representation_theory_domain.cpp

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/*
 * representation_theory_domain.cpp
 *
 *  Created on: Jan 10, 2022
 *      Author: betten
 */
 
 
 
 
#include "foundations.h"
 
using namespace std;
 
 
 
namespace orbiter {
namespace layer1_foundations {
namespace linear_algebra {
 
 
 
representation_theory_domain::representation_theory_domain()
{
    F = NULL;
}
 
representation_theory_domain::~representation_theory_domain()
{
 
}
 
void representation_theory_domain::init(field_theory::finite_field *F, int verbose_level)
{
    int f_v = (verbose_level >= 1);
 
    if (f_v) {
        cout << "representation_theory_domain::init" << endl;
    }
    representation_theory_domain::F = F;
    if (f_v) {
        cout << "representation_theory_domain::init done" << endl;
    }
 
}
 
void representation_theory_domain::representing_matrix8_R(int *A,
        int q, int a, int b, int c, int d)
{
    //int i;
 
    Int_vec_zero(A, 64);
 
    A[0 * 8 + 0] = m_term(q, d, d, d);
    A[0 * 8 + 1] = m_term(q, c, c, c);
    A[0 * 8 + 2] = m_term(q, d, d, c);
    A[0 * 8 + 3] = m_term(q, d, c, d);
    A[0 * 8 + 4] = m_term(q, c, d, d);
    A[0 * 8 + 5] = m_term(q, d, c, c);
    A[0 * 8 + 6] = m_term(q, c, c, d);
    A[0 * 8 + 7] = m_term(q, c, d, c);
 
    A[1 * 8 + 0] = m_term(q, b, b, b);
    A[1 * 8 + 1] = m_term(q, a, a, a);
    A[1 * 8 + 2] = m_term(q, b, b, a);
    A[1 * 8 + 3] = m_term(q, b, a, b);
    A[1 * 8 + 4] = m_term(q, a, b, b);
    A[1 * 8 + 5] = m_term(q, b, a, a);
    A[1 * 8 + 6] = m_term(q, a, a, b);
    A[1 * 8 + 7] = m_term(q, a, b, a);
 
    A[2 * 8 + 0] = m_term(q, d, d, b);
    A[2 * 8 + 1] = m_term(q, c, c, a);
    A[2 * 8 + 2] = m_term(q, d, d, a);
    A[2 * 8 + 3] = m_term(q, d, c, b);
    A[2 * 8 + 4] = m_term(q, c, d, b);
    A[2 * 8 + 5] = m_term(q, d, c, a);
    A[2 * 8 + 6] = m_term(q, c, c, b);
    A[2 * 8 + 7] = m_term(q, c, d, a);
 
    A[3 * 8 + 0] = m_term(q, d, b, d);
    A[3 * 8 + 1] = m_term(q, c, a, c);
    A[3 * 8 + 2] = m_term(q, d, b, c);
    A[3 * 8 + 3] = m_term(q, d, a, d);
    A[3 * 8 + 4] = m_term(q, c, b, d);
    A[3 * 8 + 5] = m_term(q, d, a, c);
    A[3 * 8 + 6] = m_term(q, c, a, d);
    A[3 * 8 + 7] = m_term(q, c, b, c);
 
    A[4 * 8 + 0] = m_term(q, b, d, d);
    A[4 * 8 + 1] = m_term(q, a, c, c);
    A[4 * 8 + 2] = m_term(q, b, d, c);
    A[4 * 8 + 3] = m_term(q, b, c, d);
    A[4 * 8 + 4] = m_term(q, a, d, d);
    A[4 * 8 + 5] = m_term(q, b, c, c);
    A[4 * 8 + 6] = m_term(q, a, c, d);
    A[4 * 8 + 7] = m_term(q, a, d, c);
 
    A[5 * 8 + 0] = m_term(q, d, b, b);
    A[5 * 8 + 1] = m_term(q, c, a, a);
    A[5 * 8 + 2] = m_term(q, d, b, a);
    A[5 * 8 + 3] = m_term(q, d, a, b);
    A[5 * 8 + 4] = m_term(q, c, b, b);
    A[5 * 8 + 5] = m_term(q, d, a, a);
    A[5 * 8 + 6] = m_term(q, c, a, b);
    A[5 * 8 + 7] = m_term(q, c, b, a);
 
    A[6 * 8 + 0] = m_term(q, b, b, d);
    A[6 * 8 + 1] = m_term(q, a, a, c);
    A[6 * 8 + 2] = m_term(q, b, b, c);
    A[6 * 8 + 3] = m_term(q, b, a, d);
    A[6 * 8 + 4] = m_term(q, a, b, d);
    A[6 * 8 + 5] = m_term(q, b, a, c);
    A[6 * 8 + 6] = m_term(q, a, a, d);
    A[6 * 8 + 7] = m_term(q, a, b, c);
 
    A[7 * 8 + 0] = m_term(q, b, d, b);
    A[7 * 8 + 1] = m_term(q, a, c, a);
    A[7 * 8 + 2] = m_term(q, b, d, a);
    A[7 * 8 + 3] = m_term(q, b, c, b);
    A[7 * 8 + 4] = m_term(q, a, d, b);
    A[7 * 8 + 5] = m_term(q, b, c, a);
    A[7 * 8 + 6] = m_term(q, a, c, b);
    A[7 * 8 + 7] = m_term(q, a, d, a);
 
    F->Linear_algebra->transpose_matrix_in_place(A, 8);
}
 
void representation_theory_domain::representing_matrix9_R(int *A,
        int q, int a, int b, int c, int d)
{
    //int i;
    int tq = 2 * q;
    int tq1 = 2 * q + 1;
    int tq2 = 2 * q + 2;
    int q1 = q + 1;
    int q2 = q + 2;
 
 
    Int_vec_zero(A, 81);
 
    A[0 * 9 + 0] = term1(d,tq2);
    A[0 * 9 + 1] = term2(c,d,q1,q1);
    A[0 * 9 + 2] = term1(c,tq2);
    A[0 * 9 + 3] = term2(c,d,q,q2);
    A[0 * 9 + 4] = term2(c,d,1,tq1);
    A[0 * 9 + 5] = term2(c,d,tq,2);
    A[0 * 9 + 6] = term2(c,d,2,tq);
    A[0 * 9 + 7] = term2(c,d,tq1,1);
    A[0 * 9 + 8] = term2(c,d,q2,q);
 
    A[1 * 9 + 0] = F->four_times(term2(b,d,q1,q1));
    A[1 * 9 + 1] = add(add(add(term2(a,d,q1,q1),term4(a,b,c,d,q,1,1,q)),term4(a,b,c,d,1,q,q,1)),term2(b,c,q1,q1));
    A[1 * 9 + 2] = F->four_times(term2(a,c,q1,q1));
    A[1 * 9 + 3] = twice(add(term3(a,b,d,q,1,q1),term3(b,c,d,q1,q,1)));
    A[1 * 9 + 4] = twice(add(term3(a,b,d,1,q,q1),term3(b,c,d,q1,1,q)));
    A[1 * 9 + 5] = F->four_times(term4(a,b,c,d,q,1,q,1));
    A[1 * 9 + 6] = F->four_times(term4(a,b,c,d,1,q,1,q));
    A[1 * 9 + 7] = twice(add(term3(a,b,c,q,1,q1),term3(a,c,d,q1,q,1)));
    A[1 * 9 + 8] = twice(add(term3(a,c,d,q1,1,q),term3(a,b,c,1,q,q1)));
 
    A[2 * 9 + 0] = term1(b,tq2);
    A[2 * 9 + 1] = term2(a,b,q1,q1);
    A[2 * 9 + 2] = term1(a,tq2);
    A[2 * 9 + 3] = term2(a,b,q,q2);
    A[2 * 9 + 4] = term2(a,b,1,tq1);
    A[2 * 9 + 5] = term2(a,b,tq,2);
    A[2 * 9 + 6] = term2(a,b,2,tq);
    A[2 * 9 + 7] = term2(a,b,tq1,1);
    A[2 * 9 + 8] = term2(a,b,q2,q);
 
