result += check_equal_lst(clifford_to_lst(lst_to_clifford(e, c), c, true), e);
/* Moebius map (both forms) checks for symmetric metrics only */
- matrix M1(2, 2), M2(2, 2);
c = clifford_unit(nu, A);
e = clifford_moebius_map(0, dirac_ONE(),
- dirac_ONE(), 0, lst{t, x, y, z}, A);
+ dirac_ONE(), 0, lst{t, x, y, z}, A);
/* this is just the inversion*/
- M1 = 0, dirac_ONE(),
- dirac_ONE(), 0;
+ matrix M1 = {{0, dirac_ONE()},
+ {dirac_ONE(), 0}};
e1 = clifford_moebius_map(M1, lst{t, x, y, z}, A);
/* the inversion again*/
result += check_equal_lst(e, e1);
result += check_equal_lst(e, e1);
e = clifford_moebius_map(dirac_ONE(), lst_to_clifford(lst{1, 2, 3, 4}, nu, A),
- 0, dirac_ONE(), lst{t, x, y, z}, A);
+ 0, dirac_ONE(), lst{t, x, y, z}, A);
/*this is just a shift*/
- M2 = dirac_ONE(), lst_to_clifford(lst{1, 2, 3, 4}, c),
- 0, dirac_ONE();
+ matrix M2 = {{dirac_ONE(), lst_to_clifford(lst{1, 2, 3, 4}, c),},
+ {0, dirac_ONE()}};
e1 = clifford_moebius_map(M2, lst{t, x, y, z}, c);
/* the same shift*/
result += check_equal_lst(e, e1);
realsymbol a("a");
varidx mu(symbol("mu", "\\mu"), 1);
- ex e = clifford_unit(mu, diag_matrix(lst{-1})), e0 = e.subs(mu==0);
+ ex e = clifford_unit(mu, diag_matrix({-1})), e0 = e.subs(mu==0);
result += ( exp(a*e0)*e0*e0 == -exp(e0*a) ) ? 0 : 1;
return result;
result += clifford_check5(); cout << '.' << flush;
// anticommuting, symmetric examples
- result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst{-1, 1, 1, 1})));
- result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, 1, 1, 1})));; cout << '.' << flush;
- result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst{-1, -1, -1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, -1, -1, -1})));; cout << '.' << flush;
- result += clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, 1, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, 1, 1, -1})));; cout << '.' << flush;
- result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst{-1, 0, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, 0, 1, -1})));; cout << '.' << flush;
- result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst{-3, 0, 2, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-3, 0, 2, -1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 1, 1, 1})));
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, 1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, -1, -1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, -1, -1, -1})));; cout << '.' << flush;
+ result += clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, 1, -1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 0, 1, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 0, 1, -1})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-3, 0, 2, -1})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-3, 0, 2, -1})));; cout << '.' << flush;
realsymbol s("s"), t("t"); // symbolic entries in matric
- result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix(lst{-1, 1, s, t})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix(lst{-1, 1, s, t})));; cout << '.' << flush;
+ result += clifford_check6<varidx>(ex_to<matrix>(diag_matrix({-1, 1, s, t})))+clifford_check6<idx>(ex_to<matrix>(diag_matrix({-1, 1, s, t})));; cout << '.' << flush;
matrix A(4, 4);
- A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=0
- 0, -1, 0, 0,
- 0, 0, 0, -1,
- 0, 0, 1, 0;
+ A = {{1, 0, 0, 0}, // anticommuting, not symmetric, Tr=0
+ {0, -1, 0, 0},
+ {0, 0, 0, -1},
+ {0, 0, 1, 0}};
result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
- A = 1, 0, 0, 0, // anticommuting, not symmetric, Tr=2
- 0, 1, 0, 0,
