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Notebook[{

Cell[CellGroupData[{
Cell[BoxData[
    \(SetDirectory["\<d:\\demolattices\>"]\)], "Input"],

Cell[BoxData[
    \("d:\\demolattices"\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Get["\<l0711-08.m\>"]\)], "Input"],

Cell[BoxData[
    \("Loading code for computation of Lax pair of lattices (July 12, \
2008)"\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("***************** MENU INTERFACE *****************  \
(page: "\[InvisibleSpace]1\[InvisibleSpace]")"\),
      SequenceForm[ 
      "***************** MENU INTERFACE *****************  (page: ", 1, ")"],
      Editable->False]], "Print"],

Cell[BoxData[
    \("---------------------------------------------------------------------"\
\)], "Print"],

Cell[BoxData[
    \("  1) discrete potential KdV Equation (l_pKdV.m)"\)], "Print"],

Cell[BoxData[
    \("  2) discrete modified KdV Equation  (l_mKdV.m)"\)], "Print"],

Cell[BoxData[
    \("  3) discrete sine-Gordon Equation (l_sG.m)"\)], "Print"],

Cell[BoxData[
    \("  4) H1 equation (ABS classification) (l_H1.m)"\)], "Print"],

Cell[BoxData[
    \("  5) H2 equation (ABS classification) (l_H2.m)"\)], "Print"],

Cell[BoxData[
    \("  6) H3 equation (delta not 0) (ABS classification) (l_H3rhs.m)"\)], \
"Print"],

Cell[BoxData[
    \("  7) H3 equation (delta = 0) (ABS classification) (l_H3zero.m)"\)], \
"Print"],

Cell[BoxData[
    \("  8) Q1 equation (delta not 0) (ABS classification) (l_Q1rhs.m)"\)], \
"Print"],

Cell[BoxData[
    \("  9) Q1 equation (delta = 0) (ABS classification) (l_Q1zero.m)"\)], \
"Print"],

Cell[BoxData[
    \("  10) Q2 equation (delta not 0) (ABS classification) (l_Q2rhs.m)"\)], \
"Print"],

Cell[BoxData[
    \(" nn) Next Page"\)], "Print"],

Cell[BoxData[
    \(" tt) Your System"\)], "Print"],

Cell[BoxData[
    \(" qq) Exit the Program"\)], "Print"],

Cell[BoxData[
    \("---------------------------------------------------------------------"\
\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("***************** MENU INTERFACE *****************  \
(page: "\[InvisibleSpace]2\[InvisibleSpace]")"\),
      SequenceForm[ 
      "***************** MENU INTERFACE *****************  (page: ", 2, ")"],
      Editable->False]], "Print"],

Cell[BoxData[
    \("---------------------------------------------------------------------"\
\)], "Print"],

Cell[BoxData[
    \("  11) Q2 equation (delta = 0) (ABS classification) (l_Q2zero.m)"\)], \
"Print"],

Cell[BoxData[
    \("  12) Q3 equation (delta not 0) (ABS classification) (l_Q3rhs.m)"\)], \
"Print"],

Cell[BoxData[
    \("  13) Q3 equation (delta = 0) (ABS classification) (l_Q3zero.m)"\)], \
"Print"],

Cell[BoxData[
    \("  14) A1 equation (delta not 0) (ABS classification) (l_A1rhs.m)"\)], \
"Print"],

Cell[BoxData[
    \("  15) A1 equation (delta = 0) (ABS classification) (l_A1zero.m)"\)], \
"Print"],

Cell[BoxData[
    \("  16) A2 equation (ABS classification) (l_A2.m)"\)], "Print"],

Cell[BoxData[
    \("  17) (alpha,beta) equation (l_abeq.m)"\)], "Print"],

Cell[BoxData[
    \("  18) discrete sine-Gordon Equation (testing parameters) \
(l_sGpar.m)"\)], "Print"],

Cell[BoxData[
    \("  19) discrete generalized modified KdV Equation (l_gmKdV.m)"\)], \
"Print"],