    A[3 * 9 + 0] = twice(term2(b,d,q,q2));
    A[3 * 9 + 1] = add(term3(a,c,d,q,1,q1),term3(b,c,d,q,q1,1));
    A[3 * 9 + 2] = twice(term2(a,c,q,q2));
    A[3 * 9 + 3] = add(term2(a,d,q,q2),term3(b,c,d,q,q,2));
    A[3 * 9 + 4] = twice(term3(b,c,d,q,1,q1));
    A[3 * 9 + 5] = twice(term3(a,c,d,q,q,2));
    A[3 * 9 + 6] = twice(term3(b,c,d,q,2,q));
    A[3 * 9 + 7] = twice(term3(a,c,d,q,q1,1));
    A[3 * 9 + 8] = add(term3(a,c,d,q,2,q),term2(b,c,q,q2));
 
    A[4 * 9 + 0] = twice(term2(b,d,1,tq1));
    A[4 * 9 + 1] = add(term3(a,c,d,1,q,q1),term3(b,c,d,1,q1,q));
    A[4 * 9 + 2] = twice(term2(a,c,1,tq1));
    A[4 * 9 + 3] = twice(term3(b,c,d,1,q,q1));
    A[4 * 9 + 4] = add(term2(a,d,1,tq1),term3(b,c,d,1,1,tq));
    A[4 * 9 + 5] = twice(term3(b,c,d,1,tq,1));
    A[4 * 9 + 6] = twice(term3(a,c,d,1,1,tq));
    A[4 * 9 + 7] = add(term3(a,c,d,1,tq,1),term2(b,c,1,tq1));
    A[4 * 9 + 8] = twice(term3(a,c,d,1,q1,q));
 
    A[5 * 9 + 0] = term2(b,d,tq,2);
    A[5 * 9 + 1] = term4(a,b,c,d,q,q,1,1);
    A[5 * 9 + 2] = term2(a,c,tq,2);
    A[5 * 9 + 3] = term3(a,b,d,q,q,2);
    A[5 * 9 + 4] = term3(b,c,d,tq,1,1);
    A[5 * 9 + 5] = term2(a,d,tq,2);
    A[5 * 9 + 6] = term2(b,c,tq,2);
    A[5 * 9 + 7] = term3(a,c,d,tq,1,1);
    A[5 * 9 + 8] = term3(a,b,c,q,q,2);
 
    A[6 * 9 + 0] = term2(b,d,2,tq);
    A[6 * 9 + 1] = term4(a,b,c,d,1,1,q,q);
    A[6 * 9 + 2] = term2(a,c,2,tq);
    A[6 * 9 + 3] = term3(b,c,d,2,q,q);
    A[6 * 9 + 4] = term3(a,b,d,1,1,tq);
    A[6 * 9 + 5] = term2(b,c,2,tq);
    A[6 * 9 + 6] = term2(a,d,2,tq);
    A[6 * 9 + 7] = term3(a,b,c,1,1,tq);
    A[6 * 9 + 8] = term3(a,c,d,2,q,q);
 
    A[7 * 9 + 0] = twice(term2(b,d,tq1,1));
    A[7 * 9 + 1] = add(term3(a,b,d,q1,q,1),term3(a,b,c,q,q1,1));
    A[7 * 9 + 2] = twice(term2(a,c,tq1,1));
    A[7 * 9 + 3] = twice(term3(a,b,d,q,q1,1));
    A[7 * 9 + 4] = add(term3(a,b,d,1,tq,1),term2(b,c,tq1,1));
    A[7 * 9 + 5] = twice(term3(a,b,d,tq,1,1));
    A[7 * 9 + 6] = twice(term3(a,b,c,1,tq,1));
    A[7 * 9 + 7] = add(term2(a,d,tq1,1),term3(a,b,c,tq,1,1));
    A[7 * 9 + 8] = twice(term3(a,b,c,q1,q,1));
 
    A[8 * 9 + 0] = twice(term2(b,d,q2,q));
    A[8 * 9 + 1] = add(term3(a,b,d,q1,1,q),term3(a,b,c,1,q1,q));
    A[8 * 9 + 2] = twice(term2(a,c,q2,q));
    A[8 * 9 + 3] = add(term3(a,b,d,q,2,q),term2(b,c,q2,q));
    A[8 * 9 + 4] = twice(term3(a,b,d,1,q1,q));
    A[8 * 9 + 5] = twice(term3(a,b,c,q,2,q));
    A[8 * 9 + 6] = twice(term3(a,b,d,2,q,q));
    A[8 * 9 + 7] = twice(term3(a,b,c,q1,1,q));
    A[8 * 9 + 8] = add(term2(a,d,q2,q),term3(a,b,c,2,q,q));
    F->Linear_algebra->transpose_matrix_in_place(A, 9);
 
}
 
void representation_theory_domain::representing_matrix9_U(int *A,
        int a, int b, int c, int d, int beta)
{
    int beta_q, delta, gamma;
    int r, q, q1,q2,tq, tq1; //, tq2;
    number_theory::number_theory_domain NT;
 
    if (!F->f_has_table) {
        cout << "representation_theory_domain::representing_matrix9_U !F->f_has_table" << endl;
        exit(1);
    }
    if (!F->has_quadratic_subfield()) {
        cout << "representation_theory_domain::representing_matrix9_U "
                "field does not have a quadratic subfield" << endl;
        exit(1);
    }
    r = F->e >> 1;
    q = NT.i_power_j(F->p, r);
    q1 = q + 1;
    q2 = q + 2;
    tq = 2 * q;
    tq1 = tq + 1;
    //tq2 = tq + 2;
    beta_q = F->frobenius_power(beta, r);
    delta = inverse(add(beta, negate(beta_q)));
    gamma = mult(delta, beta);
 
    A[0 * 9 + 0] = N2(F->square(d));
    A[0 * 9 + 1] = F->four_times(N2(mult(b, d)));
    A[0 * 9 + 2] = N2(F->square(b));
    A[0 * 9 + 3] = twice(Term3(b,d,gamma,q,q2,1));
    A[0 * 9 + 4] = twice(Term3(b,d,delta,1,tq1,1));
    A[0 * 9 + 5] = Term3(b,d,gamma,tq,2,1);
    A[0 * 9 + 6] = Term3(b,d,delta,2,tq,1);
    A[0 * 9 + 7] = twice(Term3(b,d,gamma,tq1,1,1));
    A[0 * 9 + 8] = twice(Term3(b,d,delta,q2,q,1));
 
    A[1 * 9 + 0] = N2(mult(c,d));
    A[1 * 9 + 1] = add3(N2(mult(a,d)),N2(mult(b,c)),T2(term4(a,b,c,d,q,1,1,q)));
    A[1 * 9 + 2] = N2(mult(a,b));
    A[1 * 9 + 3] = add(Term4(a,c,d,gamma,q,1,q1,1),Term4(b,c,d,gamma,q,q1,1,1));
    A[1 * 9 + 4] = add(Term4(a,c,d,delta,1,q,q1,1),Term4(b,c,d,delta,1,q1,q,1));
    A[1 * 9 + 5] = Term5(a,b,c,d,gamma,q,q,1,1,1);
    A[1 * 9 + 6] = Term5(a,b,c,d,delta,1,1,q,q,1);
    A[1 * 9 + 7] = add(Term4(a,b,d,gamma,q1,q,1,1),Term4(a,b,c,gamma,q,q1,1,1));
    A[1 * 9 + 8] = add(Term4(a,b,c,delta,1,q1,q,1),Term4(a,b,d,delta,q1,1,q,1));
 
    A[2 * 9 + 0] = N2(F->square(c));
    A[2 * 9 + 1] = F->four_times(N2(mult(a,c)));
    A[2 * 9 + 2] = N2(F->square(a));
    A[2 * 9 + 3] = twice(Term3(a,c,gamma,q,q2,1));
    A[2 * 9 + 4] = twice(Term3(a,c,delta,1,tq1,1));
    A[2 * 9 + 5] = Term3(a,c,gamma,tq,2,1);
    A[2 * 9 + 6] = Term3(a,c,delta,2,tq,1);
    A[2 * 9 + 7] = twice(Term3(a,c,gamma,tq1,1,1));
    A[2 * 9 + 8] = twice(Term3(a,c,delta,q2,q,1));
 
