orbit_lengths_tex(std::ostream &ost)
Definition: schreier_io.cpp:83

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Definition: groups.h:846

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Definition: schreier_io.cpp:1820

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Definition: groups.h:883

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Definition: schreier_io.cpp:982

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Definition: schreier_io.cpp:1831

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void export_tree_as_layered_graph(int orbit_no, std::string &fname_mask, int verbose_level)
Definition: schreier_io.cpp:1255

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Definition: groups.h:878

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Definition: schreier.cpp:1505

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int * orbit
Definition: groups.h:856

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Definition: groups.h:848

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Definition: schreier.cpp:360

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Definition: schreier.cpp:2751

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Definition: schreier_io.cpp:1986

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Definition: groups.h:879

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Definition: schreier.cpp:2707

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Definition: schreier_io.cpp:1407

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Definition: schreier.cpp:136

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Definition: groups.h:873

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void init_preferred_choice_function(void(*preferred_choice_function)(int pt, int &pt_pref, schreier *Sch, void *data, int data2, int verbose_level), void *preferred_choice_function_data, int preferred_choice_function_data2, int verbose_level)
Definition: schreier.cpp:115

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Definition: schreier.cpp:1983

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Definition: groups.h:857

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Definition: schreier.cpp:735

orbiter::layer3_group_actions::groups::schreier::stabilizer_orbit_rep
strong_generators * stabilizer_orbit_rep(actions::action *default_action, ring_theory::longinteger_object &full_group_order, int orbit_idx, int verbose_level)
Definition: schreier.cpp:2345

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Definition: schreier_io.cpp:1149

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Definition: schreier.cpp:373

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Definition: schreier.cpp:760

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Definition: schreier_io.cpp:708

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Definition: schreier_io.cpp:175

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Definition: schreier.cpp:19

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Definition: schreier.cpp:1256

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_with_original_labels_tex
void print_and_list_orbits_with_original_labels_tex(std::ostream &ost)
Definition: schreier_io.cpp:366

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbit_and_stabilizer_with_list_of_elements_tex
void print_and_list_orbit_and_stabilizer_with_list_of_elements_tex(int i, actions::action *default_action, strong_generators *gens, std::ostream &ost)
Definition: schreier_io.cpp:467

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data_structures_groups::set_and_stabilizer * get_orbit_rep(actions::action *default_action, ring_theory::longinteger_object &full_group_order, int orbit_idx, int verbose_level)
Definition: schreier.cpp:2296

orbiter::layer3_group_actions::groups::schreier::print_orbit_length_distribution
void print_orbit_length_distribution(std::ostream &ost)
Definition: schreier_io.cpp:163

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Definition: groups.h:847

orbiter::layer3_group_actions::groups::schreier::make_orbit_trees
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Definition: schreier_io.cpp:318

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int * schreier_gen1
Definition: groups.h:873

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Definition: schreier.cpp:57

orbiter::layer3_group_actions::groups::schreier::list_all_orbits_tex
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Definition: schreier_io.cpp:1109

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbit_and_stabilizer_tex
void print_and_list_orbit_and_stabilizer_tex(int i, actions::action *default_action, ring_theory::longinteger_object &full_group_order, std::ostream &ost)
Definition: schreier_io.cpp:393

orbiter::layer3_group_actions::groups::schreier::print_fancy
void print_fancy(std::ostream &ost, int f_tex, actions::action *default_action, strong_generators *gens_full_group)
Definition: schreier_io.cpp:645

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int subtree_depth_first(std::ostream &ost, int *path, int i, int last)
Definition: schreier_io.cpp:1799

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void print_and_list_orbits_sorted_by_length_tex(std::ostream &ost)
Definition: schreier_io.cpp:519

orbiter::layer3_group_actions::groups::schreier::print_fixed_points_tex
void print_fixed_points_tex(std::ostream &ost)
Definition: schreier_io.cpp:120

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double get_average_word_length()
Definition: schreier.cpp:3288

orbiter::layer3_group_actions::groups::schreier::compute_all_point_orbits_with_prefered_reps
void compute_all_point_orbits_with_prefered_reps(int *prefered_reps, int nb_prefered_reps, int verbose_level)
Definition: schreier.cpp:1070

orbiter::layer3_group_actions::groups::schreier::point_stabilizer
void point_stabilizer(actions::action *default_action, ring_theory::longinteger_object &go, groups::sims *&Stab, int orbit_no, int verbose_level)
Definition: schreier.cpp:2388

orbiter::layer3_group_actions::groups::schreier::compute_orbit_statistic
void compute_orbit_statistic(int *set, int set_size, int *orbit_count, int verbose_level)
Definition: schreier.cpp:2610

orbiter::layer3_group_actions::groups::schreier::print_orbit_lengths
void print_orbit_lengths(std::ostream &ost)
Definition: schreier_io.cpp:46

orbiter::layer3_group_actions::groups::schreier::subtree_place
void subtree_place(int *weight, int *placement_x, int left, int right, int i, int last)
Definition: schreier_io.cpp:1754

orbiter::layer3_group_actions::groups::schreier::images_append
void images_append(int verbose_level)
Definition: schreier.cpp:285

orbiter::layer3_group_actions::groups::schreier::get_orbit_reps
void get_orbit_reps(int *&Reps, int &nb_reps, int verbose_level)
Definition: schreier.cpp:2686

orbiter::layer3_group_actions::groups::schreier::label
int * label
Definition: groups.h:862

orbiter::layer3_group_actions::groups::schreier::move_point_here
void move_point_here(int here, int pt)
Definition: schreier.cpp:697

orbiter::layer3_group_actions::groups::schreier::nb_orbits
int nb_orbits
Definition: groups.h:870

orbiter::layer3_group_actions::groups::schreier::create_point_list_sorted
void create_point_list_sorted(int *&point_list, int &point_list_length)
Definition: schreier.cpp:2931

orbiter::layer3_group_actions::groups::schreier::initialize_tables
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Definition: schreier.cpp:345

orbiter::layer3_group_actions::groups::schreier::init_images_recycle
void init_images_recycle(int nb_images, int **old_images, int idx_deleted_generator, int verbose_level)
Definition: schreier.cpp:197

orbiter::layer3_group_actions::groups::schreier::print_orbit_using_callback
void print_orbit_using_callback(std::ostream &ost, int orbit_no, void(*print_point)(std::ostream &ost, int pt, void *data), void *data)
Definition: schreier_io.cpp:1086

orbiter::layer3_group_actions::groups::schreier::get_image
long int get_image(long int i, int gen_idx, int verbose_level)
Definition: schreier.cpp:615

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void intersection_vector(int *set, int len, int *intersection_cnt)
Definition: schreier.cpp:1915

orbiter::layer3_group_actions::groups::schreier::gens
data_structures_groups::vector_ge gens
Definition: groups.h:845

orbiter::layer3_group_actions::groups::schreier::subtree_draw_vertices
void subtree_draw_vertices(graphics::mp_graphics &G, graphics::layered_graph_draw_options *Opt, int parent_x, int parent_y, int *weight, int *placement_x, int max_depth, int i, int last, int f_has_point_labels, long int *point_labels, int y_max, int verbose_level)
Definition: schreier_io.cpp:1688

orbiter::layer3_group_actions::groups::schreier::Elt1
int * Elt1
Definition: groups.h:872

orbiter::layer3_group_actions::groups::schreier::print_orbit_through_labels
void print_orbit_through_labels(std::ostream &ost, int orbit_no, long int *point_labels)
Definition: schreier_io.cpp:1131

orbiter::layer3_group_actions::groups::schreier::print_orbit_sorted_with_original_labels_tex
void print_orbit_sorted_with_original_labels_tex(std::ostream &ost, int orbit_no, int f_truncate, int max_length)
Definition: schreier_io.cpp:1031

orbiter::layer3_group_actions::groups::schreier::init
void init(actions::action *A, int verbose_level)
Definition: schreier.cpp:308

orbiter::layer3_group_actions::groups::schreier::orbit_number
int orbit_number(int pt)
Definition: schreier.cpp:2793

orbiter::layer3_group_actions::groups::schreier::depth_in_tree
int depth_in_tree(int j)
Definition: schreier.cpp:724

orbiter::layer3_group_actions::groups::schreier::f_preferred_choice_function
int f_preferred_choice_function
Definition: groups.h:882

orbiter::layer3_group_actions::groups::schreier::print
void print(std::ostream &ost)
Definition: schreier_io.cpp:196

orbiter::layer3_group_actions::groups::schreier::print_orbit_using_labels
void print_orbit_using_labels(int orbit_no, long int *labels)
Definition: schreier_io.cpp:934

orbiter::layer3_group_actions::groups::schreier::get_orbit
void get_orbit(int orbit_idx, long int *set, int &len, int verbose_level)
Definition: schreier.cpp:2598

orbiter::layer3_group_actions::groups::schreier::f_images_only
int f_images_only
Definition: groups.h:843

orbiter::layer3_group_actions::groups::schreier::get_orbit_rep_to
void get_orbit_rep_to(actions::action *default_action, ring_theory::longinteger_object &full_group_order, int orbit_idx, data_structures_groups::set_and_stabilizer *Rep, int verbose_level)
Definition: schreier.cpp:2319

orbiter::layer3_group_actions::groups::schreier::preferred_choice_function_data
void * preferred_choice_function_data
Definition: groups.h:884