Cell[BoxData[
    \(" nn) Next Page"\)], "Print"],

Cell[BoxData[
    \(" tt) Your System"\)], "Print"],

Cell[BoxData[
    \(" qq) Exit the Program"\)], "Print"],

Cell[BoxData[
    \("---------------------------------------------------------------------"\
\)], "Print"],

Cell[BoxData[
    \("********************************************************************"\)\
], "Print"],

Cell[BoxData[
    \("         WELCOME TO THE MATHEMATICA PROGRAM              "\)], "Print"],

Cell[BoxData[
    \("                  by WILLY HEREMAN                       "\)], "Print"],

Cell[BoxData[
    \("     FOR THE COMPUTATION OF LAX PAIRS OF NONLINEAR       "\)], "Print"],

Cell[BoxData[
    \("  PARTIAL DIFFERENCE EQUATIONS IN 2D (ON QUAD-GRAPHS)    "\)], "Print"],

Cell[BoxData[
    \(" Collaborators: Reinout Quispel and Peter van der Kamp   "\)], "Print"],

Cell[BoxData[
    \("           First released on July 12, 2008               "\)], "Print"],

Cell[BoxData[
    \("                    Copyright 2008                       "\)], "Print"],

Cell[BoxData[
    \("********************************************************************"\)\
], "Print"],

Cell[BoxData[
    InterpretationBox[\("Working with the discrete "\[InvisibleSpace]gmKdV\
\[InvisibleSpace]" equation:"\),
      SequenceForm[ "Working with the discrete ", gmKdV, " equation:"],
      Editable->False]], "Print"],

Cell[BoxData[
    \(beta2\ x\ x1 - beta3\ x12\ x2 + 
        beta1\ \((\(-x1\)\ x12 + x\ x2)\) \[Equal] 0\)], "Print"],

Cell[BoxData[
    \("********************** CONTROL SETTINGS *************************"\)], \
"Print"],

Cell[BoxData[
    InterpretationBox[\("LaxPairGiven (L and M are given in data file) is set \
to "\[InvisibleSpace]True\),
      SequenceForm[ 
      "LaxPairGiven (L and M are given in data file) is set to ", True],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("t and s are given in data file (byhand) is set to: "\
\[InvisibleSpace]False\),
      SequenceForm[ 
      "t and s are given in data file (byhand) is set to: ", False],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Determinant method to compute t and s is set to: "\
\[InvisibleSpace]True\),
      SequenceForm[ 
      "Determinant method to compute t and s is set to: ", True],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Test consistency on cube is set to \
"\[InvisibleSpace]True\),
      SequenceForm[ "Test consistency on cube is set to ", True],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Use of powerexpand is set to "\[InvisibleSpace]False\
\),
      SequenceForm[ "Use of powerexpand is set to ", False],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Use of rootrules is set to "\[InvisibleSpace]True\),
      SequenceForm[ "Use of rootrules is set to ", True],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Computation of matrix N is set to: \
"\[InvisibleSpace]True\),
      SequenceForm[ "Computation of matrix N is set to: ", True],
      Editable->False]], "Print"],

Cell[BoxData[
    InterpretationBox[\("Application of gauge transformation is set to: "\
\[InvisibleSpace]False\),
      SequenceForm[ "Application of gauge transformation is set to: ", False],
      
      Editable->False]], "Print"],

Cell[BoxData[
    \("******************* START OF THE COMPUTATION ************************"\
\)], "Print"],

Cell[BoxData[
    \("Working with lattice defined on front (F), latticefront:"\)], "Print"],

Cell[BoxData[
    \(beta2\ x\ x1 - beta3\ x12\ x2 + 
        beta1\ \((\(-x1\)\ x12 + x\ x2)\) \[Equal] 0\)], "Print"],