    A[3 * 9 + 0] = Term2(c,d,1,tq1);
    A[3 * 9 + 1] = twice(add(Term3(a,b,d,1,q,q1),Term3(b,c,d,q1,1,q)));
    A[3 * 9 + 2] = Term2(a,b,1,tq1);
    A[3 * 9 + 3] = add3(twice(Term4(b,c,d,gamma,q,1,q1,1)),Term3(a,d,gamma,q,q2,1),Term4(b,c,d,gamma,q,q,2,1));
    A[3 * 9 + 4] = add3(twice(Term4(b,c,d,delta,1,q,q1,1)),Term3(a,d,delta,1,tq1,1),Term4(b,c,d,delta,1,1,tq,1));
    A[3 * 9 + 5] = add(Term4(a,b,d,gamma,q,q,2,1),Term4(b,c,d,gamma,tq,1,1,1));
    A[3 * 9 + 6] = add(Term4(b,c,d,delta,2,q,q,1),Term4(a,b,d,delta,1,1,tq,1));
    A[3 * 9 + 7] = add3(twice(Term4(a,b,d,gamma,q,q1,1,1)),Term4(a,b,d,gamma,1,tq,1,1),Term3(b,c,gamma,tq1,1,1));
    A[3 * 9 + 8] = add3(twice(Term4(a,b,d,delta,1,q1,q,1)),Term4(a,b,d,delta,q,2,q,1),Term3(b,c,delta,q2,q,1));
 
    A[4 * 9 + 0] = Term3(c,d,beta,1,tq1,1);
    A[4 * 9 + 1] = twice(add(Term4(a,b,d,beta,1,q,q1,1),Term4(b,c,d,beta,q1,1,q,1)));
    A[4 * 9 + 2] = Term3(a,b,beta,1,tq1,1);
    A[4 * 9 + 3] = add3(twice(Term5(b,c,d,beta,gamma,q,1,q1,1,1)),Term4(a,d,beta,gamma,q,q2,q,1),Term5(b,c,d,beta,gamma,q,q,2,q,1));
    A[4 * 9 + 4] = add3(twice(Term5(b,c,d,beta,delta,1,q,q1,q,1)),Term4(a,d,beta,delta,1,tq1,1,1),Term5(b,c,d,beta,delta,1,1,tq,1,1));
    A[4 * 9 + 5] = add(Term5(a,b,d,beta,gamma,q,q,2,q,1),Term5(b,c,d,beta,gamma,tq,1,1,1,1));
    A[4 * 9 + 6] = add(Term5(b,c,d,beta,delta,2,q,q,q,1),Term5(a,b,d,beta,delta,1,1,tq,1,1));
    A[4 * 9 + 7] = add3(twice(Term5(a,b,d,beta,gamma,q,q1,1,q,1)),Term5(a,b,d,beta,gamma,1,tq,1,1,1),Term4(b,c,beta,gamma,tq1,1,1,1));
    A[4 * 9 + 8] = add3(twice(Term5(a,b,d,beta,delta,1,q1,q,1,1)),Term5(a,b,d,beta,delta,q,2,q,q,1),Term4(b,c,beta,delta,q2,q,q,1));
 
    A[5 * 9 + 0] = Term2(c,d,2,tq);
    A[5 * 9 + 1] = F->four_times(Term4(a,b,c,d,1,q,1,q));
    A[5 * 9 + 2] = Term2(a,b,2,tq);
    A[5 * 9 + 3] = twice(add(Term4(a,c,d,gamma,q,q,2,1),Term4(b,c,d,gamma,q,2,q,1)));
    A[5 * 9 + 4] = twice(add(Term4(b,c,d,delta,1,tq,1,1),Term4(a,c,d,delta,1,1,tq,1)));
    A[5 * 9 + 5] = add(Term3(a,d,gamma,tq,2,1),Term3(b,c,gamma,tq,2,1));
    A[5 * 9 + 6] = add(Term3(a,d,delta,2,tq,1),Term3(b,c,delta,2,tq,1));
    A[5 * 9 + 7] = twice(add(Term4(a,b,d,gamma,tq,1,1,1),Term4(a,b,c,gamma,1,tq,1,1)));
    A[5 * 9 + 8] = twice(add(Term4(a,b,c,delta,q,2,q,1),Term4(a,b,d,delta,2,q,q,1)));
 
    A[6 * 9 + 0] = Term3(c,d,beta,2,tq,1);
    A[6 * 9 + 1] = F->four_times(Term5(a,b,c,d,beta,1,q,1,q,1));
    A[6 * 9 + 2] = Term3(a,b,beta,2,tq,1);
    A[6 * 9 + 3] = twice(add(Term5(a,c,d,beta,gamma,q,q,2,q,1),Term5(b,c,d,beta,gamma,q,2,q,1,1)));
    A[6 * 9 + 4] = twice(add(Term5(b,c,d,beta,delta,1,tq,1,q,1),Term5(a,c,d,beta,delta,1,1,tq,1,1)));
    A[6 * 9 + 5] = add(Term4(a,d,beta,gamma,tq,2,q,1),Term4(b,c,beta,gamma,tq,2,1,1));
    A[6 * 9 + 6] = add(Term4(a,d,beta,delta,2,tq,1,1),Term4(b,c,beta,delta,2,tq,q,1));
    A[6 * 9 + 7] = twice(add(Term5(a,b,d,beta,gamma,tq,1,1,q,1),Term5(a,b,c,beta,gamma,1,tq,1,1,1)));
    A[6 * 9 + 8] = twice(add(Term5(a,b,c,beta,delta,q,2,q,q,1),Term5(a,b,d,beta,delta,2,q,q,1,1)));
 
    A[7 * 9 + 0] = Term2(c,d,q2,q);
    A[7 * 9 + 1] = twice(add(Term3(a,c,d,q1,1,q),Term3(a,b,c,1,q,q1)));
    A[7 * 9 + 2] = Term2(a,b,q2,q);
    A[7 * 9 + 3] = add3(twice(Term4(a,c,d,gamma,q,q1,1,1)),Term4(a,c,d,gamma,q,2,q,1),Term3(b,c,gamma,q,q2,1));
    A[7 * 9 + 4] = add3(twice(Term4(a,c,d,delta,1,q1,q,1)),Term4(a,c,d,delta,1,tq,1,1),Term3(b,c,delta,1,tq1,1));
    A[7 * 9 + 5] = add(Term4(a,c,d,gamma,tq,1,1,1),Term4(a,b,c,gamma,q,q,2,1));
    A[7 * 9 + 6] = add(Term4(a,b,c,delta,1,1,tq,1),Term4(a,c,d,delta,2,q,q,1));
    A[7 * 9 + 7] = add3(twice(Term4(a,b,c,gamma,q1,q,1,1)),Term3(a,d,gamma,tq1,1,1),Term4(a,b,c,gamma,tq,1,1,1));
    A[7 * 9 + 8] = add3(twice(Term4(a,b,c,delta,q1,1,q,1)),Term3(a,d,delta,q2,q,1),Term4(a,b,c,delta,2,q,q,1));
 
    A[8 * 9 + 0] = Term3(c,d,beta,q2,q,1);
    A[8 * 9 + 1] = twice(add(Term4(a,c,d,beta,q1,1,q,1),Term4(a,b,c,beta,1,q,q1,1)));
    A[8 * 9 + 2] = Term3(a,b,beta,q2,q,1);
    A[8 * 9 + 3] = add3(twice(Term5(a,c,d,beta,gamma,q,q1,1,q,1)),Term5(a,c,d,beta,gamma,q,2,q,1,1),Term4(b,c,beta,gamma,q,q2,1,1));
    A[8 * 9 + 4] = add3(twice(Term5(a,c,d,beta,delta,1,q1,q,1,1)),Term5(a,c,d,beta,delta,1,tq,1,q,1),Term4(b,c,beta,delta,1,tq1,q,1));
    A[8 * 9 + 5] = add(Term5(a,c,d,beta,gamma,tq,1,1,q,1),Term5(a,b,c,beta,gamma,q,q,2,1,1));
    A[8 * 9 + 6] = add(Term5(a,b,c,beta,delta,1,1,tq,q,1),Term5(a,c,d,beta,delta,2,q,q,1,1));
    A[8 * 9 + 7] = add3(twice(Term5(a,b,c,beta,gamma,q1,q,1,1,1)),Term4(a,d,beta,gamma,tq1,1,q,1),Term5(a,b,c,beta,gamma,tq,1,1,q,1));
    A[8 * 9 + 8] = add3(twice(Term5(a,b,c,beta,delta,q1,1,q,q,1)),Term4(a,d,beta,delta,q2,q,1,1),Term5(a,b,c,beta,delta,2,q,q,1,1));
 
