Edit detail for SandBox Sedenion Algebra is Frobenius In Just One Way revision 2 of 5

Error: export AXIOM=/usr/local/lib/fricas/target/x86_64-unknown-linux; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/fricas/target/x86_64-unknown-linux/lib; LANG=en_US.UTF-8 $AXIOM/bin/AXIOMsys < /var/zope2/var/LatexWiki/3205365606214558365-25px.axm
Killed

Checking for foreign routines
AXIOM="/usr/local/lib/fricas/target/x86_64-unknown-linux"
spad-lib="/usr/local/lib/fricas/target/x86_64-unknown-linux/lib/libspad.so"
foreign routines found
openServer result -2
                 FriCAS (AXIOM fork) Computer Algebra System 
                         Version: FriCAS 2010-12-08
                Timestamp: Tuesday April 5, 2011 at 13:07:45 
-----------------------------------------------------------------------------
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave FriCAS and return to shell.
-----------------------------------------------------------------------------
(1) -> (1) -> (1) -> (1) -> (1) -> )library CARTEN MONAL PROP LIN CALEY
   CartesianTensor is now explicitly exposed in frame initial 
   CartesianTensor will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/CARTEN.NRLIB/CARTEN
   Monoidal is now explicitly exposed in frame initial 
   Monoidal will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/MONAL.NRLIB/MONAL
   Prop is now explicitly exposed in frame initial 
   Prop will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/PROP.NRLIB/PROP
   LinearOperator is now explicitly exposed in frame initial 
   LinearOperator will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/LIN.NRLIB/LIN
   CaleyDickson is now explicitly exposed in frame initial 
   CaleyDickson will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/CALEY.NRLIB/CALEY
(1) -> -- summation
macro Σ(x,i,n)==reduce(+,[x for i in n])

                                                                   Type: Void
list
macro Ξ(f,i,n)==[f for i in n]
                                                                   Type: Void
subscript
macro sb == subscript

                                                                   Type: Void
(4) -> dim:=16

$$
16 
\leqno(4)
$$
                                                        Type: PositiveInteger
macro ℒ == List
                                                                   Type: Void
macro ℂ == CaleyDickson
                                                                   Type: Void
macro ℚ == Expression Integer
                                                                   Type: Void
𝐋 := LinearOperator(dim, OVAR [], ℚ)


$$
LinearOperator(16,OrderedVariableList([]),Expression(Integer)) 
\leqno(8)
$$
                                                                   Type: Type
𝐞:ℒ 𝐋      := basisVectors()

$$
\left[
{| \sb {1}}, \: {| \sb {2}}, \: {| \sb {3}}, \: {| \sb {4}}, \: {| \sb {5}}, 
\: {| \sb {6}}, \: {| \sb {7}}, \: {| \sb {8}}, \: {| \sb {9}}, \: {| \sb 
{{10}}}, \: {| \sb {{11}}}, \: {| \sb {{12}}}, \: {| \sb {{13}}}, \: {| \sb 
{{14}}}, \: {| \sb {{15}}}, \: {| \sb {{16}}} 
\right]
\leqno(9)
$$
   Type: List(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
𝐝:ℒ 𝐋      := basisForms()

$$
\left[
{| \sb {{\ }} \sp {1}}, \: {| \sb {{\ }} \sp {2}}, \: {| \sb {{\ }} \sp {3}}, 
\: {| \sb {{\ }} \sp {4}}, \: {| \sb {{\ }} \sp {5}}, \: {| \sb {{\ }} \sp 
{6}}, \: {| \sb {{\ }} \sp {7}}, \: {| \sb {{\ }} \sp {8}}, \: {| \sb {{\ }} 
\sp {9}}, \: {| \sb {{\ }} \sp {{10}}}, \: {| \sb {{\ }} \sp {{11}}}, \: {| 
\sb {{\ }} \sp {{12}}}, \: {| \sb {{\ }} \sp {{13}}}, \: {| \sb {{\ }} \sp 
{{14}}}, \: {| \sb {{\ }} \sp {{15}}}, \: {| \sb {{\ }} \sp {{16}}} 
\right]
\leqno(10)
$$
   Type: List(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
I:𝐋:=[1];   -- identity for composition
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
X:𝐋:=[2,1]; -- twist
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
(13) -> --q0:=sb('q,[0])
q0:=1  -- not split-complex


$$
1 
\leqno(13)
$$
                                                        Type: PositiveInteger
--q1:=sb('q,[1])
q1:=1  -- not co-quaternion

$$
1 
\leqno(14)
$$
                                                        Type: PositiveInteger
--q2:=sb('q,[2])
q2:=1  -- not split-octonion

$$
1 
\leqno(15)
$$
                                                        Type: PositiveInteger
q3:=sb('q,[3])

$$
q \sb {3} 
\leqno(16)
$$
                                                                 Type: Symbol
--q3:=1  -- split-sedennion
QQ := ℂ(ℂ(ℂ(ℂ(ℚ,'i,q0),'j,q1),'k,q2),'l,q3);
                                                                   Type: Type
(18) -> B:ℒ QQ := map(x +-> hyper x,1$SQMATRIX(dim,ℚ)::ℒ ℒ ℚ)


$$
\left[
1, \: i, \: j, \: {ij}, \: k, \: {ik}, \: {jk}, \: {{ij}k}, \: l, \: {il}, \: 
{jl}, \: {{ij}l}, \: {kl}, \: {{ik}l}, \: {{jk}l}, \: {{{ij}k}l} 
\right]
\leqno(18)
$$

Type: List(CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Expression(Integer),i,1),j,1),k,1),l,*01q(3)))
Multiplication table:
M:Matrix QQ := matrix Ξ(Ξ(B.i*B.j, i,1..dim), j,1..dim)