Cell[BoxData[
    \("Lattice on ground (G), latticeground:"\)], "Print"],

Cell[BoxData[
    \(beta2\ x\ x1 - beta3\ x13\ x3 + 
        beta1\ \((\(-x1\)\ x13 + x\ x3)\) \[Equal] 0\)], "Print"],

Cell[BoxData[
    \("Lattice on left face (L), latticeleftface:"\)], "Print"],

Cell[BoxData[
    \(beta2\ x\ x2 - beta3\ x23\ x3 + 
        beta1\ \((\(-x2\)\ x23 + x\ x3)\) \[Equal] 0\)], "Print"],

Cell[BoxData[
    \("**************** TESTING CONSISTENCY AROUND THE CUBE ****************"\
\)], "Print"],

Cell[BoxData[
    \("Computation  x12 ="\)], "Print"],

Cell[BoxData[
    \(\(x\ \((beta2\ x1 + beta1\ x2)\)\)\/\(beta1\ x1 + beta3\ x2\)\)], \
"Print"],

Cell[BoxData[
    \("Computation  x13 = "\)], "Print"],

Cell[BoxData[
    \(\(x\ \((beta2\ x1 + beta1\ x3)\)\)\/\(beta1\ x1 + beta3\ x3\)\)], \
"Print"],

Cell[BoxData[
    \("Computation  x23 = "\)], "Print"],

Cell[BoxData[
    \(\(x\ \((beta2\ x2 + beta1\ x3)\)\)\/\(beta1\ x2 + beta3\ x3\)\)], \
"Print"],

Cell[BoxData[
    \("*****************************************************************"\)], \
"Print"],

Cell[BoxData[
    \("After factoring, computation of x123 using x23 (x123choice1), x123 \
="\)], "Print"],

Cell[BoxData[
    \(\((x1\ \((beta1\^2\ beta2\ x1\^2 + beta1\ beta2\^2\ x1\^2 + 
              beta1\^2\ beta2\ x1\ x2 + beta1\ beta2\ beta3\ x1\ x2 + 
              beta1\^3\ x1\ x3 + beta2\^2\ beta3\ x1\ x3 + 
              beta1\^2\ beta3\ x2\ x3 + 
              beta1\ beta2\ beta3\ x2\ x3)\))\)/\((beta1\^2\ beta2\ x1\^2 + 
          beta1\ beta2\ beta3\ x1\^2 + beta1\^3\ x1\ x2 + 
          beta2\ beta3\^2\ x1\ x2 + beta1\^2\ beta3\ x1\ x3 + 
          beta1\ beta2\ beta3\ x1\ x3 + beta1\^2\ beta3\ x2\ x3 + 
          beta1\ beta3\^2\ x2\ x3)\)\)], "Print"],

Cell[BoxData[
    \("After factoring, computation of x123 using x13, (x123choice2), x123 ="\
\)], "Print"],

Cell[BoxData[
    \(\((x2\ \((beta1\^2\ beta2\ x1\ x2 + beta1\ beta2\^2\ x1\ x2 + 
              beta1\^2\ beta2\ x2\^2 + beta1\ beta2\ beta3\ x2\^2 + 
              beta1\^3\ x1\ x3 + beta2\^2\ beta3\ x1\ x3 + 
              beta1\^2\ beta3\ x2\ x3 + 
              beta1\ beta2\ beta3\ x2\ x3)\))\)/\((beta1\^2\ beta2\ x1\ x2 + 
          beta1\ beta2\ beta3\ x1\ x2 + beta1\^3\ x2\^2 + 
          beta2\ beta3\^2\ x2\^2 + beta1\^2\ beta3\ x1\ x3 + 
          beta1\ beta2\ beta3\ x1\ x3 + beta1\^2\ beta3\ x2\ x3 + 
          beta1\ beta3\^2\ x2\ x3)\)\)], "Print"],

Cell[BoxData[
    \("********************************************************************"\)\
], "Print"],

Cell[BoxData[
    \("As soon as one consistency condition is violated the computation"\)], \
"Print"],