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_with_original_labels
void print_and_list_orbits_with_original_labels(std::ostream &ost)
Definition: schreier_io.cpp:267

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Definition: schreier.cpp:864

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_using_labels
void print_and_list_orbits_using_labels(std::ostream &ost, long int *labels)
Definition: schreier_io.cpp:729

orbiter::layer3_group_actions::groups::schreier::draw_tree2
void draw_tree2(std::string &fname, graphics::layered_graph_draw_options *Opt, int *weight, int *placement_x, int max_depth, int i, int last, int f_has_point_labels, long int *point_labels, int verbose_level)
Definition: schreier_io.cpp:1489

orbiter::layer3_group_actions::groups::schreier::cosetrep_tmp
int * cosetrep_tmp
Definition: groups.h:875

orbiter::layer3_group_actions::groups::schreier::subtree_draw_lines
void subtree_draw_lines(graphics::mp_graphics &G, graphics::layered_graph_draw_options *Opt, int parent_x, int parent_y, int *weight, int *placement_x, int max_depth, int i, int last, int y_max, int verbose_level)
Definition: schreier_io.cpp:1617

orbiter::layer3_group_actions::groups::schreier::stabilizer_any_point_plus_cosets
strong_generators * stabilizer_any_point_plus_cosets(actions::action *default_action, ring_theory::longinteger_object &full_group_order, int pt, data_structures_groups::vector_ge *&cosets, int verbose_level)
Definition: schreier.cpp:2148

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void read_file_binary(std::string &fname, int verbose_level)
Definition: schreier_io.cpp:2006

orbiter::layer3_group_actions::groups::schreier::print_generators_latex
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Definition: schreier_io.cpp:890

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void compute_all_orbits_on_invariant_subset(int len, long int *subset, int verbose_level)
Definition: schreier.cpp:1186

orbiter::layer3_group_actions::groups::schreier::get_orbit_in_order
void get_orbit_in_order(std::vector< int > &Orb, int orbit_idx, int verbose_level)
Definition: schreier.cpp:2134

orbiter::layer3_group_actions::groups::schreier::print_and_list_orbits_tex
void print_and_list_orbits_tex(std::ostream &ost)
Definition: schreier_io.cpp:286

orbiter::layer3_group_actions::groups::schreier::get_schreier_vector
data_structures_groups::schreier_vector * get_schreier_vector(int gen_hdl_first, int nb_gen, enum shallow_schreier_tree_strategy Shallow_schreier_tree_strategy, int verbose_level)
Definition: schreier.cpp:3146

orbiter::layer3_group_actions::groups::schreier::print_orbit_with_original_labels
void print_orbit_with_original_labels(std::ostream &ost, int orbit_no)
Definition: schreier_io.cpp:958

orbiter::layer3_group_actions::groups::schreier::print_tables_latex
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Definition: schreier_io.cpp:797

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void non_trivial_random_schreier_generator(actions::action *A_original, int *Elt, int verbose_level)
Definition: schreier.cpp:1517

orbiter::layer3_group_actions::groups::schreier::get_orbit_lengths_once_each
void get_orbit_lengths_once_each(int *&orbit_lengths, int &nb_orbit_lengths)
Definition: schreier.cpp:2773

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Definition: schreier.cpp:1896

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Definition: schreier.cpp:2112

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Definition: schreier_io.cpp:1003

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Definition: schreier.cpp:101

orbiter::layer3_group_actions::groups::schreier::print_generators_with_permutations
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Definition: schreier_io.cpp:910

orbiter::layer3_group_actions::groups::schreier::stabilizer_any_point
strong_generators * stabilizer_any_point(actions::action *default_action, ring_theory::longinteger_object &full_group_order, int pt, int verbose_level)
Definition: schreier.cpp:2233

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Definition: schreier.cpp:787

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int * Elt3
Definition: groups.h:872

orbiter::layer3_group_actions::groups::schreier::orbit_representative
int orbit_representative(int pt)
Definition: schreier.cpp:711

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Definition: schreier_io.cpp:1101

orbiter::layer3_group_actions::groups::schreier::latex
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Definition: schreier_io.cpp:19

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Definition: schreier_io.cpp:747

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Definition: schreier.cpp:3371

orbiter::layer3_group_actions::groups::schreier::init_generators_by_hdl
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Definition: schreier.cpp:529

orbiter::layer3_group_actions::groups::sims
a permutation group represented via a stabilizer chain
Definition: groups.h:1273

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Definition: sims.cpp:620

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Definition: sims_group_theory.cpp:714

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Definition: sims.cpp:1177

orbiter::layer3_group_actions::groups::sims::element_unrank
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Definition: sims.cpp:1213

orbiter::layer3_group_actions::groups::sims::freeself
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Definition: sims.cpp:97

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Definition: sims.cpp:2125

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Definition: sims_io.cpp:547

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Definition: sims_group_theory.cpp:772

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Definition: sims.cpp:1024

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Definition: sims.cpp:1628

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void init_cyclic_group_from_generator(actions::action *A, int *Elt, int verbose_level)
Definition: sims.cpp:378

orbiter::layer3_group_actions::groups::sims::order_structure_relative_to_subgroup
void order_structure_relative_to_subgroup(int *C_sub, int *Order, int *Residue, int verbose_level)
Definition: sims3.cpp:95

orbiter::layer3_group_actions::groups::sims::random_element
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Definition: sims_group_theory.cpp:23

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Definition: sims_group_theory.cpp:1823

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int get_orbit_inv(int i, int j)
Definition: sims.cpp:2151

orbiter::layer3_group_actions::groups::sims::create_Cayley_graph
void create_Cayley_graph(data_structures_groups::vector_ge *gens, int *&Adj, long int &n, int verbose_level)
Definition: sims_group_theory.cpp:1628

orbiter::layer3_group_actions::groups::sims::element_rank
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Definition: sims.cpp:1276

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Definition: sims.cpp:233

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Definition: sims_group_theory.cpp:1880

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Definition: sims.cpp:1108

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Definition: sims_group_theory.cpp:1137

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Definition: groups.h:1286

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Definition: sims.cpp:1069

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Definition: sims.cpp:53

orbiter::layer3_group_actions::groups::sims::conjugate_by_rank
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Definition: sims_group_theory.cpp:1894

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Definition: sims_group_theory.cpp:968

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void init(actions::action *A, int verbose_level)
Definition: sims.cpp:289

orbiter::layer3_group_actions::groups::sims::transitive_extension
void transitive_extension(schreier &O, data_structures_groups::vector_ge &SG, int *tl, int verbose_level)
Definition: sims_group_theory.cpp:114

orbiter::layer3_group_actions::groups::sims::extend_base_orbit
void extend_base_orbit(int new_gen_idx, int lvl, int verbose_level)
Definition: sims_main.cpp:97

orbiter::layer3_group_actions::groups::sims::dimino
void dimino(int *subgroup, int subgroup_sz, int *gens, int &nb_gens, int *cosets, int new_gen, int *group, int &group_sz, int verbose_level)
Definition: sims_group_theory.cpp:2059

orbiter::layer3_group_actions::groups::sims::transitive_extension_using_coset_representatives_extract_generators
void transitive_extension_using_coset_representatives_extract_generators(int *coset_reps, int nb_cosets, data_structures_groups::vector_ge &SG, int *tl, int verbose_level)
Definition: sims_group_theory.cpp:218

orbiter::layer3_group_actions::groups::sims::read_list_of_elements
void read_list_of_elements(actions::action *A, char *fname, int verbose_level)
Definition: sims_io.cpp:638

orbiter::layer3_group_actions::groups::sims::all_cosets
void all_cosets(int *subset, int size, long int *all_cosets, int verbose_level)
Definition: sims_group_theory.cpp:1195

orbiter::layer3_group_actions::groups::sims::extract_strong_generators_in_order
void extract_strong_generators_in_order(data_structures_groups::vector_ge &SG, int *tl, int verbose_level)
Definition: sims.cpp:1704