$$
\left[
\begin{array}{cccccccccccccccc}
1 & i & j & {ij} & k & {ik} & {jk} & {{ij}k} & l & {il} & {jl} & {{ij}l} & 
{kl} & {{ik}l} & {{jk}l} & {{{ij}k}l} \ 
i & -1 & -{ij} & j & {-ik} & k & {{ij}k} & -{jk} & {-il} & l & {{ij}l} & 
{-jl} & {{ik}l} & -{kl} & {{-{ij}k}l} & {{jk}l} \ 
j & {ij} & -1 & -i & -{jk} & {-{ij}k} & k & {ik} & {-jl} & {-{ij}l} & l & 
{il} & {{jk}l} & {{{ij}k}l} & -{kl} & {{-ik}l} \ 
{ij} & -j & i & -1 & {-{ij}k} & {jk} & {-ik} & k & {-{ij}l} & {jl} & {-il} & 
l & {{{ij}k}l} & {-{jk}l} & {{ik}l} & -{kl} \ 
k & {ik} & {jk} & {{ij}k} & -1 & -i & -j & -{ij} & -{kl} & {{-ik}l} & 
{-{jk}l} & {{-{ij}k}l} & l & {il} & {jl} & {{ij}l} \ 
{ik} & -k & {{ij}k} & -{jk} & i & -1 & {ij} & -j & {{-ik}l} & {kl} & 
{{-{ij}k}l} & {{jk}l} & {-il} & l & {-{ij}l} & {jl} \ 
{jk} & {-{ij}k} & -k & {ik} & j & -{ij} & -1 & i & {-{jk}l} & {{{ij}k}l} & 
{kl} & {{-ik}l} & {-jl} & {{ij}l} & l & {-il} \ 
{{ij}k} & {jk} & {-ik} & -k & {ij} & j & -i & -1 & {{-{ij}k}l} & {-{jk}l} & 
{{ik}l} & {kl} & {-{ij}l} & {-jl} & {il} & l \ 
l & {il} & {jl} & {{ij}l} & {kl} & {{ik}l} & {{jk}l} & {{{ij}k}l} & -{q \sb 
{3}} & {-{q \sb {3}}i} & {-{q \sb {3}}j} & {{-{q \sb {3}}i}j} & {-{q \sb 
{3}}k} & {{-{q \sb {3}}i}k} & {{-{q \sb {3}}j}k} & {{{-{q \sb {3}}i}j}k} \ 
{il} & -l & {{ij}l} & {-jl} & {{ik}l} & -{kl} & {{-{ij}k}l} & {{jk}l} & {{q 
\sb {3}}i} & -{q \sb {3}} & {{{q \sb {3}}i}j} & {-{q \sb {3}}j} & {{{q \sb 
{3}}i}k} & {-{q \sb {3}}k} & {{{-{q \sb {3}}i}j}k} & {{{q \sb {3}}j}k} \ 
{jl} & {-{ij}l} & -l & {il} & {{jk}l} & {{{ij}k}l} & -{kl} & {{-ik}l} & {{q 
\sb {3}}j} & {{-{q \sb {3}}i}j} & -{q \sb {3}} & {{q \sb {3}}i} & {{{q \sb 
{3}}j}k} & {{{{q \sb {3}}i}j}k} & {-{q \sb {3}}k} & {{-{q \sb {3}}i}k} \ 
{{ij}l} & {jl} & {-il} & -l & {{{ij}k}l} & {-{jk}l} & {{ik}l} & -{kl} & {{{q 
\sb {3}}i}j} & {{q \sb {3}}j} & {-{q \sb {3}}i} & -{q \sb {3}} & {{{{q \sb 
{3}}i}j}k} & {{-{q \sb {3}}j}k} & {{{q \sb {3}}i}k} & {-{q \sb {3}}k} \ 
{kl} & {{-ik}l} & {-{jk}l} & {{-{ij}k}l} & -l & {il} & {jl} & {{ij}l} & {{q 
\sb {3}}k} & {{-{q \sb {3}}i}k} & {{-{q \sb {3}}j}k} & {{{-{q \sb {3}}i}j}k} 
& -{q \sb {3}} & {{q \sb {3}}i} & {{q \sb {3}}j} & {{{q \sb {3}}i}j} \ 
{{ik}l} & {kl} & {{-{ij}k}l} & {{jk}l} & {-il} & -l & {-{ij}l} & {jl} & {{{q 
\sb {3}}i}k} & {{q \sb {3}}k} & {{{-{q \sb {3}}i}j}k} & {{{q \sb {3}}j}k} & 
{-{q \sb {3}}i} & -{q \sb {3}} & {{-{q \sb {3}}i}j} & {{q \sb {3}}j} \ 
{{jk}l} & {{{ij}k}l} & {kl} & {{-ik}l} & {-jl} & {{ij}l} & -l & {-il} & {{{q 
\sb {3}}j}k} & {{{{q \sb {3}}i}j}k} & {{q \sb {3}}k} & {{-{q \sb {3}}i}k} & 
{-{q \sb {3}}j} & {{{q \sb {3}}i}j} & -{q \sb {3}} & {-{q \sb {3}}i} \ 
{{{ij}k}l} & {-{jk}l} & {{ik}l} & {kl} & {-{ij}l} & {-jl} & {il} & -l & {{{{q 
\sb {3}}i}j}k} & {{-{q \sb {3}}j}k} & {{{q \sb {3}}i}k} & {{q \sb {3}}k} & 
{{-{q \sb {3}}i}j} & {-{q \sb {3}}j} & {{q \sb {3}}i} & -{q \sb {3}} 
\end{array}
\right]
\leqno(19)
$$

Type: Matrix(CaleyDickson(CaleyDickson(CaleyDickson(CaleyDickson(Expression(Integer),i,1),j,1),k,1),l,*01q(3)))
Function to divide the matrix entries by a basis element
S(y) == map(x +-> real real real real(x/y),M)

                                                                   Type: Void
The result is a nested list
ѕ :=map(S,B)::ℒ ℒ ℒ ℚ;

   Compiling function S with type CaleyDickson(CaleyDickson(
      CaleyDickson(CaleyDickson(Expression(Integer),i,1),j,1),k,1),l,
      *01q(3)) -> Matrix(Expression(Integer)) 

                                  Type: List(List(List(Expression(Integer))))
structure constants form a tensor operator
Y := Σ(Σ(Σ(ѕ(i)(k)(j)*𝐞.i*𝐝.j*𝐝.k, i,1..dim), j,1..dim), k,1..dim);

         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
arity Y



$$
2 \over 1 
\leqno(23)
$$
   Type: Prop(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
matrix Ξ(Ξ((𝐞.i*𝐞.j)/Y, i,1..dim), j,1..dim)