Cell[BoxData[
    \("will abort, unless candidates for L and M are given in the data file."\
\)], "Print"],

Cell[BoxData[
    \("Test if (x123choice1 - x123choice2) = 0, diffx123choice1choice2 ="\)], \
"Print"],

Cell[BoxData[
    \(beta1\ \((x1 - x2)\)\ \((beta1\ x1 + beta2\ x1 + beta1\ x2 + 
          beta3\ x2)\)\ \((beta1\^2\ beta2\^2\ x1\^2\ x2 + 
          beta1\ beta2\^2\ beta3\ x1\^2\ x2 + beta1\^3\ beta2\ x1\ x2\^2 + 
          beta2\^2\ beta3\^2\ x1\ x2\^2 + beta1\^2\ beta2\ beta3\ x1\^2\ x3 + 
          beta1\ beta2\^2\ beta3\ x1\^2\ x3 + 
          2\ beta1\^2\ beta2\ beta3\ x1\ x2\ x3 + 
          beta1\ beta2\^2\ beta3\ x1\ x2\ x3 + 
          beta1\ beta2\ beta3\^2\ x1\ x2\ x3 + 
          beta1\^2\ beta2\ beta3\ x2\^2\ x3 + 
          beta1\ beta2\ beta3\^2\ x2\^2\ x3 + beta1\^3\ beta3\ x1\ x3\^2 + 
          beta2\^2\ beta3\^2\ x1\ x3\^2 + beta1\^2\ beta3\^2\ x2\ x3\^2 + 
          beta1\ beta2\ beta3\^2\ x2\ x3\^2)\)\)], "Print"],

Cell[BoxData[
    \("The equation is INCONSISTENT around the cube!"\)], "Print"],

Cell[BoxData[
    \("********* TEST RESULT IS NOT ZERO! ************ numerator of \
diffx123choice1choice2 must be zero:"\)], "Print"],

Cell[BoxData[
    \(beta1\ \((x1 - x2)\)\ \((beta1\ x1 + beta2\ x1 + beta1\ x2 + 
          beta3\ x2)\)\ \((beta1\^2\ beta2\^2\ x1\^2\ x2 + 
          beta1\ beta2\^2\ beta3\ x1\^2\ x2 + beta1\^3\ beta2\ x1\ x2\^2 + 
          beta2\^2\ beta3\^2\ x1\ x2\^2 + beta1\^2\ beta2\ beta3\ x1\^2\ x3 + 
          beta1\ beta2\^2\ beta3\ x1\^2\ x3 + 
          2\ beta1\^2\ beta2\ beta3\ x1\ x2\ x3 + 
          beta1\ beta2\^2\ beta3\ x1\ x2\ x3 + 
          beta1\ beta2\ beta3\^2\ x1\ x2\ x3 + 
          beta1\^2\ beta2\ beta3\ x2\^2\ x3 + 
          beta1\ beta2\ beta3\^2\ x2\^2\ x3 + beta1\^3\ beta3\ x1\ x3\^2 + 
          beta2\^2\ beta3\^2\ x1\ x3\^2 + beta1\^2\ beta3\^2\ x2\ x3\^2 + 
          beta1\ beta2\ beta3\^2\ x2\ x3\^2)\)\)], "Print"],

Cell[BoxData[
    \("Continue with the verification of the given Lax pair!"\)], "Print"],

Cell[BoxData[
    \("*********************************************************************"\
\)], "Print"],

Cell[BoxData[
    \("************* VERIFICATION OF THE GIVEN LAX PAIR ****************"\)], \
"Print"],

Cell[BoxData[
    \("The subsequent computations might be slow for complicated lattices, in \
particular, if square roots are present!"\)], "Print"],

Cell[BoxData[
    \("******* The matrix L was given in the data file! ******"\)], "Print"],

Cell[BoxData[
    \("Candidate Lax pair, matrix L (candidateL)"\)], "Print"],

Cell[BoxData[
    \("L = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"1", \(-x1\)},
            {\(-\(k\^2\/x\)\), \(x1\/x\)}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("*********************************************************************"\
\)], "Print"],