orbiter::layer3_group_actions::groups::sims::mult_by_rank
long int mult_by_rank(long int rk_a, long int rk_b, int verbose_level)
Definition: sims_group_theory.cpp:1857

orbiter::layer3_group_actions::groups::sims::path_rank_lint
long int path_rank_lint()
Definition: sims.cpp:1094

orbiter::layer3_group_actions::groups::sims::regular_representation
void regular_representation(int *Elt, int *perm, int verbose_level)
Definition: sims_group_theory.cpp:1081

orbiter::layer3_group_actions::groups::sims::group_order
void group_order(ring_theory::longinteger_object &go)
Definition: sims.cpp:951

orbiter::layer3_group_actions::groups::sims::is_normalizing
int is_normalizing(int *Elt, int verbose_level)
Definition: sims_group_theory.cpp:1572

orbiter::layer3_group_actions::groups::sims::compute_base_orbit
void compute_base_orbit(int lvl, int verbose_level)
Definition: sims_main.cpp:189

orbiter::layer3_group_actions::groups::sims::build_up_group_from_generators
void build_up_group_from_generators(sims *K, data_structures_groups::vector_ge *gens, int f_target_go, ring_theory::longinteger_object *target_go, int f_override_choose_next_base_point, int(*choose_next_base_point_method)(actions::action *A, int *Elt, int verbose_level), int verbose_level)
Definition: sims_main.cpp:1042

orbiter::layer3_group_actions::groups::sims::print_generators_as_permutations
void print_generators_as_permutations()
Definition: sims_io.cpp:272

orbiter::layer3_group_actions::groups::sims::compute_coset_rep_path
void compute_coset_rep_path(int i, int j, int &depth, int *&Path, int *&Label, int verbose_level)
Definition: sims.cpp:1544

orbiter::layer3_group_actions::groups::sims::path
int * path
Definition: groups.h:1305

orbiter::layer3_group_actions::groups::sims::init_trivial_group
void init_trivial_group(int verbose_level)
Definition: sims.cpp:584

orbiter::layer3_group_actions::groups::sims::my_base_len
int my_base_len
Definition: groups.h:1278

orbiter::layer3_group_actions::groups::sims::print_generator_depth_and_perm
void print_generator_depth_and_perm()
Definition: sims_io.cpp:335

orbiter::layer3_group_actions::groups::sims::path_unrank_lint
void path_unrank_lint(long int a)
Definition: sims.cpp:1082

orbiter::layer3_group_actions::groups::sims::create_group_table
void create_group_table(int *&Table, long int &n, int verbose_level)
Definition: sims_group_theory.cpp:1691

orbiter::layer3_group_actions::groups::sims::transversal_length
int transversal_length
Definition: groups.h:1302

orbiter::layer3_group_actions::groups::sims::add_generator_at_level_only
void add_generator_at_level_only(int *elt, int lvl, int verbose_level)
Definition: sims_main.cpp:580

orbiter::layer3_group_actions::groups::sims::print_transversals_short
void print_transversals_short()
Definition: sims_io.cpp:123

orbiter::layer3_group_actions::groups::sims::element_as_permutation
void element_as_permutation(actions::action *A_special, long int elt_rk, int *perm, int verbose_level)
Definition: sims.cpp:2060

orbiter::layer3_group_actions::groups::sims::print_all_group_elements_with_permutations_tex
void print_all_group_elements_with_permutations_tex(std::ostream &ost)
Definition: sims_io.cpp:497

orbiter::layer3_group_actions::groups::sims::report
void report(std::ostream &ost, std::string &prefix, graphics::layered_graph_draw_options *LG_Draw_options, int verbose_level)
Definition: sims_io.cpp:760

orbiter::layer3_group_actions::groups::sims::print_generators_at_level_or_below
void print_generators_at_level_or_below(int lvl)
Definition: sims_io.cpp:380

orbiter::layer3_group_actions::groups::sims::extend_group_random_process_no_kernel
void extend_group_random_process_no_kernel(sims *extending_by_G, ring_theory::longinteger_object &target_go, int verbose_level)
Definition: sims_main.cpp:642

orbiter::layer3_group_actions::groups::sims::print_group_order_factored
void print_group_order_factored(std::ostream &ost)
Definition: sims_io.cpp:364

orbiter::layer3_group_actions::groups::sims::compute_base_orbits_known_length
void compute_base_orbits_known_length(int *tl, int verbose_level)
Definition: sims_main.cpp:57

orbiter::layer3_group_actions::groups::sims::test_element_rank_unrank
void test_element_rank_unrank()
Definition: sims.cpp:1388

orbiter::layer3_group_actions::groups::sims::least_moved_point_at_level
int least_moved_point_at_level(int lvl, int verbose_level)
Definition: sims.cpp:2084

orbiter::layer3_group_actions::groups::sims::get_image
int get_image(int i, int gen_idx)
Definition: sims.cpp:1037

orbiter::layer3_group_actions::groups::sims::find_standard_generators_int
void find_standard_generators_int(int ord_a, int ord_b, int ord_ab, int &a, int &b, int &nb_trials, int verbose_level)
Definition: sims_group_theory.cpp:1259

orbiter::layer3_group_actions::groups::sims::build_up_subgroup_random_process
void build_up_subgroup_random_process(sims *G, void(*choose_random_generator_for_subgroup)(sims *G, int *Elt, int verbose_level), int verbose_level)
Definition: sims2.cpp:53

orbiter::layer3_group_actions::groups::sims::print_basic_orbit
void print_basic_orbit(int i)
Definition: sims_io.cpp:315

orbiter::layer3_group_actions::groups::sims::nb_images
int nb_images
Definition: groups.h:1307

orbiter::layer3_group_actions::groups::sims::print_transversals
void print_transversals()
Definition: sims_io.cpp:101

orbiter::layer3_group_actions::groups::sims::zuppo_list
void zuppo_list(int *Zuppos, int &nb_zuppos, int verbose_level)
Definition: sims_group_theory.cpp:1990

orbiter::layer3_group_actions::groups::sims::images_append
void images_append()
Definition: sims.cpp:260

orbiter::layer3_group_actions::groups::sims::initialize_table
void initialize_table(int i, int verbose_level)
Definition: sims.cpp:563

orbiter::layer3_group_actions::groups::sims::print_all_group_elements_to_file
void print_all_group_elements_to_file(char *fname, int verbose_level)
Definition: sims_io.cpp:424

orbiter::layer3_group_actions::groups::sims::print_generators_as_permutations_override_action
void print_generators_as_permutations_override_action(actions::action *A)
Definition: sims_io.cpp:286

orbiter::layer3_group_actions::groups::sims::closure_group
int closure_group(int nb_times, int verbose_level)
Definition: sims_main.cpp:1353

orbiter::layer3_group_actions::groups::sims::conjugate_by_rank_b_bv_given
long int conjugate_by_rank_b_bv_given(long int rk_a, int *Elt_b, int *Elt_bv, int verbose_level)
Definition: sims_group_theory.cpp:1913

orbiter::layer3_group_actions::groups::sims::element_ranks_subgroup
void element_ranks_subgroup(sims *subgroup, int *element_ranks, int verbose_level)
Definition: sims_group_theory.cpp:1113

orbiter::layer3_group_actions::groups::sims::A
actions::action * A
Definition: groups.h:1276

orbiter::layer3_group_actions::groups::sims::print_all_group_elements_tex
void print_all_group_elements_tex(std::ostream &ost)
Definition: sims_io.cpp:474

orbiter::layer3_group_actions::groups::sims::images
int ** images
Definition: groups.h:1308

orbiter::layer3_group_actions::groups::sims::init_generators_by_hdl
void init_generators_by_hdl(int nb_gen, int *gen_hdl, int verbose_level)
Definition: sims.cpp:723

orbiter::layer3_group_actions::groups::sims::transitive_extension_using_generators
void transitive_extension_using_generators(int *Elt_gens, int nb_gens, int subgroup_index, data_structures_groups::vector_ge &SG, int *tl, int verbose_level)
Definition: sims_group_theory.cpp:333

orbiter::layer3_group_actions::groups::sims::evaluate_word_int
void evaluate_word_int(int word_len, int *word, int *Elt, int verbose_level)
Definition: sims_group_theory.cpp:1472

orbiter::layer3_group_actions::groups::sims::group_order_verbose
void group_order_verbose(ring_theory::longinteger_object &go, int verbose_level)
Definition: sims.cpp:964

orbiter::layer3_group_actions::groups::sims::print
void print(int verbose_level)
Definition: sims_io.cpp:174