$$
\left[
\begin{array}{cccccccccccccccc}
{| \sb {1}} & {| \sb {2}} & {| \sb {3}} & {| \sb {4}} & {| \sb {5}} & {| \sb 
{6}} & {| \sb {7}} & {| \sb {8}} & {| \sb {9}} & {| \sb {{10}}} & {| \sb 
{{11}}} & {| \sb {{12}}} & {| \sb {{13}}} & {| \sb {{14}}} & {| \sb {{15}}} & 
{| \sb {{16}}} \ 
{| \sb {2}} & -{| \sb {1}} & -{| \sb {4}} & {| \sb {3}} & -{| \sb {6}} & {| 
\sb {5}} & {| \sb {8}} & -{| \sb {7}} & -{| \sb {{10}}} & {| \sb {9}} & {| 
\sb {{12}}} & -{| \sb {{11}}} & {| \sb {{14}}} & -{| \sb {{13}}} & -{| \sb 
{{16}}} & {| \sb {{15}}} \ 
{| \sb {3}} & {| \sb {4}} & -{| \sb {1}} & -{| \sb {2}} & -{| \sb {7}} & -{| 
\sb {8}} & {| \sb {5}} & {| \sb {6}} & -{| \sb {{11}}} & -{| \sb {{12}}} & {| 
\sb {9}} & {| \sb {{10}}} & {| \sb {{15}}} & {| \sb {{16}}} & -{| \sb {{13}}} 
& -{| \sb {{14}}} \ 
{| \sb {4}} & -{| \sb {3}} & {| \sb {2}} & -{| \sb {1}} & -{| \sb {8}} & {| 
\sb {7}} & -{| \sb {6}} & {| \sb {5}} & -{| \sb {{12}}} & {| \sb {{11}}} & 
-{| \sb {{10}}} & {| \sb {9}} & {| \sb {{16}}} & -{| \sb {{15}}} & {| \sb 
{{14}}} & -{| \sb {{13}}} \ 
{| \sb {5}} & {| \sb {6}} & {| \sb {7}} & {| \sb {8}} & -{| \sb {1}} & -{| 
\sb {2}} & -{| \sb {3}} & -{| \sb {4}} & -{| \sb {{13}}} & -{| \sb {{14}}} & 
-{| \sb {{15}}} & -{| \sb {{16}}} & {| \sb {9}} & {| \sb {{10}}} & {| \sb 
{{11}}} & {| \sb {{12}}} \ 
{| \sb {6}} & -{| \sb {5}} & {| \sb {8}} & -{| \sb {7}} & {| \sb {2}} & -{| 
\sb {1}} & {| \sb {4}} & -{| \sb {3}} & -{| \sb {{14}}} & {| \sb {{13}}} & 
-{| \sb {{16}}} & {| \sb {{15}}} & -{| \sb {{10}}} & {| \sb {9}} & -{| \sb 
{{12}}} & {| \sb {{11}}} \ 
{| \sb {7}} & -{| \sb {8}} & -{| \sb {5}} & {| \sb {6}} & {| \sb {3}} & -{| 
\sb {4}} & -{| \sb {1}} & {| \sb {2}} & -{| \sb {{15}}} & {| \sb {{16}}} & {| 
\sb {{13}}} & -{| \sb {{14}}} & -{| \sb {{11}}} & {| \sb {{12}}} & {| \sb 
{9}} & -{| \sb {{10}}} \ 
{| \sb {8}} & {| \sb {7}} & -{| \sb {6}} & -{| \sb {5}} & {| \sb {4}} & {| 
\sb {3}} & -{| \sb {2}} & -{| \sb {1}} & -{| \sb {{16}}} & -{| \sb {{15}}} & 
{| \sb {{14}}} & {| \sb {{13}}} & -{| \sb {{12}}} & -{| \sb {{11}}} & {| \sb 
{{10}}} & {| \sb {9}} \ 
{| \sb {9}} & {| \sb {{10}}} & {| \sb {{11}}} & {| \sb {{12}}} & {| \sb 
{{13}}} & {| \sb {{14}}} & {| \sb {{15}}} & {| \sb {{16}}} & -{{q \sb {3}} \  
{| \sb {1}}} & -{{q \sb {3}} \  {| \sb {2}}} & -{{q \sb {3}} \  {| \sb {3}}} 
& -{{q \sb {3}} \  {| \sb {4}}} & -{{q \sb {3}} \  {| \sb {5}}} & -{{q \sb 
{3}} \  {| \sb {6}}} & -{{q \sb {3}} \  {| \sb {7}}} & -{{q \sb {3}} \  {| 
\sb {8}}} \ 
{| \sb {{10}}} & -{| \sb {9}} & {| \sb {{12}}} & -{| \sb {{11}}} & {| \sb 
{{14}}} & -{| \sb {{13}}} & -{| \sb {{16}}} & {| \sb {{15}}} & {{q \sb {3}} \  
{| \sb {2}}} & -{{q \sb {3}} \  {| \sb {1}}} & {{q \sb {3}} \  {| \sb {4}}} & 
-{{q \sb {3}} \  {| \sb {3}}} & {{q \sb {3}} \  {| \sb {6}}} & -{{q \sb {3}} 
\  {| \sb {5}}} & -{{q \sb {3}} \  {| \sb {8}}} & {{q \sb {3}} \  {| \sb 
{7}}} \ 
{| \sb {{11}}} & -{| \sb {{12}}} & -{| \sb {9}} & {| \sb {{10}}} & {| \sb 
{{15}}} & {| \sb {{16}}} & -{| \sb {{13}}} & -{| \sb {{14}}} & {{q \sb {3}} \  
{| \sb {3}}} & -{{q \sb {3}} \  {| \sb {4}}} & -{{q \sb {3}} \  {| \sb {1}}} 
& {{q \sb {3}} \  {| \sb {2}}} & {{q \sb {3}} \  {| \sb {7}}} & {{q \sb {3}} 
\  {| \sb {8}}} & -{{q \sb {3}} \  {| \sb {5}}} & -{{q \sb {3}} \  {| \sb 
{6}}} \ 
{| \sb {{12}}} & {| \sb {{11}}} & -{| \sb {{10}}} & -{| \sb {9}} & {| \sb 
{{16}}} & -{| \sb {{15}}} & {| \sb {{14}}} & -{| \sb {{13}}} & {{q \sb {3}} \  
{| \sb {4}}} & {{q \sb {3}} \  {| \sb {3}}} & -{{q \sb {3}} \  {| \sb {2}}} & 
-{{q \sb {3}} \  {| \sb {1}}} & {{q \sb {3}} \  {| \sb {8}}} & -{{q \sb {3}} 
\  {| \sb {7}}} & {{q \sb {3}} \  {| \sb {6}}} & -{{q \sb {3}} \  {| \sb 
{5}}} \ 
{| \sb {{13}}} & -{| \sb {{14}}} & -{| \sb {{15}}} & -{| \sb {{16}}} & -{| 
\sb {9}} & {| \sb {{10}}} & {| \sb {{11}}} & {| \sb {{12}}} & {{q \sb {3}} \  
{| \sb {5}}} & -{{q \sb {3}} \  {| \sb {6}}} & -{{q \sb {3}} \  {| \sb {7}}} 
& -{{q \sb {3}} \  {| \sb {8}}} & -{{q \sb {3}} \  {| \sb {1}}} & {{q \sb 
{3}} \  {| \sb {2}}} & {{q \sb {3}} \  {| \sb {3}}} & {{q \sb {3}} \  {| \sb 
{4}}} \ 
{| \sb {{14}}} & {| \sb {{13}}} & -{| \sb {{16}}} & {| \sb {{15}}} & -{| \sb 
{{10}}} & -{| \sb {9}} & -{| \sb {{12}}} & {| \sb {{11}}} & {{q \sb {3}} \  
{| \sb {6}}} & {{q \sb {3}} \  {| \sb {5}}} & -{{q \sb {3}} \  {| \sb {8}}} & 
{{q \sb {3}} \  {| \sb {7}}} & -{{q \sb {3}} \  {| \sb {2}}} & -{{q \sb {3}} 
\  {| \sb {1}}} & -{{q \sb {3}} \  {| \sb {4}}} & {{q \sb {3}} \  {| \sb 
{3}}} \ 
{| \sb {{15}}} & {| \sb {{16}}} & {| \sb {{13}}} & -{| \sb {{14}}} & -{| \sb 
{{11}}} & {| \sb {{12}}} & -{| \sb {9}} & -{| \sb {{10}}} & {{q \sb {3}} \  
{| \sb {7}}} & {{q \sb {3}} \  {| \sb {8}}} & {{q \sb {3}} \  {| \sb {5}}} & 
-{{q \sb {3}} \  {| \sb {6}}} & -{{q \sb {3}} \  {| \sb {3}}} & {{q \sb {3}} 
\  {| \sb {4}}} & -{{q \sb {3}} \  {| \sb {1}}} & -{{q \sb {3}} \  {| \sb 
{2}}} \ 
{| \sb {{16}}} & -{| \sb {{15}}} & {| \sb {{14}}} & {| \sb {{13}}} & -{| \sb 
{{12}}} & -{| \sb {{11}}} & {| \sb {{10}}} & -{| \sb {9}} & {{q \sb {3}} \  
{| \sb {8}}} & -{{q \sb {3}} \  {| \sb {7}}} & {{q \sb {3}} \  {| \sb {6}}} & 
{{q \sb {3}} \  {| \sb {5}}} & -{{q \sb {3}} \  {| \sb {4}}} & -{{q \sb {3}} 
\  {| \sb {3}}} & {{q \sb {3}} \  {| \sb {2}}} & -{{q \sb {3}} \  {| \sb 
{1}}} 
\end{array}
\right]
\leqno(24)
$$
 Type: Matrix(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
(25) -> U:=Σ(Σ(script('u,[[],[i,j]])*𝐝.i*𝐝.j, i,1..dim), j,1..dim);
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
(26) -> ω:𝐋 :=(YI)/U  - (IY)/U;
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
(27) -> )expose MCALCFN
   MultiVariableCalculusFunctions is now explicitly exposed in frame 
      initial 
J := jacobian(ravel ω,concat map(variables,ravel U)::ℒ Symbol);
                                            Type: Matrix(Expression(Integer))
--u := transpose matrix [concat map(variables,ravel U)::ℒ Symbol];
--J::OutputForm * u::OutputForm = 0
nrows(J),ncols(J)