 
}
 
void representation_theory_domain::representing_matrix8_U(int *A, int a, int b, int c, int d, int beta)
{
    int delta1, delta2;
    int r, q, i, j;
    int beta_2, beta_11, beta_22, beta_21, beta_12, beta_123, beta_132;
    int gamma3, gamma4, gamma5, gamma6, gamma7, gamma8;
    int *eta, *M1, *B1;
    int *zeta, *M2, *B2;
    number_theory::number_theory_domain NT;
 
 
 
    r = F->e / 3;
    if (F->e != 3 * r) {
        cout << "representation_theory_domain::representing_matrix8_U "
                "field does not have a cubic subfield" << endl;
        exit(1);
    }
    //cout << "a=" << a << " b=" << b << " c=" << c << " d=" << d << endl;
 
    q = NT.i_power_j(F->p, r);
    beta_2 = beta_trinomial(q, beta, 0, 0, 2);
    beta_11 = beta_trinomial(q, beta, 0, 1, 1);
    beta_22 = beta_trinomial(q, beta, 0, 2, 2);
    beta_21 = beta_trinomial(q, beta, 0, 2, 1);
    beta_12 = beta_trinomial(q, beta, 0, 1, 2);
    beta_123 = beta_trinomial(q, beta, 1, 2, 3);
    beta_132 = beta_trinomial(q, beta, 1, 3, 2);
    delta1 = inverse(T3(add(beta_21, negate(beta_12))));
    delta2 = inverse(T3(add(beta_123, negate(beta_132))));
    gamma3 = add(beta_trinomial(q, beta, 1, 0, 2), negate(beta_trinomial(q, beta, 2, 0, 1)));
    gamma4 = add(beta_trinomial(q, beta, 2, 0, 0), negate(beta_trinomial(q, beta, 0, 0, 2)));
    gamma5 = add(beta_trinomial(q, beta, 0, 0, 1), negate(beta_trinomial(q, beta, 1, 0, 0)));
    gamma6 = add(beta_trinomial(q, beta, 1, 2, 3), negate(beta_trinomial(q, beta, 2, 1, 3)));
    gamma7 = add(beta_trinomial(q, beta, 2, 0, 2), negate(beta_trinomial(q, beta, 0, 2, 2)));
    gamma8 = add(beta_trinomial(q, beta, 0, 1, 1), negate(beta_trinomial(q, beta, 1, 0, 1)));
    //cout << "delta1=" << delta1 << endl;
    //cout << "delta2=" << delta2 << endl;
    //cout << "gamma8=" << gamma8 << endl;
    //cout << "beta_trinomial(q, beta, 1, 2, 3)=" << beta_trinomial(q, beta, 1, 2, 3) << endl;
    //cout << "beta_trinomial(q, beta, 2, 1, 3)=" << beta_trinomial(q, beta, 2, 1, 3) << endl;
 
    eta = NEW_int(2 * 3);
    zeta = NEW_int(2 * 3);
    M1 = NEW_int(2 * 3);
    M2 = NEW_int(2 * 3);
    B1 = NEW_int(3 * 3);
    B2 = NEW_int(3 * 3);
 
    M1[0 * 3 + 0] = m_term(q, d, b, c);
    M1[0 * 3 + 1] = m_term(q, d, a, d);
    M1[0 * 3 + 2] = m_term(q, c, b, d);
    M1[1 * 3 + 0] = m_term(q, b, b, c);
    M1[1 * 3 + 1] = m_term(q, b, a, d);
    M1[1 * 3 + 2] = m_term(q, a, b, d);
 
    M2[0 * 3 + 0] = m_term(q, d, a, c);
    M2[0 * 3 + 1] = m_term(q, c, a, d);
    M2[0 * 3 + 2] = m_term(q, c, b, c);
    M2[1 * 3 + 0] = m_term(q, b, a, c);
    M2[1 * 3 + 1] = m_term(q, a, a, d);
    M2[1 * 3 + 2] = m_term(q, a, b, c);
 
    B1[0 * 3 + 0] = 1;
    B1[0 * 3 + 1] = beta_trinomial(q, beta, 0, 0, 1);
    B1[0 * 3 + 2] = beta_trinomial(q, beta, 0, 0, 2);
    B1[1 * 3 + 0] = 1;
    B1[1 * 3 + 1] = beta_trinomial(q, beta, 0, 1, 0);
    B1[1 * 3 + 2] = beta_trinomial(q, beta, 0, 2, 0);
    B1[2 * 3 + 0] = 1;
    B1[2 * 3 + 1] = beta_trinomial(q, beta, 1, 0, 0);
    B1[2 * 3 + 2] = beta_trinomial(q, beta, 2, 0, 0);
 
    B2[0 * 3 + 0] = 1;
    B2[0 * 3 + 1] = beta_trinomial(q, beta, 0, 1, 1);
    B2[0 * 3 + 2] = beta_trinomial(q, beta, 0, 2, 2);
    B2[1 * 3 + 0] = 1;
    B2[1 * 3 + 1] = beta_trinomial(q, beta, 1, 1, 0);
    B2[1 * 3 + 2] = beta_trinomial(q, beta, 2, 2, 0);
    B2[2 * 3 + 0] = 1;
    B2[2 * 3 + 1] = beta_trinomial(q, beta, 1, 0, 1);
    B2[2 * 3 + 2] = beta_trinomial(q, beta, 2, 0, 2);
 
    F->Linear_algebra->mult_matrix_matrix(M1, B1, eta, 2, 3, 3, 0 /* verbose_level */);
    F->Linear_algebra->mult_matrix_matrix(M2, B2, zeta, 2, 3, 3, 0 /* verbose_level */);
    int eta11, eta12, eta13;
    int eta21, eta22, eta23;
    int zeta11, zeta12, zeta13;
    int zeta21, zeta22, zeta23;
    eta11 = eta[0*3+0];
    eta12 = eta[0*3+1];
    eta13 = eta[0*3+2];
    eta21 = eta[1*3+0];
    eta22 = eta[1*3+1];
    eta23 = eta[1*3+2];
    zeta11 = zeta[0*3+0];
    zeta12 = zeta[0*3+1];
    zeta13 = zeta[0*3+2];
    zeta21 = zeta[1*3+0];
    zeta22 = zeta[1*3+1];
    zeta23 = zeta[1*3+2];
 
    //cout << "eta22=" << eta22 << endl;
    //cout << "eta22 gamma8=" << mult(eta22,gamma8) << endl;
 
    A[0 * 8 + 0] = N3(d);
    A[0 * 8 + 1] = N3(b);
    A[0 * 8 + 2] = T3product2(m_term(q, d, b, d), gamma3);
    A[0 * 8 + 3] = T3product2(m_term(q, d, b, d), gamma4);
    A[0 * 8 + 4] = T3product2(m_term(q, d, b, d), gamma5);
    A[0 * 8 + 5] = T3product2(m_term(q, b, b, d), gamma6);
    A[0 * 8 + 6] = T3product2(m_term(q, b, b, d), gamma7);
    A[0 * 8 + 7] = T3product2(m_term(q, b, b, d), gamma8);
 
    A[1 * 8 + 0] = N3(c);
    A[1 * 8 + 1] = N3(a);
    A[1 * 8 + 2] = T3product2(m_term(q, c, a, c), gamma3);
    A[1 * 8 + 3] = T3product2(m_term(q, c, a, c), gamma4);
    A[1 * 8 + 4] = T3product2(m_term(q, c, a, c), gamma5);
    A[1 * 8 + 5] = T3product2(m_term(q, a, a, c), gamma6);
    A[1 * 8 + 6] = T3product2(m_term(q, a, a, c), gamma7);
    A[1 * 8 + 7] = T3product2(m_term(q, a, a, c), gamma8);
 
    A[2 * 8 + 0] = T3(m_term(q, d, d, c));
    A[2 * 8 + 1] = T3(m_term(q, b, b, a));
    A[2 * 8 + 2] = T3product2(eta11, gamma3);
    A[2 * 8 + 3] = T3product2(eta11, gamma4);
    A[2 * 8 + 4] = T3product2(eta11, gamma5);
    A[2 * 8 + 5] = T3product2(eta21, gamma6);
    A[2 * 8 + 6] = T3product2(eta21, gamma7);
    A[2 * 8 + 7] = T3product2(eta21, gamma8);
 