orbiter::layer3_group_actions::groups::sims::all_elements
void all_elements(data_structures_groups::vector_ge *&vec, int verbose_level)
Definition: sims.cpp:2205

orbiter::layer3_group_actions::groups::sims::print_generators_tex
void print_generators_tex(std::ostream &ost)
Definition: sims_io.cpp:231

orbiter::layer3_group_actions::groups::sims::print_generators
void print_generators()
Definition: sims_io.cpp:206

orbiter::layer3_group_actions::groups::sims::write_all_group_elements
void write_all_group_elements(char *fname, int verbose_level)
Definition: sims_io.cpp:395

orbiter::layer3_group_actions::groups::sims::add_generator_at_level
void add_generator_at_level(int *elt, int lvl, int verbose_level)
Definition: sims_main.cpp:543

orbiter::layer3_group_actions::groups::sims::subgroup_order_verbose
void subgroup_order_verbose(ring_theory::longinteger_object &go, int level, int verbose_level)
Definition: sims.cpp:984

orbiter::layer3_group_actions::groups::sims::write_as_magma_permutation_group
void write_as_magma_permutation_group(std::string &fname_base, data_structures_groups::vector_ge *gens, int verbose_level)
Definition: sims_io.cpp:677

orbiter::layer3_group_actions::groups::sims::compute_coset_rep_depth
int compute_coset_rep_depth(int i, int j, int verbose_level)
Definition: sims.cpp:1508

orbiter::layer3_group_actions::groups::sims::is_trivial_group
int is_trivial_group()
Definition: sims.cpp:1012

orbiter::layer3_group_actions::groups::sims::print_basic_orbits
void print_basic_orbits()
Definition: sims_io.cpp:301

orbiter::layer3_group_actions::groups::sims::create_group_tree
void create_group_tree(const char *fname, int f_full, int verbose_level)
Definition: sims_io.cpp:23

orbiter::layer3_group_actions::groups::sims::print_all_group_elements
void print_all_group_elements()
Definition: sims_io.cpp:453

orbiter::layer3_group_actions::groups::sims::is_element_of
int is_element_of(int *elt)
Definition: sims.cpp:1362

orbiter::layer3_group_actions::groups::sims::normalizer_based_on_characteristic_vector
void normalizer_based_on_characteristic_vector(int *C_sub, int *Gen_idx, int nb_gens, int *N, long int &N_go, int verbose_level)
Definition: sims3.cpp:48

orbiter::layer3_group_actions::groups::sims::subgroup_make_characteristic_vector
void subgroup_make_characteristic_vector(sims *Sub, int *C, int verbose_level)
Definition: sims3.cpp:18

orbiter::layer3_group_actions::groups::sims::~sims
~sims()
Definition: sims.cpp:92

orbiter::layer3_group_actions::groups::sims::gens
data_structures_groups::vector_ge gens
Definition: groups.h:1280

orbiter::layer3_group_actions::groups::sims::print_all_transversal_elements
void print_all_transversal_elements()
Definition: sims_io.cpp:569

orbiter::layer3_group_actions::groups::sims::delete_images
void delete_images()
Definition: sims.cpp:219

orbiter::layer3_group_actions::groups::sims::transitive_extension_tolerant
int transitive_extension_tolerant(schreier &O, data_structures_groups::vector_ge &SG, int *tl, int f_tolerant, int verbose_level)
Definition: sims_group_theory.cpp:121

orbiter::layer3_group_actions::groups::sims::element_unrank_lint
void element_unrank_lint(long int rk, int *Elt, int verbose_level)
Definition: sims.cpp:1326

orbiter::layer3_group_actions::groups::sims::add_generator
void add_generator(int *elt, int verbose_level)
Definition: sims.cpp:803

orbiter::layer3_group_actions::groups::sims::random_schreier_generator
void random_schreier_generator(int *Elt, int verbose_level)
Definition: sims.cpp:1803

orbiter::layer3_group_actions::groups::sims::random_element_of_order
void random_element_of_order(int *elt, int order, int verbose_level)
Definition: sims_group_theory.cpp:55

orbiter::layer3_group_actions::groups::sims::element_rank_lint
long int element_rank_lint(int *Elt)
Definition: sims.cpp:1354

orbiter::layer3_group_actions::groups::sims::build_up_group_random_process_no_kernel
void build_up_group_random_process_no_kernel(sims *old_G, int verbose_level)
Definition: sims_main.cpp:606

orbiter::layer3_group_actions::groups::sims::coset_rep
void coset_rep(int *Elt, int i, int j, int verbose_level)
Definition: sims.cpp:1414

orbiter::layer3_group_actions::groups::sims::all_elements_save_csv
void all_elements_save_csv(std::string &fname, int verbose_level)
Definition: sims.cpp:2236

orbiter::layer3_group_actions::groups::sims::gens_inv
data_structures_groups::vector_ge gens_inv
Definition: groups.h:1281

orbiter::layer3_group_actions::groups::sims::print_orbit_len
void print_orbit_len()
Definition: sims_io.cpp:162

orbiter::layer3_group_actions::groups::sims::reallocate_base
void reallocate_base(int old_base_len, int verbose_level)
Definition: sims.cpp:445

orbiter::layer3_group_actions::groups::sims::strip
int strip(int *elt, int *residue, int &drop_out_level, int &image, int verbose_level)
Definition: sims_main.cpp:433

orbiter::layer3_group_actions::groups::sims::Cayley_graph
void Cayley_graph(int *&Adj, int &sz, data_structures_groups::vector_ge *gens_S, int verbose_level)
Definition: sims_group_theory.cpp:2124

orbiter::layer3_group_actions::groups::sims::find_element_of_given_order_int
long int find_element_of_given_order_int(int ord, int &nb_trials, int verbose_level)
Definition: sims_group_theory.cpp:1304

orbiter::layer3_group_actions::groups::sims::init_generators
void init_generators(data_structures_groups::vector_ge &generators, int verbose_level)
Definition: sims.cpp:660

orbiter::layer3_group_actions::groups::sims::save_list_of_elements
void save_list_of_elements(char *fname, int verbose_level)
Definition: sims_io.cpp:602

orbiter::layer3_group_actions::groups::sims::print_transversal_lengths
void print_transversal_lengths()
Definition: sims_io.cpp:147

orbiter::layer3_group_actions::groups::sims::sims
sims()
Definition: sims.cpp:17

orbiter::layer3_group_actions::groups::sims::compute_base_orbits
void compute_base_orbits(int verbose_level)
Definition: sims_main.cpp:25

orbiter::layer3_group_actions::groups::sims::compute_conjugacy_classes
void compute_conjugacy_classes(actions::action *&Aconj, induced_actions::action_by_conjugation *&ABC, schreier *&Sch, strong_generators *&SG, int &nb_classes, int *&class_size, int *&class_rep, int verbose_level)
Definition: sims_group_theory.cpp:1745

orbiter::layer3_group_actions::groups::sims::group_order_lint
long int group_order_lint()
Definition: sims.cpp:1004

orbiter::layer3_group_actions::groups::sims::print_group_order
void print_group_order(std::ostream &ost)
Definition: sims_io.cpp:357

orbiter::layer3_group_actions::groups::sims::generator_depth
int generator_depth(int gen_idx)
Definition: sims.cpp:919

orbiter::layer3_group_actions::groups::sims::get_orbit_length
int get_orbit_length(int i)
Definition: sims.cpp:2177

orbiter::layer3_group_actions::groups::sims::point_stabilizer_with_action
void point_stabilizer_with_action(actions::action *A2, data_structures_groups::vector_ge &SG, int *tl, int pt, int verbose_level)
Definition: sims_group_theory.cpp:733

orbiter::layer3_group_actions::groups::sims::sylow_subgroup
void sylow_subgroup(int p, sims *P, int verbose_level)
Definition: sims_group_theory.cpp:1494

orbiter::layer3_group_actions::groups::sims::init_without_base
void init_without_base(actions::action *A, int verbose_level)
Definition: sims.cpp:400

orbiter::layer3_group_actions::groups::sims::table_of_group_elements_in_data_form
void table_of_group_elements_in_data_form(int *&Table, int &len, int &sz, int verbose_level)
Definition: sims_group_theory.cpp:1055

orbiter::layer3_group_actions::groups::sims::find_element_with_exactly_n_fixpoints_in_given_action
int find_element_with_exactly_n_fixpoints_in_given_action(int *Elt, int nb_fixpoints, actions::action *A_given, int verbose_level)
Definition: sims_group_theory.cpp:1014

orbiter::layer3_group_actions::groups::sims::gen_perm
int * gen_perm
Definition: groups.h:1284