$$
\left[
{4096}, \: {256} 
\right]
\leqno(28)
$$
                                                 Type: Tuple(PositiveInteger)
(29) -> Ñ:=nullSpace(J);
                                      Type: List(Vector(Expression(Integer)))
ℰ:=map((x,y)+->x=y, concat
       map(variables,ravel U), entries Σ(sb('p,[i])*Ñ.i, i,1..#Ñ) )

$$
\left[
{{u \sp {{1, \: 1}}}=-{{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{1, \: 
2}}}=0}, \: {{u \sp {{1, \: 3}}}=0}, \: {{u \sp {{1, \: 4}}}=0}, \: {{u \sp 
{{1, \: 5}}}=0}, \: {{u \sp {{1, \: 6}}}=0}, \: {{u \sp {{1, \: 7}}}=0}, \: 
{{u \sp {{1, \: 8}}}=0}, \: {{u \sp {{1, \: 9}}}=0}, \: {{u \sp {{1, \: 
{10}}}}=0}, \: {{u \sp {{1, \: {11}}}}=0}, \: {{u \sp {{1, \: {12}}}}=0}, \: 
{{u \sp {{1, \: {13}}}}=0}, \: {{u \sp {{1, \: {14}}}}=0}, \: {{u \sp {{1, \: 
{15}}}}=0}, \: {{u \sp {{1, \: {16}}}}=0}, \: {{u \sp {{2, \: 1}}}=0}, \: {{u 
\sp {{2, \: 2}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{2, \: 
3}}}=0}, \: {{u \sp {{2, \: 4}}}=0}, \: {{u \sp {{2, \: 5}}}=0}, \: {{u \sp 
{{2, \: 6}}}=0}, \: {{u \sp {{2, \: 7}}}=0}, \: {{u \sp {{2, \: 8}}}=0}, \: 
{{u \sp {{2, \: 9}}}=0}, \: {{u \sp {{2, \: {10}}}}=0}, \: {{u \sp {{2, \: 
{11}}}}=0}, \: {{u \sp {{2, \: {12}}}}=0}, \: {{u \sp {{2, \: {13}}}}=0}, \: 
{{u \sp {{2, \: {14}}}}=0}, \: {{u \sp {{2, \: {15}}}}=0}, \: {{u \sp {{2, \: 
{16}}}}=0}, \: {{u \sp {{3, \: 1}}}=0}, \: {{u \sp {{3, \: 2}}}=0}, \: {{u 
\sp {{3, \: 3}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{3, \: 
4}}}=0}, \: {{u \sp {{3, \: 5}}}=0}, \: {{u \sp {{3, \: 6}}}=0}, \: {{u \sp 
{{3, \: 7}}}=0}, \: {{u \sp {{3, \: 8}}}=0}, \: {{u \sp {{3, \: 9}}}=0}, \: 
{{u \sp {{3, \: {10}}}}=0}, \: {{u \sp {{3, \: {11}}}}=0}, \: {{u \sp {{3, \: 
{12}}}}=0}, \: {{u \sp {{3, \: {13}}}}=0}, \: {{u \sp {{3, \: {14}}}}=0}, \: 
{{u \sp {{3, \: {15}}}}=0}, \: {{u \sp {{3, \: {16}}}}=0}, \: {{u \sp {{4, \: 
1}}}=0}, \: {{u \sp {{4, \: 2}}}=0}, \: {{u \sp {{4, \: 3}}}=0}, \: {{u \sp 
{{4, \: 4}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{4, \: 5}}}=0}, \: 
{{u \sp {{4, \: 6}}}=0}, \: {{u \sp {{4, \: 7}}}=0}, \: {{u \sp {{4, \: 
8}}}=0}, \: {{u \sp {{4, \: 9}}}=0}, \: {{u \sp {{4, \: {10}}}}=0}, \: {{u 
\sp {{4, \: {11}}}}=0}, \: {{u \sp {{4, \: {12}}}}=0}, \: {{u \sp {{4, \: 
{13}}}}=0}, \: {{u \sp {{4, \: {14}}}}=0}, \: {{u \sp {{4, \: {15}}}}=0}, \: 
{{u \sp {{4, \: {16}}}}=0}, \: {{u \sp {{5, \: 1}}}=0}, \: {{u \sp {{5, \: 
2}}}=0}, \: {{u \sp {{5, \: 3}}}=0}, \: {{u \sp {{5, \: 4}}}=0}, \: {{u \sp 
{{5, \: 5}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{5, \: 6}}}=0}, \: 
{{u \sp {{5, \: 7}}}=0}, \: {{u \sp {{5, \: 8}}}=0}, \: {{u \sp {{5, \: 
9}}}=0}, \: {{u \sp {{5, \: {10}}}}=0}, \: {{u \sp {{5, \: {11}}}}=0}, \: {{u 
\sp {{5, \: {12}}}}=0}, \: {{u \sp {{5, \: {13}}}}=0}, \: {{u \sp {{5, \: 
{14}}}}=0}, \: {{u \sp {{5, \: {15}}}}=0}, \: {{u \sp {{5, \: {16}}}}=0}, \: 
{{u \sp {{6, \: 1}}}=0}, \: {{u \sp {{6, \: 2}}}=0}, \: {{u \sp {{6, \: 
3}}}=0}, \: {{u \sp {{6, \: 4}}}=0}, \: {{u \sp {{6, \: 5}}}=0}, \: {{u \sp 
{{6, \: 6}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{6, \: 7}}}=0}, \: 
{{u \sp {{6, \: 8}}}=0}, \: {{u \sp {{6, \: 9}}}=0}, \: {{u \sp {{6, \: 
{10}}}}=0}, \: {{u \sp {{6, \: {11}}}}=0}, \: {{u \sp {{6, \: {12}}}}=0}, \: 
{{u \sp {{6, \: {13}}}}=0}, \: {{u \sp {{6, \: {14}}}}=0}, \: {{u \sp {{6, \: 
{15}}}}=0}, \: {{u \sp {{6, \: {16}}}}=0}, \: {{u \sp {{7, \: 1}}}=0}, \: {{u 
\sp {{7, \: 2}}}=0}, \: {{u \sp {{7, \: 3}}}=0}, \: {{u \sp {{7, \: 4}}}=0}, 
\: {{u \sp {{7, \: 5}}}=0}, \: {{u \sp {{7, \: 6}}}=0}, \: {{u \sp {{7, \: 
7}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{7, \: 8}}}=0}, \: {{u \sp 
{{7, \: 9}}}=0}, \: {{u \sp {{7, \: {10}}}}=0}, \: {{u \sp {{7, \: 
{11}}}}=0}, \: {{u \sp {{7, \: {12}}}}=0}, \: {{u \sp {{7, \: {13}}}}=0}, \: 
{{u \sp {{7, \: {14}}}}=0}, \: {{u \sp {{7, \: {15}}}}=0}, \: {{u \sp {{7, \: 
{16}}}}=0}, \: {{u \sp {{8, \: 1}}}=0}, \: {{u \sp {{8, \: 2}}}=0}, \: {{u 
\sp {{8, \: 3}}}=0}, \: {{u \sp {{8, \: 4}}}=0}, \: {{u \sp {{8, \: 5}}}=0}, 
\: {{u \sp {{8, \: 6}}}=0}, \: {{u \sp {{8, \: 7}}}=0}, \: {{u \sp {{8, \: 
8}}}={{p \sb {1}} \over {q \sb {3}}}}, \: {{u \sp {{8, \: 9}}}=0}, \: {{u \sp 
{{8, \: {10}}}}=0}, \: {{u \sp {{8, \: {11}}}}=0}, \: {{u \sp {{8, \: 
{12}}}}=0}, \: {{u \sp {{8, \: {13}}}}=0}, \: {{u \sp {{8, \: {14}}}}=0}, \: 