- 0, 0, 0, -1,
- 0, 0, 1, 0;
+ A = {{1, 0, 0, 0}, // anticommuting, not symmetric, Tr=2
+ {0, 1, 0, 0},
+ {0, 0, 0, -1},
+ {0, 0, 1, 0}};
result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
- A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=0
- 0, -1, 0, 0,
- 0, 0, 0, -1,
- 0, 0, -1, 0;
+ A = {{1, 0, 0, 0}, // not anticommuting, symmetric, Tr=0
+ {0, -1, 0, 0},
+ {0, 0, 0, -1},
+ {0, 0, -1, 0}};
result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
- A = 1, 0, 0, 0, // not anticommuting, symmetric, Tr=2
- 0, 1, 0, 0,
- 0, 0, 0, -1,
- 0, 0, -1, 0;
+ A = {{1, 0, 0, 0}, // not anticommuting, symmetric, Tr=2
+ {0, 1, 0, 0},
+ {0, 0, 0, -1},
+ {0, 0, -1, 0}};
result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
- A = 1, 1, 0, 0, // not anticommuting, not symmetric, Tr=4
- 0, 1, 1, 0,
- 0, 0, 1, 1,
- 0, 0, 0, 1;
+ A = {{1, 1, 0, 0}, // not anticommuting, not symmetric, Tr=4
+ {0, 1, 1, 0},
+ {0, 0, 1, 1},
+ {0, 0, 0, 1}};
result += clifford_check6<varidx>(A)+clifford_check6<idx>(A);; cout << '.' << flush;
symbol dim("D");
symbol g("g"), h("h"), i("i");
// check symbolic trivial matrix determinant
- m1.set(0,0,a);
+ m1 = matrix{{a}};
det = m1.determinant();
if (det != a) {
clog << "determinant of 1x1 matrix " << m1
}
// check generic dense symbolic 2x2 matrix determinant
- m2.set(0,0,a).set(0,1,b);
- m2.set(1,0,c).set(1,1,d);
+ m2 = matrix{{a, b},
+ {c, d}};
det = m2.determinant();
if (det != (a*d-b*c)) {
clog << "determinant of 2x2 matrix " << m2
}
// check generic dense symbolic 3x3 matrix determinant
- m3.set(0,0,a).set(0,1,b).set(0,2,c);
- m3.set(1,0,d).set(1,1,e).set(1,2,f);
- m3.set(2,0,g).set(2,1,h).set(2,2,i);
+ m3 = matrix{{a, b, c},
+ {d, e, f},
+ {g, h, i}};
det = m3.determinant();
if (det != (a*e*i - a*f*h - d*b*i + d*c*h + g*b*f - g*c*e)) {
clog << "determinant of 3x3 matrix " << m3
}
// check dense numeric 3x3 matrix determinant
- m3.set(0,0,numeric(0)).set(0,1,numeric(-1)).set(0,2,numeric(3));
- m3.set(1,0,numeric(3)).set(1,1,numeric(-2)).set(1,2,numeric(2));
- m3.set(2,0,numeric(3)).set(2,1,numeric(4)).set(2,2,numeric(-2));
+ m3 = matrix{{0, -1, 3},
+ {3, -2, 2},
+ {3, 4, -2}};
det = m3.determinant();
if (det != 42) {
clog << "determinant of 3x3 matrix " << m3
}
// check dense symbolic 2x2 matrix determinant
- m2.set(0,0,a/(a-b)).set(0,1,1);
- m2.set(1,0,b/(a-b)).set(1,1,1);
+ m2 = matrix{{a/(a-b), 1},
+ {b/(a-b), 1}};
det = m2.determinant();
if (det != 1) {
if (det.normal() == 1) // only half wrong
}
// check characteristic polynomial
- m3.set(0,0,a).set(0,1,-2).set(0,2,2);
- m3.set(1,0,3).set(1,1,a-1).set(1,2,2);
- m3.set(2,0,3).set(2,1,4).set(2,2,a-3);
+ m3 = matrix{{a, -2, 2},
+ {3, a-1, 2},
+ {3, 4, a-3}};
ex p = m3.charpoly(a);
if (p != 0) {
clog << "charpoly of 3x3 matrix " << m3
static unsigned matrix_invert2()
{
unsigned result = 0;
- matrix m(2,2);
symbol a("a"), b("b"), c("c"), d("d");
- m.set(0,0,a).set(0,1,b);
- m.set(1,0,c).set(1,1,d);
+ matrix m = {{a, b},
+ {c, d}};
matrix m_i = m.inverse();
ex det = m.determinant();
static unsigned matrix_invert3()
{
unsigned result = 0;
- matrix m(3,3);
symbol a("a"), b("b"), c("c");
symbol d("d"), e("e"), f("f");
symbol g("g"), h("h"), i("i");
- m.set(0,0,a).set(0,1,b).set(0,2,c);
- m.set(1,0,d).set(1,1,e).set(1,2,f);
- m.set(2,0,g).set(2,1,h).set(2,2,i);
+ matrix m = {{a, b, c},
+ {d, e, f},
+ {g, h, i}};
matrix m_i = m.inverse();
ex det = m.determinant();
static unsigned matrix_solve2()
{
// check the solution of the multiple system A*X = B:
- // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
- // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ]