orbiter::layer3_group_actions::groups::sims::point_stabilizer_stabchain_with_action
void point_stabilizer_stabchain_with_action(actions::action *A2, sims &S, int pt, int verbose_level)
Definition: sims_group_theory.cpp:419

orbiter::layer3_group_actions::groups::sims::compute_base_orbit_known_length
void compute_base_orbit_known_length(int lvl, int target_length, int verbose_level)
Definition: sims_main.cpp:267

orbiter::layer3_group_actions::groups::sims::gen_depth
int * gen_depth
Definition: groups.h:1283

orbiter::layer3_group_actions::groups::sims::test_if_in_set_stabilizer
int test_if_in_set_stabilizer(actions::action *A, long int *set, int size, int verbose_level)
Definition: sims_group_theory.cpp:925

orbiter::layer3_group_actions::groups::sims::random_elements_of_order
void random_elements_of_order(data_structures_groups::vector_ge *elts, int *orders, int nb, int verbose_level)
Definition: sims_group_theory.cpp:92

orbiter::layer3_group_actions::groups::sims::transitive_extension_using_coset_representatives
void transitive_extension_using_coset_representatives(int *coset_reps, int nb_cosets, int verbose_level)
Definition: sims_group_theory.cpp:241

orbiter::layer3_group_actions::groups::sims::build_up_group_random_process
void build_up_group_random_process(sims *K, sims *old_G, ring_theory::longinteger_object &target_go, int f_override_choose_next_base_point, int(*choose_next_base_point_method)(actions::action *A, int *Elt, int verbose_level), int verbose_level)
Definition: sims_main.cpp:675

orbiter::layer3_group_actions::groups::sims::find_element_of_prime_power_order
void find_element_of_prime_power_order(int p, int *Elt, int &e, int &nb_trials, int verbose_level)
Definition: sims_group_theory.cpp:1436

orbiter::layer3_group_actions::groups::sims::print_all_group_elements_as_permutations
void print_all_group_elements_as_permutations()
Definition: sims_io.cpp:526

orbiter::layer3_group_actions::groups::sims::strip_and_add
int strip_and_add(int *elt, int *residue, int verbose_level)
Definition: sims_main.cpp:379

orbiter::layer3_group_actions::groups::sims::init_generator_depth_and_perm
void init_generator_depth_and_perm(int verbose_level)
Definition: sims.cpp:747

orbiter::layer3_group_actions::groups::strong_generators
a strong generating set for a permutation group with respect to a fixed action
Definition: groups.h:1703

orbiter::layer3_group_actions::groups::strong_generators::init_trivial_group
void init_trivial_group(actions::action *A, int verbose_level)
Definition: strong_generators_groups.cpp:367

orbiter::layer3_group_actions::groups::strong_generators::init_copy
void init_copy(strong_generators *S, int verbose_level)
Definition: strong_generators.cpp:166

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_monomial_group
void generators_for_the_monomial_group(actions::action *A, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:392

orbiter::layer3_group_actions::groups::strong_generators::Janko1
void Janko1(actions::action *A, field_theory::finite_field *F, int verbose_level)
Definition: strong_generators_groups.cpp:3250

orbiter::layer3_group_actions::groups::strong_generators::compute_and_print_orbits_on_a_given_set
void compute_and_print_orbits_on_a_given_set(actions::action *A_given, long int *set, int len, int verbose_level)
Definition: strong_generators.cpp:3048

orbiter::layer3_group_actions::groups::strong_generators::init_linear_group_from_scratch
void init_linear_group_from_scratch(actions::action *&A, field_theory::finite_field *F, int n, linear_group_description *Descr, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:22

orbiter::layer3_group_actions::groups::strong_generators::init_centralizer_of_matrix_general_linear
void init_centralizer_of_matrix_general_linear(actions::action *A_projective, actions::action *A_general_linear, int *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1235

orbiter::layer3_group_actions::groups::strong_generators::print_generators_even_odd
void print_generators_even_odd()
Definition: strong_generators.cpp:1515

orbiter::layer3_group_actions::groups::strong_generators::print_generators_gap
void print_generators_gap(std::ostream &ost)
Definition: strong_generators.cpp:1290

orbiter::layer3_group_actions::groups::strong_generators::compute_schreier_with_given_action_on_a_given_set
void compute_schreier_with_given_action_on_a_given_set(actions::action *A_given, schreier *&Sch, long int *set, int len, int verbose_level)
Definition: strong_generators.cpp:2150

orbiter::layer3_group_actions::groups::strong_generators::orbits_on_points_with_given_action
void orbits_on_points_with_given_action(actions::action *A_given, int &nb_orbits, int *&orbit_reps, int verbose_level)
Definition: strong_generators.cpp:2210

orbiter::layer3_group_actions::groups::strong_generators::create_group_table
void create_group_table(int *&Table, long int &go, int verbose_level)
Definition: strong_generators.cpp:2076

orbiter::layer3_group_actions::groups::strong_generators::init_from_data
void init_from_data(actions::action *A, int *data, int nb_elements, int elt_size, int *transversal_length, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators.cpp:320

orbiter::layer3_group_actions::groups::strong_generators::init
void init(actions::action *A)
Definition: strong_generators.cpp:67

orbiter::layer3_group_actions::groups::strong_generators::generators_for_parabolic_subgroup
void generators_for_parabolic_subgroup(actions::action *A_PGL_n_q, matrix_group *Mtx, int k, int verbose_level)
Definition: strong_generators_groups.cpp:2278

orbiter::layer3_group_actions::groups::strong_generators::init_by_hdl_and_with_tl
void init_by_hdl_and_with_tl(actions::action *A, std::vector< int > &gen_handle, std::vector< int > &tl, int verbose_level)
Definition: strong_generators.cpp:193

orbiter::layer3_group_actions::groups::strong_generators::orbits_on_points
void orbits_on_points(int &nb_orbits, int *&orbit_reps, int verbose_level)
Definition: strong_generators.cpp:2178

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_F13_surface
void stabilizer_of_F13_surface(actions::action *A, field_theory::finite_field *F, int a, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:2934

orbiter::layer3_group_actions::groups::strong_generators::diagonally_repeat
void diagonally_repeat(actions::action *An, strong_generators *Sn, int verbose_level)
Definition: strong_generators_groups.cpp:3824

orbiter::layer3_group_actions::groups::strong_generators::export_group_and_copy_to_latex
void export_group_and_copy_to_latex(std::string &label_txt, std::ostream &ost, actions::action *A2, int verbose_level)
Definition: strong_generators.cpp:3454

orbiter::layer3_group_actions::groups::strong_generators::get_gens_data
void get_gens_data(int *&data, int &sz, int verbose_level)
Definition: strong_generators.cpp:3527

orbiter::layer3_group_actions::groups::strong_generators::test_if_set_is_invariant_under_given_action
void test_if_set_is_invariant_under_given_action(actions::action *A_given, long int *set, int set_sz, int verbose_level)
Definition: strong_generators.cpp:3193

orbiter::layer3_group_actions::groups::strong_generators::print_generators_as_permutations_tex
void print_generators_as_permutations_tex(std::ostream &ost, actions::action *A2)
Definition: strong_generators.cpp:1836

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_cubic_surface_from_catalogue
void stabilizer_of_cubic_surface_from_catalogue(actions::action *A, field_theory::finite_field *F, int iso, int verbose_level)
Definition: strong_generators_groups.cpp:2643

orbiter::layer3_group_actions::groups::strong_generators::print_generators_MAGMA
void print_generators_MAGMA(actions::action *A, std::ostream &ost)
Definition: strong_generators.cpp:1534

orbiter::layer3_group_actions::groups::strong_generators::exterior_square
void exterior_square(actions::action *A_detached, strong_generators *SG_original, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:3683

orbiter::layer3_group_actions::groups::strong_generators::strong_generators
strong_generators()
Definition: strong_generators.cpp:19

orbiter::layer3_group_actions::groups::strong_generators::print_elements_with_special_orthogonal_action_ost
void print_elements_with_special_orthogonal_action_ost(std::ostream &ost)
Definition: strong_generators.cpp:1914

orbiter::layer3_group_actions::groups::strong_generators::normalizer_of_a_Hall_reflection
void normalizer_of_a_Hall_reflection(int nb_pairs, int &degree, int verbose_level)
Definition: strong_generators_groups.cpp:3455

orbiter::layer3_group_actions::groups::strong_generators::point_stabilizer
strong_generators * point_stabilizer(int pt, int verbose_level)
Definition: strong_generators.cpp:3216