{{u \sp {{8, \: {15}}}}=0}, \: {{u \sp {{8, \: {16}}}}=0}, \: {{u \sp {{9, \: 
1}}}=0}, \: {{u \sp {{9, \: 2}}}=0}, \: {{u \sp {{9, \: 3}}}=0}, \: {{u \sp 
{{9, \: 4}}}=0}, \: {{u \sp {{9, \: 5}}}=0}, \: {{u \sp {{9, \: 6}}}=0}, \: 
{{u \sp {{9, \: 7}}}=0}, \: {{u \sp {{9, \: 8}}}=0}, \: {{u \sp {{9, \: 
9}}}={p \sb {1}}}, \: {{u \sp {{9, \: {10}}}}=0}, \: {{u \sp {{9, \: 
{11}}}}=0}, \: {{u \sp {{9, \: {12}}}}=0}, \: {{u \sp {{9, \: {13}}}}=0}, \: 
{{u \sp {{9, \: {14}}}}=0}, \: {{u \sp {{9, \: {15}}}}=0}, \: {{u \sp {{9, \: 
{16}}}}=0}, \: {{u \sp {{{10}, \: 1}}}=0}, \: {{u \sp {{{10}, \: 2}}}=0}, \: 
{{u \sp {{{10}, \: 3}}}=0}, \: {{u \sp {{{10}, \: 4}}}=0}, \: {{u \sp {{{10}, 
\: 5}}}=0}, \: {{u \sp {{{10}, \: 6}}}=0}, \: {{u \sp {{{10}, \: 7}}}=0}, \: 
{{u \sp {{{10}, \: 8}}}=0}, \: {{u \sp {{{10}, \: 9}}}=0}, \: {{u \sp {{{10}, 
\: {10}}}}={p \sb {1}}}, \: {{u \sp {{{10}, \: {11}}}}=0}, \: {{u \sp {{{10}, 
\: {12}}}}=0}, \: {{u \sp {{{10}, \: {13}}}}=0}, \: {{u \sp {{{10}, \: 
{14}}}}=0}, \: {{u \sp {{{10}, \: {15}}}}=0}, \: {{u \sp {{{10}, \: 
{16}}}}=0}, \: {{u \sp {{{11}, \: 1}}}=0}, \: {{u \sp {{{11}, \: 2}}}=0}, \: 
{{u \sp {{{11}, \: 3}}}=0}, \: {{u \sp {{{11}, \: 4}}}=0}, \: {{u \sp {{{11}, 
\: 5}}}=0}, \: {{u \sp {{{11}, \: 6}}}=0}, \: {{u \sp {{{11}, \: 7}}}=0}, \: 
{{u \sp {{{11}, \: 8}}}=0}, \: {{u \sp {{{11}, \: 9}}}=0}, \: {{u \sp {{{11}, 
\: {10}}}}=0}, \: {{u \sp {{{11}, \: {11}}}}={p \sb {1}}}, \: {{u \sp {{{11}, 
\: {12}}}}=0}, \: {{u \sp {{{11}, \: {13}}}}=0}, \: {{u \sp {{{11}, \: 
{14}}}}=0}, \: {{u \sp {{{11}, \: {15}}}}=0}, \: {{u \sp {{{11}, \: 
{16}}}}=0}, \: {{u \sp {{{12}, \: 1}}}=0}, \: {{u \sp {{{12}, \: 2}}}=0}, \: 
{{u \sp {{{12}, \: 3}}}=0}, \: {{u \sp {{{12}, \: 4}}}=0}, \: {{u \sp {{{12}, 
\: 5}}}=0}, \: {{u \sp {{{12}, \: 6}}}=0}, \: {{u \sp {{{12}, \: 7}}}=0}, \: 
{{u \sp {{{12}, \: 8}}}=0}, \: {{u \sp {{{12}, \: 9}}}=0}, \: {{u \sp {{{12}, 
\: {10}}}}=0}, \: {{u \sp {{{12}, \: {11}}}}=0}, \: {{u \sp {{{12}, \: 
{12}}}}={p \sb {1}}}, \: {{u \sp {{{12}, \: {13}}}}=0}, \: {{u \sp {{{12}, \: 
{14}}}}=0}, \: {{u \sp {{{12}, \: {15}}}}=0}, \: {{u \sp {{{12}, \: 
{16}}}}=0}, \: {{u \sp {{{13}, \: 1}}}=0}, \: {{u \sp {{{13}, \: 2}}}=0}, \: 
{{u \sp {{{13}, \: 3}}}=0}, \: {{u \sp {{{13}, \: 4}}}=0}, \: {{u \sp {{{13}, 
\: 5}}}=0}, \: {{u \sp {{{13}, \: 6}}}=0}, \: {{u \sp {{{13}, \: 7}}}=0}, \: 
{{u \sp {{{13}, \: 8}}}=0}, \: {{u \sp {{{13}, \: 9}}}=0}, \: {{u \sp {{{13}, 
\: {10}}}}=0}, \: {{u \sp {{{13}, \: {11}}}}=0}, \: {{u \sp {{{13}, \: 
{12}}}}=0}, \: {{u \sp {{{13}, \: {13}}}}={p \sb {1}}}, \: {{u \sp {{{13}, \: 
{14}}}}=0}, \: {{u \sp {{{13}, \: {15}}}}=0}, \: {{u \sp {{{13}, \: 
{16}}}}=0}, \: {{u \sp {{{14}, \: 1}}}=0}, \: {{u \sp {{{14}, \: 2}}}=0}, \: 
{{u \sp {{{14}, \: 3}}}=0}, \: {{u \sp {{{14}, \: 4}}}=0}, \: {{u \sp {{{14}, 
\: 5}}}=0}, \: {{u \sp {{{14}, \: 6}}}=0}, \: {{u \sp {{{14}, \: 7}}}=0}, \: 
{{u \sp {{{14}, \: 8}}}=0}, \: {{u \sp {{{14}, \: 9}}}=0}, \: {{u \sp {{{14}, 
\: {10}}}}=0}, \: {{u \sp {{{14}, \: {11}}}}=0}, \: {{u \sp {{{14}, \: 
{12}}}}=0}, \: {{u \sp {{{14}, \: {13}}}}=0}, \: {{u \sp {{{14}, \: 
{14}}}}={p \sb {1}}}, \: {{u \sp {{{14}, \: {15}}}}=0}, \: {{u \sp {{{14}, \: 
{16}}}}=0}, \: {{u \sp {{{15}, \: 1}}}=0}, \: {{u \sp {{{15}, \: 2}}}=0}, \: 
{{u \sp {{{15}, \: 3}}}=0}, \: {{u \sp {{{15}, \: 4}}}=0}, \: {{u \sp {{{15}, 
\: 5}}}=0}, \: {{u \sp {{{15}, \: 6}}}=0}, \: {{u \sp {{{15}, \: 7}}}=0}, \: 
{{u \sp {{{15}, \: 8}}}=0}, \: {{u \sp {{{15}, \: 9}}}=0}, \: {{u \sp {{{15}, 
\: {10}}}}=0}, \: {{u \sp {{{15}, \: {11}}}}=0}, \: {{u \sp {{{15}, \: 
{12}}}}=0}, \: {{u \sp {{{15}, \: {13}}}}=0}, \: {{u \sp {{{15}, \: 
{14}}}}=0}, \: {{u \sp {{{15}, \: {15}}}}={p \sb {1}}}, \: {{u \sp {{{15}, \: 
{16}}}}=0}, \: {{u \sp {{{16}, \: 1}}}=0}, \: {{u \sp {{{16}, \: 2}}}=0}, \: 
{{u \sp {{{16}, \: 3}}}=0}, \: {{u \sp {{{16}, \: 4}}}=0}, \: {{u \sp {{{16}, 
\: 5}}}=0}, \: {{u \sp {{{16}, \: 6}}}=0}, \: {{u \sp {{{16}, \: 7}}}=0}, \: 
{{u \sp {{{16}, \: 8}}}=0}, \: {{u \sp {{{16}, \: 9}}}=0}, \: {{u \sp {{{16}, 
\: {10}}}}=0}, \: {{u \sp {{{16}, \: {11}}}}=0}, \: {{u \sp {{{16}, \: 
{12}}}}=0}, \: {{u \sp {{{16}, \: {13}}}}=0}, \: {{u \sp {{{16}, \: 
{14}}}}=0}, \: {{u \sp {{{16}, \: {15}}}}=0}, \: {{u \sp {{{16}, \: 
{16}}}}={p \sb {1}}} 
\right]
\leqno(30)
$$
                                    Type: List(Equation(Expression(Integer)))
(31) -> zero? eval(ω,ℰ)