    A[3 * 8 + 0] = T3product2(m_term(q, d, d, c), beta);
    A[3 * 8 + 1] = T3product2(m_term(q, b, b, a), beta);
    A[3 * 8 + 2] = T3product2(eta12, gamma3);
    A[3 * 8 + 3] = T3product2(eta12, gamma4);
    A[3 * 8 + 4] = T3product2(eta12, gamma5);
    A[3 * 8 + 5] = T3product2(eta22, gamma6);
    A[3 * 8 + 6] = T3product2(eta22, gamma7);
    A[3 * 8 + 7] = T3product2(eta22, gamma8);
 
    A[4 * 8 + 0] = T3product2(m_term(q, d, d, c), beta_2);
    A[4 * 8 + 1] = T3product2(m_term(q, b, b, a), beta_2);
    A[4 * 8 + 2] = T3product2(eta13, gamma3);
    A[4 * 8 + 3] = T3product2(eta13, gamma4);
    A[4 * 8 + 4] = T3product2(eta13, gamma5);
    A[4 * 8 + 5] = T3product2(eta23, gamma6);
    A[4 * 8 + 6] = T3product2(eta23, gamma7);
    A[4 * 8 + 7] = T3product2(eta23, gamma8);
 
    A[5 * 8 + 0] = T3product2(m_term(q, d, c, c), 1);
    A[5 * 8 + 1] = T3product2(m_term(q, b, a, a), 1);
    A[5 * 8 + 2] = T3product2(zeta11, gamma3);
    A[5 * 8 + 3] = T3product2(zeta11, gamma4);
    A[5 * 8 + 4] = T3product2(zeta11, gamma5);
    A[5 * 8 + 5] = T3product2(zeta21, gamma6);
    A[5 * 8 + 6] = T3product2(zeta21, gamma7);
    A[5 * 8 + 7] = T3product2(zeta21, gamma8);
 
    A[6 * 8 + 0] = T3product2(m_term(q, d, c, c), beta_11);
    A[6 * 8 + 1] = T3product2(m_term(q, b, a, a), beta_11);
    A[6 * 8 + 2] = T3product2(zeta12, gamma3);
    A[6 * 8 + 3] = T3product2(zeta12, gamma4);
    A[6 * 8 + 4] = T3product2(zeta12, gamma5);
    A[6 * 8 + 5] = T3product2(zeta22, gamma6);
    A[6 * 8 + 6] = T3product2(zeta22, gamma7);
    A[6 * 8 + 7] = T3product2(zeta22, gamma8);
 
    A[7 * 8 + 0] = T3product2(m_term(q, d, c, c), beta_22);
    A[7 * 8 + 1] = T3product2(m_term(q, b, a, a), beta_22);
    A[7 * 8 + 2] = T3product2(zeta13, gamma3);
    A[7 * 8 + 3] = T3product2(zeta13, gamma4);
    A[7 * 8 + 4] = T3product2(zeta13, gamma5);
    A[7 * 8 + 5] = T3product2(zeta23, gamma6);
    A[7 * 8 + 6] = T3product2(zeta23, gamma7);
    A[7 * 8 + 7] = T3product2(zeta23, gamma8);
 
    for (j = 2; j <= 4; j++) {
        for (i = 0; i < 8; i++) {
            A[i * 8 + j] = mult(A[i * 8 + j], delta1);
        }
    }
    for (j = 5; j <= 7; j++) {
        for (i = 0; i < 8; i++) {
            A[i * 8 + j] = mult(A[i * 8 + j], delta2);
        }
    }
    FREE_int(eta);
    FREE_int(zeta);
    FREE_int(M1);
    FREE_int(M2);
    FREE_int(B1);
    FREE_int(B2);
}
 
void representation_theory_domain::representing_matrix8_V(int *A, int beta)
{
    int delta1, delta2;
    int beta_21, beta_12, beta_123, beta_132;
    int r, q, i, j;
    number_theory::number_theory_domain NT;
 
 
 
    r = F->e / 3;
    if (F->e != 3 * r) {
        cout << "representation_theory_domain::representing_matrix8_V "
                "field does not have a cubic subfield" << endl;
        exit(1);
    }
    //cout << "a=" << a << " b=" << b << " c=" << c << " d=" << d << endl;
 
    q = NT.i_power_j(F->p, r);
    beta_21 = beta_trinomial(q, beta, 0, 2, 1);
    beta_12 = beta_trinomial(q, beta, 0, 1, 2);
    beta_123 = beta_trinomial(q, beta, 1, 2, 3);
    beta_132 = beta_trinomial(q, beta, 1, 3, 2);
    delta1 = inverse(T3(add(beta_21, negate(beta_12))));
    delta2 = inverse(T3(add(beta_123, negate(beta_132))));
 
    Int_vec_zero(A, 64);
 
    A[0 * 8 + 0] = 1;
    A[1 * 8 + 1] = 1;
    A[2 * 8 + 2] = T3(add(beta_trinomial(q, beta, 0, 2, 1), negate(beta_trinomial(q, beta, 0, 1, 2))));
    A[2 * 8 + 3] = T3(add(beta_trinomial(q, beta, 0, 0, 2), negate(beta_trinomial(q, beta, 0, 2, 0))));
    A[2 * 8 + 4] = T3(add(beta_trinomial(q, beta, 0, 1, 0), negate(beta_trinomial(q, beta, 0, 0, 1))));
    A[3 * 8 + 2] = T3(add(beta_trinomial(q, beta, 0, 3, 1), negate(beta_trinomial(q, beta, 0, 2, 2))));
    A[3 * 8 + 3] = T3(add(beta_trinomial(q, beta, 0, 1, 2), negate(beta_trinomial(q, beta, 0, 3, 0))));
    A[3 * 8 + 4] = T3(add(beta_trinomial(q, beta, 0, 2, 0), negate(beta_trinomial(q, beta, 0, 1, 1))));
    A[4 * 8 + 2] = T3(add(beta_trinomial(q, beta, 0, 4, 1), negate(beta_trinomial(q, beta, 0, 3, 2))));
    A[4 * 8 + 3] = T3(add(beta_trinomial(q, beta, 0, 2, 2), negate(beta_trinomial(q, beta, 0, 4, 0))));
    A[4 * 8 + 4] = T3(add(beta_trinomial(q, beta, 0, 3, 0), negate(beta_trinomial(q, beta, 0, 2, 1))));
 
    A[5 * 8 + 5] = T3(add(beta_trinomial(q, beta, 2, 3, 1), negate(beta_trinomial(q, beta, 1, 3, 2))));
    A[5 * 8 + 6] = T3(add(beta_trinomial(q, beta, 0, 2, 2), negate(beta_trinomial(q, beta, 2, 2, 0))));
    A[5 * 8 + 7] = T3(add(beta_trinomial(q, beta, 1, 1, 0), negate(beta_trinomial(q, beta, 0, 1, 1))));
    A[6 * 8 + 5] = T3(add(beta_trinomial(q, beta, 3, 4, 1), negate(beta_trinomial(q, beta, 2, 4, 2))));
    A[6 * 8 + 6] = T3(add(beta_trinomial(q, beta, 1, 3, 2), negate(beta_trinomial(q, beta, 3, 3, 0))));
    A[6 * 8 + 7] = T3(add(beta_trinomial(q, beta, 2, 2, 0), negate(beta_trinomial(q, beta, 1, 2, 1))));
    A[7 * 8 + 5] = T3(add(beta_trinomial(q, beta, 4, 5, 1), negate(beta_trinomial(q, beta, 3, 5, 2))));
    A[7 * 8 + 6] = T3(add(beta_trinomial(q, beta, 2, 4, 2), negate(beta_trinomial(q, beta, 4, 4, 0))));
    A[7 * 8 + 7] = T3(add(beta_trinomial(q, beta, 3, 3, 0), negate(beta_trinomial(q, beta, 2, 3, 1))));
 
    for (j = 2; j <= 4; j++) {
        for (i = 2; i <= 4; i++) {
            A[i * 8 + j] = mult(A[i * 8 + j], delta1);
        }
    }
    for (j = 5; j <= 7; j++) {
        for (i = 5; i <= 7; i++) {
            A[i * 8 + j] = mult(A[i * 8 + j], delta2);
        }
    }
}
 
 
void representation_theory_domain::representing_matrix9b(int *A, int beta)
{
    int r, /*q,*/ beta_q, delta, minus_one; //, i;
        // gamma, betagamma, i, Tgamma, Tbetagamma, nTgamma;
 
    r = F->e / 2;
    if (F->e != 2 * r) {
        cout << "representation_theory_domain::representing_matrix9b field "
                "does not have a quadratic subfield" << endl;
        exit(1);
    }
    //q = i_power_j(p, r);
    minus_one = negate(1);
    beta_q = F->frobenius_power(beta, r);
    delta = add(beta_q, beta);
    //gamma = mult(delta, beta);
    //betagamma = mult(beta, gamma);
    //Tgamma = T2(gamma);
    //Tbetagamma = T2(betagamma);
    //nTgamma = negate(Tgamma);
    //cout << "gamma=" << gamma << endl;
    //cout << "betagamma=" << betagamma << endl;
    //cout << "Tgamma=" << Tgamma << endl;
    //cout << "nTgamma=" << nTgamma << endl;
    //cout << "Tbetagamma=" << Tbetagamma << endl;
 