orbiter::layer3_group_actions::groups::strong_generators::add_single_generator
void add_single_generator(int *Elt, int group_index, int verbose_level)
Definition: strong_generators.cpp:1226

orbiter::layer3_group_actions::groups::strong_generators::init_single_with_target_go
void init_single_with_target_go(actions::action *A, int *Elt, int target_go, int verbose_level)
Definition: strong_generators_groups.cpp:347

orbiter::layer3_group_actions::groups::strong_generators::print_elements_ost
void print_elements_ost(std::ostream &ost)
Definition: strong_generators.cpp:1890

orbiter::layer3_group_actions::groups::strong_generators::print_group_order
void print_group_order(std::ostream &ost)
Definition: strong_generators.cpp:1282

orbiter::layer3_group_actions::groups::strong_generators::print_generators_in_source_code
void print_generators_in_source_code()
Definition: strong_generators.cpp:1474

orbiter::layer3_group_actions::groups::strong_generators::init_point_stabilizer_of_arbitrary_point_through_schreier
void init_point_stabilizer_of_arbitrary_point_through_schreier(schreier *Sch, int pt, int &orbit_idx, ring_theory::longinteger_object &full_group_order, int verbose_level)
Definition: strong_generators.cpp:507

orbiter::layer3_group_actions::groups::strong_generators::create_copy
strong_generators * create_copy()
Definition: strong_generators.cpp:157

orbiter::layer3_group_actions::groups::strong_generators::print_elements_latex_ost_with_print_point_function
void print_elements_latex_ost_with_print_point_function(actions::action *A, std::ostream &ost, void(*point_label)(std::stringstream &sstr, long int pt, void *data), void *point_label_data)
Definition: strong_generators.cpp:2013

orbiter::layer3_group_actions::groups::strong_generators::init_single
void init_single(actions::action *A, int *Elt, int verbose_level)
Definition: strong_generators_groups.cpp:327

orbiter::layer3_group_actions::groups::strong_generators::export_group_to_magma_and_copy_to_latex
void export_group_to_magma_and_copy_to_latex(std::string &label_txt, std::ostream &ost, actions::action *A2, int verbose_level)
Definition: strong_generators.cpp:3348

orbiter::layer3_group_actions::groups::strong_generators::create_sims
sims * create_sims(int verbose_level)
Definition: strong_generators.cpp:1112

orbiter::layer3_group_actions::groups::strong_generators::init_point_stabilizer_orbit_rep_schreier
void init_point_stabilizer_orbit_rep_schreier(schreier *Sch, int orbit_idx, ring_theory::longinteger_object &full_group_order, int verbose_level)
Definition: strong_generators.cpp:539

orbiter::layer3_group_actions::groups::strong_generators::init_from_permutation_representation
void init_from_permutation_representation(actions::action *A, sims *parent_group_S, int *data, int nb_elements, long int group_order, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators.cpp:250

orbiter::layer3_group_actions::groups::strong_generators::init_by_hdl
void init_by_hdl(actions::action *A, int *gen_hdl, int nb_gen, int verbose_level)
Definition: strong_generators.cpp:225

orbiter::layer3_group_actions::groups::strong_generators::orbit_of_one_point_schreier
schreier * orbit_of_one_point_schreier(actions::action *A_given, int pt, int verbose_level)
Definition: strong_generators.cpp:2295

orbiter::layer3_group_actions::groups::strong_generators::Hall_reflection
void Hall_reflection(int nb_pairs, int &degree, int verbose_level)
Definition: strong_generators_groups.cpp:3358

orbiter::layer3_group_actions::groups::strong_generators::print_elements_with_given_action
void print_elements_with_given_action(std::ostream &ost, actions::action *A2)
Definition: strong_generators.cpp:1949

orbiter::layer3_group_actions::groups::strong_generators::decode_ascii_coding
void decode_ascii_coding(char *ascii_coding, int verbose_level)
Definition: strong_generators.cpp:2897

orbiter::layer3_group_actions::groups::strong_generators::generators_for_stabilizer_of_three_collinear_points_in_PGL4
void generators_for_stabilizer_of_three_collinear_points_in_PGL4(actions::action *A_PGL_4_q, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:2378

orbiter::layer3_group_actions::groups::strong_generators::init_from_ascii_coding
void init_from_ascii_coding(actions::action *A, char *ascii_coding, int verbose_level)
Definition: strong_generators.cpp:116

orbiter::layer3_group_actions::groups::strong_generators::report_fixed_objects_in_P3
void report_fixed_objects_in_P3(std::ostream &ost, geometry::projective_space *P3, int verbose_level)
Definition: strong_generators.cpp:3475

orbiter::layer3_group_actions::groups::strong_generators::freeself
void freeself()
Definition: strong_generators.cpp:36

orbiter::layer3_group_actions::groups::strong_generators::print_generators_tex
void print_generators_tex()
Definition: strong_generators.cpp:1687

orbiter::layer3_group_actions::groups::strong_generators::switch_to_subgroup
void switch_to_subgroup(const char *rank_vector_text, const char *subgroup_order_text, sims *S, int *&subgroup_gens_idx, int &nb_subgroup_gens, int verbose_level)
Definition: strong_generators.cpp:887

orbiter::layer3_group_actions::groups::strong_generators::print_generators_in_source_code_to_file
void print_generators_in_source_code_to_file(const char *fname)
Definition: strong_generators.cpp:1493

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_orthogonal_group
void generators_for_the_orthogonal_group(actions::action *A, field_theory::finite_field *F, int n, int epsilon, int f_semilinear, int verbose_level)
Definition: strong_generators_groups.cpp:2576

orbiter::layer3_group_actions::groups::strong_generators::init_generators_for_the_conjugate_group_aGav
void init_generators_for_the_conjugate_group_aGav(strong_generators *SG, int *Elt_a, int verbose_level)
Definition: strong_generators.cpp:614

orbiter::layer3_group_actions::groups::strong_generators::print_elements_latex_ost
void print_elements_latex_ost(std::ostream &ost)
Definition: strong_generators.cpp:1982

orbiter::layer3_group_actions::groups::strong_generators::list_of_elements_of_subgroup
void list_of_elements_of_subgroup(strong_generators *gens_subgroup, long int *&Subgroup_elements_by_index, long int &sz_subgroup, int verbose_level)
Definition: strong_generators.cpp:2093

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_quartic_curve_from_catalogue
void stabilizer_of_quartic_curve_from_catalogue(actions::action *A, field_theory::finite_field *F, int iso, int verbose_level)
Definition: strong_generators_groups.cpp:2715

orbiter::layer3_group_actions::groups::strong_generators::print_generators_tex_with_print_point_function
void print_generators_tex_with_print_point_function(actions::action *A, std::ostream &ost, void(*point_label)(std::stringstream &sstr, long int pt, void *data), void *point_label_data)
Definition: strong_generators.cpp:1758

orbiter::layer3_group_actions::groups::strong_generators::find_cyclic_subgroup_with_exactly_n_fixpoints
strong_generators * find_cyclic_subgroup_with_exactly_n_fixpoints(int nb_fixpoints, actions::action *A_given, int verbose_level)
Definition: strong_generators.cpp:3261

orbiter::layer3_group_actions::groups::strong_generators::group_order_as_lint
long int group_order_as_lint()
Definition: strong_generators.cpp:1273

orbiter::layer3_group_actions::groups::strong_generators::compute_and_print_orbits
void compute_and_print_orbits(actions::action *A_given, int verbose_level)
Definition: strong_generators.cpp:3096

orbiter::layer3_group_actions::groups::strong_generators::print_generators
void print_generators(std::ostream &ost)
Definition: strong_generators.cpp:1375

orbiter::layer3_group_actions::groups::strong_generators::swap_with
void swap_with(strong_generators *SG)
Definition: strong_generators.cpp:47

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_G13_surface
void stabilizer_of_G13_surface(actions::action *A, field_theory::finite_field *F, int a, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:2866

orbiter::layer3_group_actions::groups::strong_generators::orbits_on_points_schreier
schreier * orbits_on_points_schreier(actions::action *A_given, int verbose_level)
Definition: strong_generators.cpp:2242