Cell[BoxData[
    \("Entry L11 of candidate L (entrycandidateL11) "\)], "Print"],

Cell[BoxData[
    \("L11 = "\)], "Print"],

Cell[BoxData[
    \(1\)], "Print"],

Cell[BoxData[
    \("Entry L12 of candidate L (entrycandidateL12) "\)], "Print"],

Cell[BoxData[
    \("L12 = "\)], "Print"],

Cell[BoxData[
    \(\(-x1\)\)], "Print"],

Cell[BoxData[
    \("Entry L21 of candidate L (entrycandidateL21) "\)], "Print"],

Cell[BoxData[
    \("L21 = "\)], "Print"],

Cell[BoxData[
    \(\(-\(k\^2\/x\)\)\)], "Print"],

Cell[BoxData[
    \("Entry L22 of candidate L (entrycandidateL22) "\)], "Print"],

Cell[BoxData[
    \("L22 = "\)], "Print"],

Cell[BoxData[
    \(x1\/x\)], "Print"],

Cell[BoxData[
    \("*********************************************************************"\
\)], "Print"],

Cell[BoxData[
    \("****** The matrix M was given in the data file! ******"\)], "Print"],

Cell[BoxData[
    \("Candidate Lax pair, matrix M (candidateM)"\)], "Print"],

Cell[BoxData[
    \("M = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {\(beta2\/\(beta2\ beta3 - 
                    beta1\^2\ k\^2\)\), \(-\(\(beta1\ x2\)\/\(\(-beta2\)\ \
beta3 + beta1\^2\ k\^2\)\)\)},
            {\(-\(\(beta1\ k\^2\)\/\(\((\(-beta2\)\ beta3 + 
                          beta1\^2\ k\^2)\)\ x\)\)\), \(\(beta3\ \
x2\)\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("*********************************************************************"\
\)], "Print"],

Cell[BoxData[
    \("Entry M11 of candidate M (entrycandidateM11) "\)], "Print"],

Cell[BoxData[
    \("M11 = "\)], "Print"],

Cell[BoxData[
    \(beta2\/\(beta2\ beta3 - beta1\^2\ k\^2\)\)], "Print"],

Cell[BoxData[
    \("Entry M12 of candidate M (entrycandidateM12) "\)], "Print"],

Cell[BoxData[
    \("M12 = "\)], "Print"],

Cell[BoxData[
    \(\(-\(\(beta1\ x2\)\/\(\(-beta2\)\ beta3 + 
            beta1\^2\ k\^2\)\)\)\)], "Print"],

Cell[BoxData[
    \("Entry M21 of candidate M (entrycandidateM21) "\)], "Print"],

Cell[BoxData[
    \("M21 = "\)], "Print"],

Cell[BoxData[
    \(\(-\(\(beta1\ k\^2\)\/\(\((\(-beta2\)\ beta3 + 
                beta1\^2\ k\^2)\)\ x\)\)\)\)], "Print"],

Cell[BoxData[
    \("Entry M22 of candidate M (entrycandidateM22) "\)], "Print"],

Cell[BoxData[
    \("M22 = "\)], "Print"],

Cell[BoxData[
    \(\(beta3\ x2\)\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)], "Print"],

Cell[BoxData[
    \("******************************************************************"\)],\
 "Print"],

Cell[BoxData[
    \("*********** COMPUTATION OF CONSTRAINTS FOR t AND s \
***************"\)], "Print"],

Cell[BoxData[
    \("The subsequent computations might be slow for complicated \
lattices!"\)], "Print"],

Cell[BoxData[
    \("Compatibility equation, (1-1) element ON LATTICE,"\)], "Print"],

Cell[BoxData[
    \("compatibilityeq11onlattice = "\)], "Print"],

Cell[BoxData[
    \(True\)], "Print"],

Cell[BoxData[
    \("Compatibility equation, (1-2) element ON LATTICE, "\)], "Print"],