    Int_vec_zero(A, 81);
 
    // changed to n e w base:
    // attention, now transposed!
    A[0 * 9 + 0] = 1;
    A[1 * 9 + 1] = 1;
    A[2 * 9 + 2] = 1;
    A[3 * 9 + 3] = 1;
    A[4 * 9 + 3] = delta;
    A[4 * 9 + 4] = minus_one;
    A[5 * 9 + 5] = 1;
    A[6 * 9 + 5] = delta;
    A[6 * 9 + 6] = minus_one;
    A[7 * 9 + 7] = 1;
    A[8 * 9 + 7] = delta;
    A[8 * 9 + 8] = minus_one;
#if 0
    // changed to n e w base:
    A[0 * 9 + 0] = 1;
    A[1 * 9 + 1] = 1;
    A[2 * 9 + 2] = 1;
    A[4 * 9 + 4] = Tgamma;
    A[4 * 9 + 3] = Tbetagamma;
    A[6 * 9 + 6] = Tgamma;
    A[6 * 9 + 5] = Tbetagamma;
    A[3 * 9 + 3] = nTgamma;
    A[8 * 9 + 8] = Tgamma;
    A[8 * 9 + 7] = Tbetagamma;
    A[5 * 9 + 5] = nTgamma;
    A[7 * 9 + 7] = nTgamma;
#endif
}
 
void representation_theory_domain::representing_matrix8a(int *A,
        int a, int b, int c, int d, int beta)
{
 
 
#if 0
    int delta, omega, gamma, eta, zeta, epsilon, xi, tau;
    int r, q;
 
    r = e / 3;
    if (e != 3 * r) {
        cout << "representation_theory_domain::representing_matrix8a "
                "field does not have a cubic subfield" << endl;
        exit(1);
        }
    q = i_power_j(p, r);
 
    delta = inverse(add(T3(power(beta, 2*q+1)),negate(T3(power(beta,q+2)))));
    omega = inverse(add(T3(power(beta,q*q+2*q+3)),negate(T3(power(beta,q*q+3*q+2)))));
    gamma = add(power(beta,2*q),negate(power(beta,2*q*q)));
    eta = add(power(beta,2*q*q+q),negate(power(beta,q*q+2*q)));
    zeta = add(power(beta,q),negate(power(beta,1)));
    epsilon = add(power(beta,3*q*q+q+2),negate(power(beta,3*q*q+2*q+1)));
    xi = add(power(beta,2*q*q+2*q),negate(power(beta,2*q*q+2)));
    tau = add(power(beta,q*q+1),negate(power(beta,q*q+q)));
 
    //cout << "delta=" << delta << endl;
    //cout << "omega=" << omega << endl;
    //cout << "gamma=" << gamma << endl;
    //cout << "eta=" << eta << endl;
    //cout << "zeta=" << zeta << endl;
    //cout << "epsilon=" << epsilon << endl;
    //cout << "xi=" << xi << endl;
    //cout << "tau=" << tau << endl;
 
A[0 * 8 + 0] = N3(d);
A[0 * 8 + 1] = T3(term3(beta,c,d,1,1,q*q+q));
A[0 * 8 + 2] = T3(term2(c,d,1,q*q+q));
A[0 * 8 + 3] = T3(term2(c,d,q+1,q*q));
A[0 * 8 + 4] = T3(term3(beta,c,d,2,1,q*q+q));
A[0 * 8 + 5] = T3(term3(beta,c,d,q+1,q+1,q*q));
A[0 * 8 + 6] = T3(term3(beta,c,d,2*q+2,q+1,q*q));
A[0 * 8 + 7] = N3(c);
 
A[1*8+0]=mult(delta,T3(term3(gamma,b,d,1,1,q*q+q)));
A[1*8+1]=mult(delta,T3(mult(beta,add(add(term3(gamma,a,d,1,1,q*q+q),term4(gamma,b,c,d,q,q,1,q*q)),term4(gamma,b,c,d,q*q,q*q,1,q)))));
A[1*8+2]=mult(delta,T3(mult(gamma,add(add(term2(a,d,1,q*q+q),term3(b,c,d,1,q,q*q)),term3(b,c,d,1,q*q,q)))));
A[1*8+3]=mult(delta,T3(mult(gamma,add(add(term3(a,c,d,1,q,q*q),term2(b,c,1,q*q+q)),term3(a,c,d,1,q*q,q)))));
A[1*8+4]=mult(delta,T3(mult(mult(beta,beta),add(add(term3(gamma,a,d,1,1,q*q+q),term4(gamma,b,c,d,q,q,1,q*q)),term4(gamma,b,c,d,q*q,q*q,1,q)))));
A[1*8+5]=mult(delta,T3(mult(power(beta,q+1),add(add(term4(gamma,a,c,d,1,1,q,q*q),term4(gamma,a,c,d,q,q,1,q*q)),term3(gamma,b,c,q*q,q*q,q+1)))));
A[1*8+6]=mult(delta,T3(mult(power(beta,2*q+2),add(add(term4(gamma,a,c,d,1,1,q,q*q),term4(gamma,a,c,d,q,q,1,q*q)),term3(gamma,b,c,q*q,q*q,q+1)))));
A[1*8+7]=mult(delta,T3(term3(gamma,a,c,1,1,q*q+q)));
 
A[2*8+0]=mult(delta,T3(term3(eta,b,d,1,1,q*q+q)));
A[2*8+1]=mult(delta,T3(mult(beta,add(add(term3(eta,a,d,1,1,q*q+q),term4(eta,b,c,d,q,q,1,q*q)),term4(eta,b,c,d,q*q,q*q,1,q)))));
A[2*8+2]=mult(delta,T3(mult(eta,add(add(term3(b,c,d,1,q,q*q),term2(a,d,1,q*q+q)),term3(b,c,d,1,q*q,q)))));
A[2*8+3]=mult(delta,T3(mult(eta,add(add(term3(a,c,d,1,q,q*q),term2(b,c,1,q*q+q)),term3(a,c,d,1,q*q,q)))));
A[2*8+4]=mult(delta,T3(mult(power(beta,2),add(add(term3(eta,a,d,1,1,q*q+q),term4(eta,b,c,d,q,q,1,q*q)),term4(eta,b,c,d,q*q,q*q,1,q)))));
A[2*8+5]=mult(delta,T3(mult(power(beta,q+1),add(add(term4(eta,a,c,d,1,1,q,q*q),term4(eta,a,c,d,q,q,1,q*q)),term3(eta,b,c,q*q,q*q,q+1)))));
A[2*8+6]=mult(delta,T3(mult(power(beta,2*q+2),add(add(term4(eta,a,c,d,1,1,q,q*q),term4(eta,a,c,d,q,q,1,q*q)),term3(eta,b,c,q*q,q*q,q+1)))));
A[2*8+7]=mult(delta,T3(term3(eta,a,c,1,1,q*q+q)));
 