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_stabilizer_of_two_components
void generators_for_the_stabilizer_of_two_components(actions::action *A_PGL_n_q, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1679

orbiter::layer3_group_actions::groups::strong_generators::reverse_isomorphism_exterior_square
void reverse_isomorphism_exterior_square(int verbose_level)
Definition: strong_generators.cpp:3502

orbiter::layer3_group_actions::groups::strong_generators::canonical_image_GAP
void canonical_image_GAP(std::string &input_set_text, std::ostream &ost)
Definition: strong_generators.cpp:1648

orbiter::layer3_group_actions::groups::strong_generators::read_from_file_binary
void read_from_file_binary(actions::action *A, std::ifstream &fp, int verbose_level)
Definition: strong_generators.cpp:2608

orbiter::layer3_group_actions::groups::strong_generators::compute_ascii_coding
void compute_ascii_coding(char *&ascii_coding, int verbose_level)
Definition: strong_generators.cpp:2853

orbiter::layer3_group_actions::groups::strong_generators::read_file
void read_file(actions::action *A, std::string &fname, int verbose_level)
Definition: strong_generators.cpp:2672

orbiter::layer3_group_actions::groups::strong_generators::init_from_data_with_target_go
void init_from_data_with_target_go(actions::action *A, int *data_gens, int data_gens_size, int nb_gens, ring_theory::longinteger_object &target_go, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators.cpp:377

orbiter::layer3_group_actions::groups::strong_generators::export_magma
void export_magma(actions::action *A, std::ostream &ost, int verbose_level)
Definition: strong_generators.cpp:1553

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_null_polarity_group
void generators_for_the_null_polarity_group(actions::action *A, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1099

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_identity_subgroup
void generators_for_the_identity_subgroup(actions::action *A_linear, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:2193

orbiter::layer3_group_actions::groups::strong_generators::write_to_file_binary
void write_to_file_binary(std::ofstream &fp, int verbose_level)
Definition: strong_generators.cpp:2559

orbiter::layer3_group_actions::groups::strong_generators::export_permutation_group_to_GAP
void export_permutation_group_to_GAP(std::string &fname, actions::action *A2, int verbose_level)
Definition: strong_generators.cpp:3005

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_singer_cycle
void generators_for_the_singer_cycle(actions::action *A, matrix_group *Mtx, int power_of_singer, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:736

orbiter::layer3_group_actions::groups::strong_generators::print_generators_as_permutations
void print_generators_as_permutations()
Definition: strong_generators.cpp:1812

orbiter::layer3_group_actions::groups::strong_generators::special_subgroup
void special_subgroup(int verbose_level)
Definition: strong_generators_groups.cpp:195

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_spread_from_catalogue
void stabilizer_of_spread_from_catalogue(actions::action *A, int q, int k, int iso, int verbose_level)
Definition: strong_generators_groups.cpp:3080

orbiter::layer3_group_actions::groups::strong_generators::print_generators_compact
void print_generators_compact(std::ostream &ost)
Definition: strong_generators.cpp:1353

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_diagonal_group
void generators_for_the_diagonal_group(actions::action *A, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:595

orbiter::layer3_group_actions::groups::strong_generators::hyperplane_lifting_with_two_lines_fixed
void hyperplane_lifting_with_two_lines_fixed(strong_generators *SG_hyperplane, geometry::projective_space *P, int line1, int line2, int verbose_level)
Definition: strong_generators_groups.cpp:3559

orbiter::layer3_group_actions::groups::strong_generators::tl
int * tl
Definition: groups.h:1707

orbiter::layer3_group_actions::groups::strong_generators::init_centralizer_of_matrix
void init_centralizer_of_matrix(actions::action *A, int *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1216

orbiter::layer3_group_actions::groups::strong_generators::print_with_given_action
void print_with_given_action(std::ostream &ost, actions::action *A2)
Definition: strong_generators.cpp:1861

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_pencil_of_conics
void stabilizer_of_pencil_of_conics(actions::action *A, field_theory::finite_field *F, int verbose_level)
Definition: strong_generators_groups.cpp:3161

orbiter::layer3_group_actions::groups::strong_generators::print_for_make_element
void print_for_make_element(std::ostream &ost)
Definition: strong_generators.cpp:1716

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_borel_subgroup_lower
void generators_for_the_borel_subgroup_lower(actions::action *A_linear, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:2068

orbiter::layer3_group_actions::groups::strong_generators::even_subgroup
void even_subgroup(int verbose_level)
Definition: strong_generators_groups.cpp:276

orbiter::layer3_group_actions::groups::strong_generators::print_generators_in_different_action_tex
void print_generators_in_different_action_tex(std::ostream &ost, actions::action *A2)
Definition: strong_generators.cpp:1728

orbiter::layer3_group_actions::groups::strong_generators::init_from_sims
void init_from_sims(groups::sims *S, int verbose_level)
Definition: strong_generators.cpp:85

orbiter::layer3_group_actions::groups::strong_generators::orbits_light
void orbits_light(actions::action *A_given, int *&Orbit_reps, int *&Orbit_lengths, int &nb_orbits, int **&Pts_per_generator, int *&Nb_per_generator, int verbose_level)
Definition: strong_generators.cpp:2321

orbiter::layer3_group_actions::groups::strong_generators::init_generators_for_the_conjugate_group_avGa
void init_generators_for_the_conjugate_group_avGa(strong_generators *SG, int *Elt_a, int verbose_level)
Definition: strong_generators.cpp:559

orbiter::layer3_group_actions::groups::strong_generators::export_to_orbiter_as_bsgs
void export_to_orbiter_as_bsgs(actions::action *A2, std::string &fname, std::string &label, std::string &label_tex, int verbose_level)
Definition: strong_generators.cpp:3566

orbiter::layer3_group_actions::groups::strong_generators::export_group_to_GAP_and_copy_to_latex
void export_group_to_GAP_and_copy_to_latex(std::string &label_txt, std::ostream &ost, actions::action *A2, int verbose_level)
Definition: strong_generators.cpp:3401

orbiter::layer3_group_actions::groups::strong_generators::field_reduction
void field_reduction(actions::action *Aq, int n, int s, field_theory::finite_field *Fq, int verbose_level)
Definition: strong_generators_groups.cpp:1318

orbiter::layer3_group_actions::groups::strong_generators::add_generators
void add_generators(data_structures_groups::vector_ge *coset_reps, int group_index, int verbose_level)
Definition: strong_generators.cpp:1172

orbiter::layer3_group_actions::groups::strong_generators::print_generators_for_make_element
void print_generators_for_make_element(std::ostream &ost)
Definition: strong_generators.cpp:1797

orbiter::layer3_group_actions::groups::strong_generators::projectivity_subgroup
void projectivity_subgroup(sims *S, int verbose_level)
Definition: strong_generators_groups.cpp:237

orbiter::layer3_group_actions::groups::strong_generators::compute_schreier_with_given_action
void compute_schreier_with_given_action(actions::action *A_given, schreier *&Sch, int verbose_level)
Definition: strong_generators.cpp:2126

orbiter::layer3_group_actions::groups::strong_generators::regulus_stabilizer
void regulus_stabilizer(actions::action *A_PGL_n_q, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1769

orbiter::layer3_group_actions::groups::strong_generators::generators_for_stabilizer_of_triangle_in_PGL4
void generators_for_stabilizer_of_triangle_in_PGL4(actions::action *A_PGL_4_q, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:2480

orbiter::layer3_group_actions::groups::strong_generators::generators_for_translation_plane_in_andre_model
void generators_for_translation_plane_in_andre_model(actions::action *A_PGL_n1_q, actions::action *A_PGL_n_q, matrix_group *Mtx_n1, matrix_group *Mtx_n, data_structures_groups::vector_ge *spread_stab_gens, ring_theory::longinteger_object &spread_stab_go, int verbose_level)
Definition: strong_generators_groups.cpp:1489