$$
true 
\leqno(31)
$$
                                                                Type: Boolean
(32) -> Ų:𝐋 := eval(U,ℰ)

$$
-{{{p \sb {1}} \over {q \sb {3}}} \  {| \sb {{\ }} \sp {{1 \  1}}}}+{{{p \sb 
{1}} \over {q \sb {3}}} \  {| \sb {{\ }} \sp {{2 \  2}}}}+{{{p \sb {1}} \over 
{q \sb {3}}} \  {| \sb {{\ }} \sp {{3 \  3}}}}+{{{p \sb {1}} \over {q \sb 
{3}}} \  {| \sb {{\ }} \sp {{4 \  4}}}}+{{{p \sb {1}} \over {q \sb {3}}} \  
{| \sb {{\ }} \sp {{5 \  5}}}}+{{{p \sb {1}} \over {q \sb {3}}} \  {| \sb {{\ 
}} \sp {{6 \  6}}}}+{{{p \sb {1}} \over {q \sb {3}}} \  {| \sb {{\ }} \sp {{7 
\  7}}}}+{{{p \sb {1}} \over {q \sb {3}}} \  {| \sb {{\ }} \sp {{8 \  
8}}}}+{{p \sb {1}} \  {| \sb {{\ }} \sp {{9 \  9}}}}+{{p \sb {1}} \  {| \sb 
{{\ }} \sp {{{10} \  {10}}}}}+{{p \sb {1}} \  {| \sb {{\ }} \sp {{{11} \  
{11}}}}}+{{p \sb {1}} \  {| \sb {{\ }} \sp {{{12} \  {12}}}}}+{{p \sb {1}} \  
{| \sb {{\ }} \sp {{{13} \  {13}}}}}+{{p \sb {1}} \  {| \sb {{\ }} \sp {{{14} 
\  {14}}}}}+{{p \sb {1}} \  {| \sb {{\ }} \sp {{{15} \  {15}}}}}+{{p \sb {1}} 
\  {| \sb {{\ }} \sp {{{16} \  {16}}}}} 
\leqno(32)
$$
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
matrix Ξ(Ξ((𝐞.i 𝐞.j)/Ų, i,1..dim), j,1..dim)

$$
\left[
\begin{array}{cccccccccccccccc}
-{{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 
& 0 & 0 & 0 & 0 \ 
0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & {{p \sb {1}} \over {q \sb {3}}} & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 & 0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {p \sb {1}} 
\end{array}
\right]
\leqno(33)
$$
 Type: Matrix(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
(34) -> Ů:=determinant Ξ(Ξ(retract((𝐞.i * 𝐞.j)/Ų), j,1..dim), i,1..dim)

$$
-{{{p \sb {1}} \sp {16}} \over {{q \sb {3}} \sp 8}} 
\leqno(34)
$$
                                                    Type: Expression(Integer)
factor Ů

$$
-{{{p \sb {1}} \sp {16}} \over {{q \sb {3}} \sp 8}} 
\leqno(35)
$$
                                          Type: Factored(Expression(Integer))
(36) -> Um:=matrix Ξ(Ξ((𝐞.i*𝐞.j)/Ų, i,1..dim), j,1..dim);
 Type: Matrix(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
mU:=transpose inverse map(retract,Um);
                                            Type: Matrix(Expression(Integer))
Ω:=Σ(Σ(mU(i,j)*(𝐞.i*𝐞.j), i,1..dim), j,1..dim)


$$
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  1}}}}+{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{2 \  2}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{3 \  3}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  4}}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  5}}}}+{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{6 \  6}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  
7}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  8}}}}+{{1 \over {p 
\sb {1}}} \  {| \sb {{9 \  9}}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{10} \  
{10}}}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{11} \  {11}}}}}+{{1 \over {p \sb 
{1}}} \  {| \sb {{{12} \  {12}}}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  
{13}}}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{14} \  {14}}}}}+{{1 \over {p \sb 
{1}}} \  {| \sb {{{15} \  {15}}}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  
{16}}}}} 
\leqno(38)
$$
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
matrix Ξ(Ξ(Ω/(𝐝.i*𝐝.j), i,1..dim), j,1..dim)

$$
\left[
\begin{array}{cccccccccccccccc}
-{{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 
& 0 & 0 & 0 & 0 \ 
0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & {{q \sb {3}} \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 
0 & 0 & 0 & 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 & 0 & 0 & 0 & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 & 0 & 0 & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 & 0 & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} & 0 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb {1}}} 
& 0 \ 
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & {1 \over {p \sb 
{1}}} 
\end{array}
\right]
\leqno(39)
$$
 Type: Matrix(LinearOperator(16,OrderedVariableList([]),Expression(Integer)))
(40) -> d:𝐋:=
       Ω    /
       X    /
       Ų