A[3*8+0]=mult(omega,T3(term3(epsilon,b,d,1,q+1,q*q)));
A[3*8+1]=mult(omega,T3(mult(beta,add(add(term4(epsilon,a,b,d,1,1,q,q*q),term3(epsilon,b,c,q,q*q+q,1)),term4(epsilon,a,b,d,q*q,1,q*q,q)))));
A[3*8+2]=mult(omega,T3(mult(epsilon,add(add(term3(a,b,d,q,1,q*q),term3(a,b,d,1,q,q*q)),term2(b,c,q+1,q*q)))));
A[3*8+3]=mult(omega,T3(mult(epsilon,add(add(term2(a,d,q+1,q*q),term3(a,b,c,q,1,q*q)),term3(a,b,c,1,q,q*q)))));
A[3*8+4]=mult(omega,T3(mult(power(beta,2),add(add(term4(epsilon,a,b,d,1,1,q,q*q),term3(epsilon,b,c,q,q*q+q,1)),term4(epsilon,a,b,d,q*q,1,q*q,q)))));
A[3*8+5]=mult(omega,T3(mult(power(beta,q+1),add(add(term3(epsilon,a,d,1,q+1,q*q),term4(epsilon,a,b,c,q,q,q*q,1)),term4(epsilon,a,b,c,q*q,1,q*q,q)))));
A[3*8+6]=mult(omega,T3(mult(power(beta,2*q+2),add(add(term3(epsilon,a,d,1,q+1,q*q),term4(epsilon,a,b,c,q,q,q*q,1)),term4(epsilon,a,b,c,q*q,1,q*q,q)))));
A[3*8+7]=mult(omega,T3(term3(epsilon,a,c,1,q+1,q*q)));
 
 
A[4*8+0]=mult(delta,T3(term3(zeta,b,d,1,q*q,q+1)));
A[4*8+1]=mult(delta,T3(mult(beta,add(add(term4(zeta,b,c,d,1,q*q,1,q),term3(zeta,a,d,q,1,q*q+q)),term4(zeta,b,c,d,q*q,q,1,q*q)))));
A[4*8+2]=mult(delta,T3(mult(zeta,add(add(term3(b,c,d,q*q,q,1),term3(b,c,d,q*q,1,q)),term2(a,d,q*q,q+1)))));
A[4*8+3]=mult(delta,T3(mult(zeta,add(add(term2(b,c,q*q,q+1),term3(a,c,d,q*q,q,1)),term3(a,c,d,q*q,1,q)))));
A[4*8+4]=mult(delta,T3(mult(power(beta,2),add(add(term4(zeta,b,c,d,1,q*q,1,q),term3(zeta,a,d,q,1,q*q+q)),term4(zeta,b,c,d,q*q,q,1,q*q)))));
A[4*8+5]=mult(delta,T3(mult(power(beta,q+1),add(add(term3(zeta,b,c,1,q*q,q+1),term4(zeta,a,c,d,q,1,q,q*q)),term4(zeta,a,c,d,q*q,q,1,q*q)))));
A[4*8+6]=mult(delta,T3(mult(power(beta,2*q+2),add(add(term3(zeta,b,c,1,q*q,q+1),term4(zeta,a,c,d,q,1,q,q*q)),term4(zeta,a,c,d,q*q,q,1,q*q)))));
A[4*8+7]=mult(delta,T3(term3(zeta,a,c,1,q*q,q+1)));
 
A[5*8+0]=mult(omega,T3(term3(xi,b,d,1,q+1,q*q)));
A[5*8+1]=mult(omega,T3(mult(beta,add(add(term4(xi,a,b,d,1,1,q,q*q),term3(xi,b,c,q,q*q+q,1)),term4(xi,a,b,d,q*q,1,q*q,q)))));
A[5*8+2]=mult(omega,T3(mult(xi,add(add(term3(a,b,d,q,1,q*q),term3(a,b,d,1,q,q*q)),term2(b,c,q+1,q*q)))));
A[5*8+3]=mult(omega,T3(mult(xi,add(add(term2(a,d,q+1,q*q),term3(a,b,c,q,1,q*q)),term3(a,b,c,1,q,q*q)))));
A[5*8+4]=mult(omega,T3(mult(power(beta,2),add(add(term4(xi,a,b,d,1,1,q,q*q),term3(xi,b,c,q,q*q+q,1)),term4(xi,a,b,d,q*q,1,q*q,q)))));
A[5*8+5]=mult(omega,T3(mult(power(beta,q+1),add(add(term3(xi,a,d,1,q+1,q*q),term4(xi,a,b,c,q,q,q*q,1)),term4(xi,a,b,c,q*q,1,q*q,q)))));
A[5*8+6]=mult(omega,T3(mult(power(beta,2*q+2),add(add(term3(xi,a,d,1,q+1,q*q),term4(xi,a,b,c,q,q,q*q,1)),term4(xi,a,b,c,q*q,1,q*q,q)))));
A[5*8+7]=mult(omega,T3(term3(xi,a,c,1,q+1,q*q)));
 
A[6*8+0]=mult(omega,T3(term3(tau,b,d,1,q+1,q*q)));
A[6*8+1]=mult(omega,T3(mult(beta,add(add(term4(tau,a,b,d,1,1,q,q*q),term3(tau,b,c,q,q*q+q,1)),term4(tau,a,b,d,q*q,1,q*q,q)))));
A[6*8+2]=mult(omega,T3(mult(tau,add(add(term3(a,b,d,q,1,q*q),term3(a,b,d,1,q,q*q)),term2(b,c,q+1,q*q)))));
A[6*8+3]=mult(omega,T3(mult(tau,add(add(term2(a,d,q+1,q*q),term3(a,b,c,q,1,q*q)),term3(a,b,c,1,q,q*q)))));
A[6*8+4]=mult(omega,T3(mult(power(beta,2),add(add(term4(tau,a,b,d,1,1,q,q*q),term3(tau,b,c,q,q*q+q,1)),term4(tau,a,b,d,q*q,1,q*q,q)))));
A[6*8+5]=mult(omega,T3(mult(power(beta,q+1),add(add(term3(tau,a,d,1,q+1,q*q),term4(tau,a,b,c,q,q,q*q,1)),term4(tau,a,b,c,q*q,1,q*q,q)))));
A[6*8+6]=mult(omega,T3(mult(power(beta,2*q+2),add(add(term3(tau,a,d,1,q+1,q*q),term4(tau,a,b,c,q,q,q*q,1)),term4(tau,a,b,c,q*q,1,q*q,q)))));
A[6*8+7]=mult(omega,T3(term3(tau,a,c,1,q+1,q*q)));
 
A[7 * 8 + 0] = N3(b);
A[7 * 8 + 1] = T3(term3(beta,a,b,1,1,q*q+q));
A[7 * 8 + 2] = T3(term2(a,b,1,q*q+q));
A[7 * 8 + 3] = T3(term2(a,b,q+1,q*q));
A[7 * 8 + 4] = T3(term3(beta,a,b,2,1,q*q+q));
A[7 * 8 + 5] = T3(term3(beta,a,b,q+1,q+1,q*q));
A[7 * 8 + 6] = T3(term3(beta,a,b,2*q+2,q+1,q*q));
A[7 * 8 + 7] = N3(a);
#endif
}
 
void representation_theory_domain::representing_matrix8b(int *A, int beta)
{
    int r, q, delta, omega; //, i;
    number_theory::number_theory_domain NT;
 
    r = F->e / 3;
    if (F->e != 3 * r) {
        cout << "representation_theory_domain::representing_matrix8b "
                "field does not have a cubic subfield" << endl;
        exit(1);
    }
    q = NT.i_power_j(F->p, r);
 
    delta = inverse(add(T3(power(beta, 2*q+1)),negate(T3(power(beta,q+2)))));
    omega = inverse(add(T3(power(beta,q*q+2*q+3)),negate(T3(power(beta,q*q+3*q+2)))));
    cout << "delta=" << delta << endl;
    cout << "omega=" << omega << endl;
 
    Int_vec_zero(A, 64);
 