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_singer_cycle_and_the_Frobenius
void generators_for_the_singer_cycle_and_the_Frobenius(actions::action *A, matrix_group *Mtx, int power_of_singer, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:912

orbiter::layer3_group_actions::groups::strong_generators::write_file
void write_file(std::string &fname, int verbose_level)
Definition: strong_generators.cpp:2650

orbiter::layer3_group_actions::groups::strong_generators::~strong_generators
~strong_generators()
Definition: strong_generators.cpp:24

orbiter::layer3_group_actions::groups::strong_generators::init_from_data_with_go
void init_from_data_with_go(actions::action *A, std::string &generators_data, std::string &go_text, int verbose_level)
Definition: strong_generators.cpp:455

orbiter::layer3_group_actions::groups::strong_generators::init_subgroup
void init_subgroup(actions::action *A, int *subgroup_gens_idx, int nb_subgroup_gens, const char *subgroup_order_text, sims *S, int verbose_level)
Definition: strong_generators.cpp:967

orbiter::layer3_group_actions::groups::strong_generators::init_transposed_group
void init_transposed_group(strong_generators *SG, int verbose_level)
Definition: strong_generators.cpp:670

orbiter::layer3_group_actions::groups::strong_generators::export_permutation_group_to_magma
void export_permutation_group_to_magma(std::string &fname, actions::action *A2, int verbose_level)
Definition: strong_generators.cpp:2967

orbiter::layer3_group_actions::groups::strong_generators::print_generators_gap_in_different_action
void print_generators_gap_in_different_action(std::ostream &ost, actions::action *A2)
Definition: strong_generators.cpp:1327

orbiter::layer3_group_actions::groups::strong_generators::init_subgroup_by_generators
void init_subgroup_by_generators(actions::action *A, int nb_subgroup_gens, int *subgroup_gens, std::string &subgroup_order_text, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators.cpp:1035

orbiter::layer3_group_actions::groups::strong_generators::create_sims_in_different_action
sims * create_sims_in_different_action(actions::action *A_given, int verbose_level)
Definition: strong_generators.cpp:1145

orbiter::layer3_group_actions::groups::strong_generators::Sylow_subgroup
void Sylow_subgroup(sims *S, int p, int verbose_level)
Definition: strong_generators_groups.cpp:307

orbiter::layer3_group_actions::groups::strong_generators::generators_for_the_borel_subgroup_upper
void generators_for_the_borel_subgroup_upper(actions::action *A_linear, matrix_group *Mtx, int verbose_level)
Definition: strong_generators_groups.cpp:1944

orbiter::layer3_group_actions::groups::strong_generators::init_group_extension
void init_group_extension(strong_generators *subgroup, int *data, int index, int verbose_level)
Definition: strong_generators.cpp:726

orbiter::layer3_group_actions::groups::strong_generators::stabilizer_of_Eckardt_surface
void stabilizer_of_Eckardt_surface(actions::action *A, field_theory::finite_field *F, int f_with_normalizer, int f_semilinear, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators_groups.cpp:2792

orbiter::layer3_group_actions::groups::strong_generators::make_element_which_moves_a_point_from_A_to_B
void make_element_which_moves_a_point_from_A_to_B(actions::action *A_given, int pt_A, int pt_B, int *Elt, int verbose_level)
Definition: strong_generators.cpp:3308

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Definition: strong_generators.cpp:3162

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Definition: strong_generators.cpp:29

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Definition: strong_generators_groups.cpp:1145

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void init_from_data_with_target_go_ascii(actions::action *A, int *data, int nb_elements, int elt_size, const char *ascii_target_go, data_structures_groups::vector_ge *&nice_gens, int verbose_level)
Definition: strong_generators.cpp:348

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Definition: groups.h:1708

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Definition: strong_generators_groups.cpp:3003

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Definition: groups.h:1706

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Definition: strong_generators.cpp:3546

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Definition: strong_generators.cpp:1266

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Definition: strong_generators.cpp:1422

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Definition: groups.h:2039

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Definition: subgroup.cpp:107

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Definition: groups.h:2044

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Definition: subgroup.cpp:30

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Definition: groups.h:2042

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Definition: subgroup.cpp:63

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Definition: groups.h:2047

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Definition: groups.h:2046

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Definition: subgroup.cpp:116

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Definition: subgroup.cpp:18

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Definition: groups.h:2043

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Definition: subgroup.cpp:96

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Definition: groups.h:2045

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Definition: subgroup.cpp:35

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Definition: subgroup.cpp:46

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Definition: subgroup.cpp:129

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Definition: groups.h:2041

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Definition: groups.h:2068

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Definition: sylow_structure.cpp:42

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Definition: sylow_structure.cpp:56

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Definition: groups.h:2071

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Definition: sylow_structure.cpp:109

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Definition: groups.h:2075

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Definition: groups.h:2073

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Definition: sylow_structure.cpp:33

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Definition: groups.h:2070

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Definition: sylow_structure.cpp:23

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Definition: groups.h:2072

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Definition: sylow_structure.cpp:28

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Definition: groups.h:2076

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Definition: groups.h:2093

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Definition: wreath_product.cpp:820

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Definition: groups.h:2152

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Definition: wreath_product.cpp:1451

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Definition: groups.h:2142

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Definition: groups.h:2153

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Definition: wreath_product.cpp:769

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Definition: wreath_product.cpp:670

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Definition: wreath_product.cpp:953

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Definition: wreath_product.cpp:841

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Definition: groups.h:2128

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uint32_t PG_rank_to_affine_rank(long int PG_rk)
Definition: wreath_product.cpp:1465

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Definition: wreath_product.cpp:1918

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Definition: groups.h:2122

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Definition: wreath_product.cpp:594

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Definition: wreath_product.cpp:416

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Definition: groups.h:2137

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Definition: groups.h:2135

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Definition: groups.h:2099

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Definition: groups.h:2156

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Definition: wreath_product.cpp:406

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Definition: wreath_product.cpp:650

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Definition: groups.h:2121

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Definition: wreath_product.cpp:94

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Definition: groups.h:2158

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Definition: wreath_product.cpp:1427

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Definition: groups.h:2098

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Definition: wreath_product.cpp:604

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Definition: groups.h:2144

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void orbits_restricted_compute(strong_generators *SG, actions::action *A, int *&result, int &nb_gens, int &degree, int nb_factors, std::string &orbits_restricted_fname, int verbose_level)
Definition: wreath_product.cpp:2918

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Definition: groups.h:2136

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Definition: groups.h:2139

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Definition: wreath_product.cpp:973

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Definition: wreath_product.cpp:191

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Definition: groups.h:2125

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Definition: wreath_product.cpp:445

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Definition: groups.h:2146

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Definition: wreath_product.cpp:2396

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Definition: wreath_product.cpp:941

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Definition: groups.h:2109

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Definition: wreath_product.cpp:882

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Definition: groups.h:2103

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Definition: wreath_product.cpp:1044

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Definition: wreath_product.cpp:689

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Definition: groups.h:2165

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Definition: wreath_product.cpp:1456

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Definition: groups.h:2162

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Definition: wreath_product.cpp:2391

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Definition: wreath_product.cpp:709

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void create_all_rank_one_tensors(uint32_t *&rank_one_tensors, int &nb_rank_one_tensors, int verbose_level)
Definition: wreath_product.cpp:1314

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Definition: groups.h:2129

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Definition: wreath_product.cpp:1124

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Definition: groups.h:2154

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Definition: wreath_product.cpp:1474

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Definition: groups.h:2143

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Definition: wreath_product.cpp:764

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Definition: groups.h:2133

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Definition: groups.h:2149

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Definition: groups.h:2132

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Definition: groups.h:2148

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Definition: groups.h:2130

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Definition: groups.h:2164

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Definition: groups.h:2140

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Definition: wreath_product.cpp:550

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Definition: wreath_product.cpp:25

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void make_element(int *Elt, int *data, int verbose_level)
Definition: wreath_product.cpp:910

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Definition: wreath_product.cpp:99

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Definition: groups.h:2102

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Definition: groups.h:2150

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Definition: groups.h:2100

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Definition: groups.h:2107

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void orbits_using_files_and_union_find(strong_generators *SG, actions::action *A, int *&result, int &nb_gens, int &degree, int nb_factors, int verbosity)
Definition: wreath_product.cpp:2410

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Definition: wreath_product.cpp:862

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Definition: groups.h:2134

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Definition: wreath_product.cpp:803

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Definition: groups.h:2113

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Definition: wreath_product.cpp:89

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Definition: wreath_product.cpp:627

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Definition: groups.h:2161

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Definition: groups.h:2159

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Definition: groups.h:2097

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void compute_permutations_and_write_to_file(strong_generators *SG, actions::action *A, int *&result, int &nb_gens, int &degree, int nb_factors, int verbose_level)
Definition: wreath_product.cpp:1977

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void orbits_restricted(strong_generators *SG, actions::action *A, int *&result, int &nb_gens, int &degree, int nb_factors, std::string &orbits_restricted_fname, int verbose_level)
Definition: wreath_product.cpp:2682

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Definition: groups.h:2111

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Definition: wreath_product.cpp:898

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Definition: wreath_product.cpp:997

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Definition: groups.h:2138

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Definition: wreath_product.cpp:1443

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Definition: groups.h:2105

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Definition: groups.h:2096

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uint32_t tensor_affine_rank(int *tensor)
Definition: wreath_product.cpp:1412

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Definition: groups.h:2116

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Definition: wreath_product.cpp:434

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Definition: groups.h:2118

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Definition: groups.h:2131

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induced action by conjugation on the elements of a given group
Definition: induced_actions.h:29

uchar
unsigned char uchar
Definition: foundations.h:204

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Definition: sims2.cpp:18

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Definition: group_actions.h:186

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the strategy which is employed to create shallow Schreier trees
Definition: group_actions.h:174

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Definition: classification.h:18