$$
16 
\leqno(40)
$$
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))

test
    (    I Ω     )  /
    (     Ų I    )  =  I
$$
true 
\leqno(41)
$$
                                                                Type: Boolean

test
    (     Ω I    )  /
    (    I Ų     )  =  I
$$
true 
\leqno(42)
$$
                                                                Type: Boolean
(43) -> W:=(Y,I)/Ų;
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))
(44) -> λ:= (I,Ω) / (Y,I)

$$
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  1}} \sp {1}}}+{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{2 \  2}} \sp {1}}}+{{{q \sb {3}} \over {p 
\sb {1}}} \  {| \sb {{3 \  3}} \sp {1}}}+{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{4 \  4}} \sp {1}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  
5}} \sp {1}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  6}} \sp 
{1}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  7}} \sp {1}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  8}} \sp {1}}}+{{1 \over {p \sb 
{1}}} \  {| \sb {{9 \  9}} \sp {1}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{10} 
\  {10}}} \sp {1}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{11} \  {11}}} \sp 
{1}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{12} \  {12}}} \sp {1}}}+{{1 \over 
{p \sb {1}}} \  {| \sb {{{13} \  {13}}} \sp {1}}}+{{1 \over {p \sb {1}}} \  
{| \sb {{{14} \  {14}}} \sp {1}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{15} \  
{15}}} \sp {1}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  {16}}} \sp {1}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  2}} \sp {2}}} -{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{2 \  1}} \sp {2}}} -{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{3 \  4}} \sp {2}}}+{{{q \sb {3}} \over {p \sb {1}}} 
\  {| \sb {{4 \  3}} \sp {2}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{5 \  6}} \sp {2}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  5}} 
\sp {2}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  8}} \sp {2}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  7}} \sp {2}}} -{{1 \over 
{p \sb {1}}} \  {| \sb {{9 \  {10}}} \sp {2}}}+{{1 \over {p \sb {1}}} \  {| 
\sb {{{10} \  9}} \sp {2}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{11} \  {12}}} 
\sp {2}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{12} \  {11}}} \sp {2}}}+{{1 
\over {p \sb {1}}} \  {| \sb {{{13} \  {14}}} \sp {2}}} -{{1 \over {p \sb 
{1}}} \  {| \sb {{{14} \  {13}}} \sp {2}}} -{{1 \over {p \sb {1}}} \  {| \sb 
{{{15} \  {16}}} \sp {2}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  {15}}} 
\sp {2}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  3}} \sp 
{3}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  4}} \sp {3}}} -{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  1}} \sp {3}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{4 \  2}} \sp {3}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{5 \  7}} \sp {3}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{6 \  8}} \sp {3}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  
5}} \sp {3}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  6}} \sp {3}}} 
-{{1 \over {p \sb {1}}} \  {| \sb {{9 \  {11}}} \sp {3}}} -{{1 \over {p \sb 
{1}}} \  {| \sb {{{10} \  {12}}} \sp {3}}}+{{1 \over {p \sb {1}}} \  {| \sb 
{{{11} \  9}} \sp {3}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{12} \  {10}}} \sp 
{3}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  {15}}} \sp {3}}}+{{1 \over 
{p \sb {1}}} \  {| \sb {{{14} \  {16}}} \sp {3}}} -{{1 \over {p \sb {1}}} \  
{| \sb {{{15} \  {13}}} \sp {3}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  
{14}}} \sp {3}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  4}} \sp 
{4}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  3}} \sp {4}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  2}} \sp {4}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{4 \  1}} \sp {4}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{5 \  8}} \sp {4}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{6 \  7}} \sp {4}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  
6}} \sp {4}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  5}} \sp {4}}} 
-{{1 \over {p \sb {1}}} \  {| \sb {{9 \  {12}}} \sp {4}}}+{{1 \over {p \sb 
{1}}} \  {| \sb {{{10} \  {11}}} \sp {4}}} -{{1 \over {p \sb {1}}} \  {| \sb 
{{{11} \  {10}}} \sp {4}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{12} \  9}} \sp 
{4}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  {16}}} \sp {4}}} -{{1 \over 
{p \sb {1}}} \  {| \sb {{{14} \  {15}}} \sp {4}}}+{{1 \over {p \sb {1}}} \  
{| \sb {{{15} \  {14}}} \sp {4}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  
{13}}} \sp {4}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  5}} \sp 
{5}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  6}} \sp {5}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  7}} \sp {5}}}+{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{4 \  8}} \sp {5}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{5 \  1}} \sp {5}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{6 \  2}} \sp {5}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  
3}} \sp {5}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  4}} \sp 
{5}}} -{{1 \over {p \sb {1}}} \  {| \sb {{9 \  {13}}} \sp {5}}} -{{1 \over {p 
\sb {1}}} \  {| \sb {{{10} \  {14}}} \sp {5}}} -{{1 \over {p \sb {1}}} \  {| 
\sb {{{11} \  {15}}} \sp {5}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{12} \  
{16}}} \sp {5}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  9}} \sp {5}}}+{{1 
\over {p \sb {1}}} \  {| \sb {{{14} \  {10}}} \sp {5}}}+{{1 \over {p \sb 
{1}}} \  {| \sb {{{15} \  {11}}} \sp {5}}}+{{1 \over {p \sb {1}}} \  {| \sb 
{{{16} \  {12}}} \sp {5}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  
6}} \sp {6}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  5}} \sp 
{6}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  8}} \sp {6}}} -{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  7}} \sp {6}}}+{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{5 \  2}} \sp {6}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{6 \  1}} \sp {6}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{7 \  4}} \sp {6}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  
3}} \sp {6}}} -{{1 \over {p \sb {1}}} \  {| \sb {{9 \  {14}}} \sp {6}}}+{{1 
\over {p \sb {1}}} \  {| \sb {{{10} \  {13}}} \sp {6}}} -{{1 \over {p \sb 
{1}}} \  {| \sb {{{11} \  {16}}} \sp {6}}}+{{1 \over {p \sb {1}}} \  {| \sb 
{{{12} \  {15}}} \sp {6}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  {10}}} 
\sp {6}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{14} \  9}} \sp {6}}} -{{1 \over 
{p \sb {1}}} \  {| \sb {{{15} \  {12}}} \sp {6}}}+{{1 \over {p \sb {1}}} \  
{| \sb {{{16} \  {11}}} \sp {6}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{1 \  7}} \sp {7}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  8}} 
\sp {7}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  5}} \sp 
{7}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  6}} \sp {7}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  3}} \sp {7}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{6 \  4}} \sp {7}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{7 \  1}} \sp {7}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{8 \  2}} \sp {7}}} -{{1 \over {p \sb {1}}} \  {| \sb {{9 \  {15}}} \sp 
{7}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{10} \  {16}}} \sp {7}}}+{{1 \over 
{p \sb {1}}} \  {| \sb {{{11} \  {13}}} \sp {7}}} -{{1 \over {p \sb {1}}} \  
{| \sb {{{12} \  {14}}} \sp {7}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{13} \  
{11}}} \sp {7}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{14} \  {12}}} \sp 
{7}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{15} \  9}} \sp {7}}} -{{1 \over {p 
\sb {1}}} \  {| \sb {{{16} \  {10}}} \sp {7}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{1 \  8}} \sp {8}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{2 \  7}} \sp {8}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  
6}} \sp {8}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  5}} \sp 
{8}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  4}} \sp {8}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  3}} \sp {8}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{7 \  2}} \sp {8}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{8 \  1}} \sp {8}}} -{{1 \over {p \sb {1}}} \  {| \sb {{9 \  
{16}}} \sp {8}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{10} \  {15}}} \sp 
{8}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{11} \  {14}}} \sp {8}}}+{{1 \over 
{p \sb {1}}} \  {| \sb {{{12} \  {13}}} \sp {8}}} -{{1 \over {p \sb {1}}} \  
{| \sb {{{13} \  {12}}} \sp {8}}} -{{1 \over {p \sb {1}}} \  {| \sb {{{14} \  
{11}}} \sp {8}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{15} \  {10}}} \sp 
{8}}}+{{1 \over {p \sb {1}}} \  {| \sb {{{16} \  9}} \sp {8}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{1 \  9}} \sp {9}}}+{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{2 \  {10}}} \sp {9}}}+{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{3 \  {11}}} \sp {9}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 