    A[0 * 8 + 0] = 1;
    A[7 * 8 + 7] = 1;
#if 1
    A[1 * 8 + 1] = mult(delta,T3(add(power(beta,3),negate(power(beta,2*q+1)))));
    A[1 * 8 + 2] = mult(delta,T3(add(power(beta,2),negate(power(beta,2*q)))));
    A[1 * 8 + 4] = mult(delta,T3(add(power(beta,4),negate(power(beta,2*q+2)))));
    A[2 * 8 + 1] = mult(delta,T3(add(power(beta,2*q+2),negate(power(beta,q+3)))));
    A[2 * 8 + 2] = mult(delta,T3(add(power(beta,2*q+1),negate(power(beta,q+2)))));
    A[2 * 8 + 4] = mult(delta,T3(add(power(beta,2*q+3),negate(power(beta,q+4)))));
    A[3 * 8 + 3] = mult(omega,T3(add(power(beta,q*q+2*q+3),negate(power(beta,2*q*q+q+3)))));
    A[3 * 8 + 5] = mult(omega,T3(add(power(beta,2*q*q+4*q+2),negate(power(beta,q*q+4*q+3)))));
    A[3 * 8 + 6] = mult(omega,T3(add(power(beta,2*q*q+5*q+3),negate(power(beta,q*q+5*q+4)))));
    A[4 * 8 + 1] = mult(delta,T3(add(power(beta,q+1),negate(power(beta,2)))));
    A[4 * 8 + 2] = mult(delta,T3(add(power(beta,q),negate(power(beta,1)))));
    A[4 * 8 + 4] = mult(delta,T3(add(power(beta,q+2),negate(power(beta,3)))));
    A[5 * 8 + 3] = mult(omega,T3(add(power(beta,2*q*q+2),negate(power(beta,2*q+2)))));
    A[5 * 8 + 5] = mult(omega,T3(add(power(beta,3*q+3),negate(power(beta,2*q*q+3*q+1)))));
    A[5 * 8 + 6] = mult(omega,T3(add(power(beta,4*q+4),negate(power(beta,2*q*q+4*q+2)))));
    A[6 * 8 + 3] = mult(omega,T3(add(power(beta,q+1),negate(power(beta,q*q+1)))));
    A[6 * 8 + 5] = mult(omega,T3(add(power(beta,q*q+2*q+1),negate(power(beta,2*q+2)))));
    A[6 * 8 + 6] = mult(omega,T3(add(power(beta,q*q+3*q+2),negate(power(beta,3*q+3)))));
#else
    A[1 * 8 + 1] = mult(delta,T3(add(power(beta,q+2),negate(power(beta,3*q)))));
    A[1 * 8 + 2] = mult(delta,T3(add(power(beta,2),negate(power(beta,2*q)))));
    A[1 * 8 + 4] = mult(delta,T3(add(power(beta,2*q+2),negate(power(beta,4*q)))));
    A[2 * 8 + 1] = mult(delta,T3(add(power(beta,2*q+1),negate(power(beta,2*q+2)))));
    A[2 * 8 + 2] = mult(delta,T3(add(power(beta,2*q+1),negate(power(beta,q+2)))));
    A[2 * 8 + 4] = mult(delta,T3(add(power(beta,4*q+1),negate(power(beta,3*q+2)))));
    A[4 * 8 + 1] = mult(delta,T3(add(power(beta,2),negate(power(beta,q*q+1)))));
    A[4 * 8 + 2] = mult(delta,T3(add(power(beta,1),negate(power(beta,q*q)))));
    A[4 * 8 + 4] = mult(delta,T3(add(power(beta,3),negate(power(beta,q*q+2)))));
    A[3 * 8 + 3] = mult(omega,T3(add(power(beta,q*q+2*q+3),negate(power(beta,2*q*q+q+3)))));
    A[3 * 8 + 5] = mult(omega,T3(add(power(beta,q*q+3*q+4),negate(power(beta,2*q*q+2*q+4)))));
    A[3 * 8 + 6] = mult(omega,T3(add(power(beta,q*q+4*q+5),negate(power(beta,2*q*q+3*q+5)))));
    A[5 * 8 + 3] = mult(omega,T3(add(power(beta,2*q*q+2),negate(power(beta,2*q+2)))));
    A[5 * 8 + 5] = mult(omega,T3(add(power(beta,2*q*q+q+3),negate(power(beta,3*q+3)))));
    A[5 * 8 + 6] = mult(omega,T3(add(power(beta,2*q*q+2*q+4),negate(power(beta,4*q+4)))));
    A[6 * 8 + 3] = mult(omega,T3(add(power(beta,q+1),negate(power(beta,q*q+1)))));
    A[6 * 8 + 5] = mult(omega,T3(add(power(beta,2*q+2),negate(power(beta,q*q+q+2)))));
    A[6 * 8 + 6] = mult(omega,T3(add(power(beta,3*q+3),negate(power(beta,q*q+2*q+3)))));
    //transpose_matrix_in_place(A, 8);
#endif
}
 
int representation_theory_domain::Term1(int a1, int e1)
{
    int x;
 
    x = term1(a1, e1);
    return T2(x);
}
 
int representation_theory_domain::Term2(int a1, int a2, int e1, int e2)
{
    int x;
 
    x = term2(a1, a2, e1, e2);
    return T2(x);
}
 
int representation_theory_domain::Term3(int a1, int a2, int a3, int e1, int e2, int e3)
{
    int x;
 
    x = term3(a1, a2, a3, e1, e2, e3);
    return T2(x);
}
 
int representation_theory_domain::Term4(int a1, int a2, int a3, int a4,
        int e1, int e2, int e3, int e4)
{
    int x;
 
    x = term4(a1, a2, a3, a4, e1, e2, e3, e4);
    return T2(x);
}
 
int representation_theory_domain::Term5(int a1, int a2, int a3, int a4, int a5,
        int e1, int e2, int e3, int e4, int e5)
{
    int x;
 
    x = term5(a1, a2, a3, a4, a5, e1, e2, e3, e4, e5);
    return T2(x);
}
 
int representation_theory_domain::term1(int a1, int e1)
{
    int x;
 
    x = 1;
    if (e1) {
        x = mult(x, power(a1, e1));
    }
    return x;
}
 
int representation_theory_domain::term2(int a1, int a2, int e1, int e2)
{
    int x;
 
    x = 1;
    if (e1) {
        x = mult(x, power(a1, e1));
    }
    if (e2) {
        x = mult(x, power(a2, e2));
    }
    return x;
}
 
int representation_theory_domain::term3(int a1, int a2, int a3, int e1, int e2, int e3)
{
    int x;
 
    x = 1;
    if (e1) {
        x = mult(x, power(a1, e1));
    }
    if (e2) {
        x = mult(x, power(a2, e2));
    }
    if (e3) {
        x = mult(x, power(a3, e3));
    }
    return x;
}
 
int representation_theory_domain::term4(int a1, int a2, int a3, int a4,
        int e1, int e2, int e3, int e4)
{
    int x;
 
    x = 1;
    if (e1) {
        x = mult(x, power(a1, e1));
    }
    if (e2) {
        x = mult(x, power(a2, e2));
    }
    if (e3) {
        x = mult(x, power(a3, e3));
    }
    if (e4) {
        x = mult(x, power(a4, e4));
    }
    return x;
}
 
int representation_theory_domain::term5(int a1, int a2, int a3, int a4, int a5,
        int e1, int e2, int e3, int e4, int e5)
{
    int x;
 
    x = 1;
    if (e1) {
        x = mult(x, power(a1, e1));
    }
    if (e2) {
        x = mult(x, power(a2, e2));
    }
    if (e3) {
        x = mult(x, power(a3, e3));
    }
    if (e4) {
        x = mult(x, power(a4, e4));
    }
    if (e5) {
        x = mult(x, power(a5, e5));
    }
    return x;
}
 
int representation_theory_domain::m_term(int q, int a1, int a2, int a3)
{
    int x;
 
    x = 1;
    x = mult(x, power(a1, q * q));
    x = mult(x, power(a2, q));
    x = mult(x, a3);
    return x;
}
 
int representation_theory_domain::beta_trinomial(int q, int beta, int a1, int a2, int a3)
{
    int x;
 
    x = 1;
    x = mult(x, power(beta, a1 * q * q));
    x = mult(x, power(beta, a2 * q));
    x = mult(x, power(beta, a3));
    return x;
}
 
int representation_theory_domain::T3product2(int a1, int a2)
{
    int x;
 
    x = mult(a1, a2);
    return T3(x);
}
 
int representation_theory_domain::add(int a, int b)
{
    return F->add(a, b);
}
 
int representation_theory_domain::add3(int a, int b, int c)
{
    return F->add3(a, b, c);
}
 
int representation_theory_domain::negate(int a)
{
    return F->negate(a);
}
 
int representation_theory_domain::twice(int a)
{
    return F->twice(a);
}
 
 
 
int representation_theory_domain::mult(int a, int b)
{
    return F->mult(a, b);
}
 
int representation_theory_domain::inverse(int a)
{
    return F->inverse(a);
}
 
 
int representation_theory_domain::power(int a, int n)
{
    return F->power(a, n);
}
 
int representation_theory_domain::T2(int a)
{
    return F->T2(a);
}
 
int representation_theory_domain::T3(int a)
{
    return F->T3(a);
}
 
int representation_theory_domain::N2(int a)
{
    return F->N2(a);
}
 
int representation_theory_domain::N3(int a)
{
    return F->N3(a);
}
 
}}}