- // [ a -2 2 ] [ x2 y2 ] [ a 4 ]
+ // [ 1 2 -1 ] [ x0 y0 ] [ 4 0 ]
+ // [ 1 4 -2 ]*[ x1 y1 ] = [ 7 0 ]
+ // [ a -2 2 ] [ x2 y2 ] [ a 4 ]
unsigned result = 0;
symbol a("a");
symbol x0("x0"), x1("x1"), x2("x2");
symbol y0("y0"), y1("y1"), y2("y2");
- matrix A(3,3);
- A.set(0,0,1).set(0,1,2).set(0,2,-1);
- A.set(1,0,1).set(1,1,4).set(1,2,-2);
- A.set(2,0,a).set(2,1,-2).set(2,2,2);
- matrix B(3,2);
- B.set(0,0,4).set(1,0,7).set(2,0,a);
- B.set(0,1,0).set(1,1,0).set(2,1,4);
- matrix X(3,2);
- X.set(0,0,x0).set(1,0,x1).set(2,0,x2);
- X.set(0,1,y0).set(1,1,y1).set(2,1,y2);
- matrix cmp(3,2);
- cmp.set(0,0,1).set(1,0,3).set(2,0,3);
- cmp.set(0,1,0).set(1,1,2).set(2,1,4);
+ matrix A = {{1, 2, -1},
+ {1, 4, -2},
+ {a, -2, 2}};
+ matrix B = {{4, 0},
+ {7, 0},
+ {a, 4}};
+ matrix X = {{x0 ,y0},
+ {x1, y1},
+ {x2, y2}};
+ matrix cmp = {{1, 0},
+ {3, 2},
+ {3, 4}};
matrix sol(A.solve(X, B));
- for (unsigned ro=0; ro<3; ++ro)
- for (unsigned co=0; co<2; ++co)
- if (cmp(ro,co) != sol(ro,co))
- result = 1;
- if (result) {
+ if (cmp != sol) {
clog << "Solving " << A << " * " << X << " == " << B << endl
<< "erroneously returned " << sol << endl;
+ result = 1;
}
-
+
return result;
}
{
unsigned result = 0;
- matrix S(2, 2, lst{
- 1, 2,
- 3, 4
- }), T(2, 2, lst{
- 1, 1,
- 2, -1
- }), R(2, 2, lst{
- 27, 14,
- 36, 26
- });
+ matrix S {{1, 2},
+ {3, 4}};
+ matrix T {{1, 1},
+ {2, -1}};
+ matrix R {{27, 14},
+ {36, 26}};
ex e = ((S + T) * (S + 2*T));
ex f = e.evalm();
}
// a trivial rank one example
- m = 1, 0, 0,
- 2, 0, 0,
- 3, 0, 0;
+ m = {{1, 0, 0},
+ {2, 0, 0},
+ {3, 0, 0}};
if (m.rank() != 1) {
clog << "The rank of " << m << " was not computed correctly." << endl;
++result;
}
// an example from Maple's help with rank two
- m = x, 1, 0,
- 0, 0, 1,
- x*y, y, 1;
+ m = {{x, 1, 0},
+ {0, 0, 1},
+ {x*y, y, 1}};
if (m.rank() != 2) {
clog << "The rank of " << m << " was not computed correctly." << endl;
++result;
static unsigned matrix_misc()
{
unsigned result = 0;
- matrix m1(2,2);
symbol a("a"), b("b"), c("c"), d("d"), e("e"), f("f");
- m1.set(0,0,a).set(0,1,b);
- m1.set(1,0,c).set(1,1,d);
+ matrix m1 = {{a, b},
+ {c, d}};
ex tr = trace(m1);
// check a simple trace
<< " erroneously returned " << m2 << endl;
++result;
}
- matrix m3(3,2);
- m3.set(0,0,a).set(0,1,b);
- m3.set(1,0,c).set(1,1,d);
- m3.set(2,0,e).set(2,1,f);
+ matrix m3 = {{a, b},
+ {c, d},
+ {e, f}};
if (transpose(transpose(m3)) != m3) {
clog << "transposing 3x2 matrix " << m3 << " twice"
<< " erroneously returned " << transpose(transpose(m3)) << endl;
static const ex det1()
{
- matrix d1(15,15);
- d1 = a6, a5, a4, a3, a2, a1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0,
- 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0,
- 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0,
- 0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1,
- 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0,
- 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0,
- 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0,
- 0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1,
- 0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1,
- 0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0,
- 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0;
+ matrix d1 = {{a6, a5, a4, a3, a2, a1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0},
+ {0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0},
+ {0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0},
+ {0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1},
+ {0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0},