\  {12}}} \sp {9}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {13}}} 
\sp {9}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {14}}} \sp 
{9}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {15}}} \sp {9}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {16}}} \sp {9}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{9 \  1}} \sp {9}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{10} \  2}} \sp {9}}} -{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{{11} \  3}} \sp {9}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{{12} \  4}} \sp {9}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{13} \  
5}} \sp {9}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{14} \  6}} \sp 
{9}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{15} \  7}} \sp {9}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{16} \  8}} \sp {9}}} -{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{1 \  {10}}} \sp {{10}}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{2 \  9}} \sp {{10}}}}+{{{q \sb {3}} \over {p 
\sb {1}}} \  {| \sb {{3 \  {12}}} \sp {{10}}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{4 \  {11}}} \sp {{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{5 \  {14}}} \sp {{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{6 \  {13}}} \sp {{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  
{16}}} \sp {{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {15}}} 
\sp {{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  2}} \sp 
{{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{10} \  1}} \sp 
{{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{11} \  4}} \sp 
{{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{12} \  3}} \sp 
{{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{13} \  6}} \sp 
{{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{14} \  5}} \sp 
{{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{15} \  8}} \sp 
{{10}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{16} \  7}} \sp 
{{10}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  {11}}} \sp 
{{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  {12}}} \sp 
{{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  9}} \sp 
{{11}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  {10}}} \sp 
{{11}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {15}}} \sp 
{{11}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {16}}} \sp 
{{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {13}}} \sp 
{{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {14}}} \sp 
{{11}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  3}} \sp {{11}}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{10} \  4}} \sp {{11}}}} -{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{{11} \  1}} \sp {{11}}}}+{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{{12} \  2}} \sp {{11}}}}+{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{{13} \  7}} \sp {{11}}}}+{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{{14} \  8}} \sp {{11}}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{15} \  5}} \sp {{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} 
\  {| \sb {{{16} \  6}} \sp {{11}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{1 \  {12}}} \sp {{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 
\  {11}}} \sp {{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  
{10}}} \sp {{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  9}} 
\sp {{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {16}}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {15}}} \sp 
{{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {14}}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {13}}} \sp 
{{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  4}} \sp 
{{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{10} \  3}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{11} \  2}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{12} \  1}} \sp 
{{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{13} \  8}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{14} \  7}} \sp 
{{12}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{15} \  6}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{16} \  5}} \sp 
{{12}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  {13}}} \sp 
{{13}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  {14}}} \sp 
{{13}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  {15}}} \sp 
{{13}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  {16}}} \sp 
{{13}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  9}} \sp 
{{13}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {10}}} \sp 
{{13}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {11}}} \sp 
{{13}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {12}}} \sp 
{{13}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  5}} \sp {{13}}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{10} \  6}} \sp {{13}}}} -{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{{11} \  7}} \sp {{13}}}} -{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{{12} \  8}} \sp {{13}}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{{13} \  1}} \sp {{13}}}}+{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{{14} \  2}} \sp {{13}}}}+{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{15} \  3}} \sp {{13}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{{16} \  4}} \sp {{13}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{1 \  {14}}} \sp {{14}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  
{13}}} \sp {{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  {16}}} 
\sp {{14}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  {15}}} \sp 
{{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {10}}} \sp 
{{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  9}} \sp {{14}}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {12}}} \sp {{14}}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {11}}} \sp {{14}}}}+{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{9 \  6}} \sp {{14}}}}+{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{{10} \  5}} \sp {{14}}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{11} \  8}} \sp {{14}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  
{| \sb {{{12} \  7}} \sp {{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{{13} \  2}} \sp {{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{14} 
\  1}} \sp {{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{15} \  4}} 
\sp {{14}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{16} \  3}} \sp 
{{14}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  {15}}} \sp 
{{15}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  {16}}} \sp 
{{15}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  {13}}} \sp 
{{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  {14}}} \sp 
{{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {11}}} \sp 
{{15}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {12}}} \sp 
{{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  9}} \sp {{15}}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  {10}}} \sp {{15}}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  7}} \sp {{15}}}}+{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{{10} \  8}} \sp {{15}}}}+{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{{11} \  5}} \sp {{15}}}} -{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{12} \  6}} \sp {{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} 
\  {| \sb {{{13} \  3}} \sp {{15}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| 
\sb {{{14} \  4}} \sp {{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb 
{{{15} \  1}} \sp {{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{16} 
\  2}} \sp {{15}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{1 \  {16}}} 
\sp {{16}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{2 \  {15}}} \sp 
{{16}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{3 \  {14}}} \sp 
{{16}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{4 \  {13}}} \sp 
{{16}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{5 \  {12}}} \sp 
{{16}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{6 \  {11}}} \sp 
{{16}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{7 \  {10}}} \sp 
{{16}}}} -{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{8 \  9}} \sp 
{{16}}}}+{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{9 \  8}} \sp {{16}}}} 
-{{{q \sb {3}} \over {p \sb {1}}} \  {| \sb {{{10} \  7}} \sp {{16}}}}+{{{q 
\sb {3}} \over {p \sb {1}}} \  {| \sb {{{11} \  6}} \sp {{16}}}}+{{{q \sb 
{3}} \over {p \sb {1}}} \  {| \sb {{{12} \  5}} \sp {{16}}}} -{{{q \sb {3}} 
\over {p \sb {1}}} \  {| \sb {{{13} \  4}} \sp {{16}}}} -{{{q \sb {3}} \over 
{p \sb {1}}} \  {| \sb {{{14} \  3}} \sp {{16}}}}+{{{q \sb {3}} \over {p \sb 
{1}}} \  {| \sb {{{15} \  2}} \sp {{16}}}} -{{{q \sb {3}} \over {p \sb {1}}} 
\  {| \sb {{{16} \  1}} \sp {{16}}}} 
\leqno(44)
$$
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))

test( (Ω,I) / (I,Y) = λ)
$$
true 
\leqno(45)
$$
                                                                Type: Boolean
(46) -> Χ := Y / λ ;
         Type: LinearOperator(16,OrderedVariableList([]),Expression(Integer))

Χr := (λ,I)/(I,Y)

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