+ {0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0},
+ {0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0},
+ {0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1},
+ {0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1},
+ {0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0},
+ {0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0}};
return d1.determinant();
}
static const ex det2()
{
- matrix d2(15,15);
- d2 = b6, b5, b4, b3, b2, b1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0,
- 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0,
- 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0,
- 0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1,
- 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0,
- 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0,
- 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0,
- 0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1,
- 0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1,
- 0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0,
- 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0;
+ matrix d2 = {{b6, b5, b4, b3, b2, b1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0},
+ {0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0, 0},
+ {0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0},
+ {0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1},
+ {0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0},
+ {0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0},
+ {0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0},
+ {0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1},
+ {0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1},
+ {0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0},
+ {0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0}};
return d2.determinant();
}
static const ex det3()
{
- matrix d3(15,15);
- d3 = c6, c5, c4, c3, c2, c1, 0, 0, 0, 0, 0, 0, 0, 0, 0,
- 0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0,
- 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0,
- 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0,
- 0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1,
- 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0,
- 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0,
- 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0,
- 0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1,
- 0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1,
- 0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0,
- 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0,
- 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0;
+ matrix d3 = {{c6, c5, c4, c3, c2, c1, 0, 0, 0, 0, 0, 0, 0, 0, 0},
+ {0, 0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0},
+ {0, c6, 0, c5, c4, 0, c3, c2, c1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0, 0},
+ {0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1, 0},
+ {0, 0, 0, 0, 0, c6, 0, 0, c5, c4, 0, 0, c3, c2, c1},
+ {0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0, 0},
+ {0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1, 0},
+ {0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0, 0},
+ {0, 0, a6, 0, a5, a4, 0, a3, a2, a1, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, 0, a6, 0, 0, a5, a4, 0, 0, a3, a2, a1},
+ {0, 0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1},
+ {0, 0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0},
+ {0, b6, 0, b5, b4, 0, b3, b2, b1, 0, 0, 0, 0, 0, 0},
+ {0, 0, 0, 0, b6, 0, 0, b5, b4, 0, 0, b3, b2, b1, 0}};
return d3.determinant();
}