Cell[BoxData[
    \("compatibilityeq12onlattice = "\)], "Print"],

Cell[BoxData[
    \(True\)], "Print"],

Cell[BoxData[
    \("Compatibility equation, (2-1) element ON LATTICE, "\)], "Print"],

Cell[BoxData[
    \("compatibilityeq21onlattice = "\)], "Print"],

Cell[BoxData[
    \(True\)], "Print"],

Cell[BoxData[
    \("Compatibility equation, (2-2) element ON LATTICE, "\)], "Print"],

Cell[BoxData[
    \("compatibilityeq22onlattice = "\)], "Print"],

Cell[BoxData[
    \(True\)], "Print"],

Cell[BoxData[
    \("******************************************************************"\)],\
 "Print"],

Cell[BoxData[
    \("************** FINAL TEST OF THE COMPUTED LAX PAIR \
***************"\)], "Print"],

Cell[BoxData[
    \("The subsequent computations might be slow for complicated lattices, in \
particular, if square roots are present!"\)], "Print"],

Cell[BoxData[
    \("Candidate compatibility matrix L2.M - M1.L, ON LATTICE,"\)], "Print"],

Cell[BoxData[
    \("candidatecompatibilitymatrixonlattice ="\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"0", "0"},
            {"0", "0"}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("********************************************************************"\)\
], "Print"],

Cell[BoxData[
    \("****************** START COMPUTATION OF MATRIX N \
*******************"\)], "Print"],

Cell[BoxData[
    \("********* THIS PIECE OF THE CODE IS STILL UNDER DEVELOPMENT \
********"\)], "Print"],

Cell[BoxData[
    \("LaxPairGiven is true, given candidate for L (candidateL) = "\)], \
"Print"],

Cell[BoxData[
    \("L = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"1", \(-x1\)},
            {\(-\(k\^2\/x\)\), \(x1\/x\)}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("LaxPairGiven is true, given candidate for M (candidateM) = "\)], \
"Print"],

Cell[BoxData[
    \("M = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {\(beta2\/\(beta2\ beta3 - 
                    beta1\^2\ k\^2\)\), \(-\(\(beta1\ x2\)\/\(\(-beta2\)\ \
beta3 + beta1\^2\ k\^2\)\)\)},
            {\(-\(\(beta1\ k\^2\)\/\(\((\(-beta2\)\ beta3 + 
                          beta1\^2\ k\^2)\)\ x\)\)\), \(\(beta3\ \
x2\)\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("prodnamematrixN = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"0", \(gmKdV\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)},
            {\(\(gmKdV\ k\^2\)\/\(\((\(-beta2\)\ beta3 + 
                        beta1\^2\ k\^2)\)\ x\ x1\ x2\)\), "0"}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("******** CHECK BY INSPECTION ******* NOT FULLY CODED YET! "\)], "Print"],

Cell[BoxData[
    InterpretationBox[\("Check if prodnamematrixN (above) has the common \
factor: "\[InvisibleSpace]gmKdV\),
      SequenceForm[ 
      "Check if prodnamematrixN (above) has the common factor: ", gmKdV],
      Editable->False]], "Print"],

Cell[BoxData[
    \("This is the matrix N (matrixN)"\)], "Print"],

Cell[BoxData[
    \("N = "\)], "Print"],

Cell[BoxData[
    TagBox[
      RowBox[{"(", "\[NoBreak]", GridBox[{
            {"0", \(1\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)},
            {\(k\^2\/\(\((\(-beta2\)\ beta3 + 
                        beta1\^2\ k\^2)\)\ x\ x1\ x2\)\), "0"}
            }], "\[NoBreak]", ")"}],
      Function[ BoxForm`e$, 
        MatrixForm[ BoxForm`e$]]]], "Print"],

Cell[BoxData[
    \("*********************************************************************"\
\)], "Print"],

Cell[BoxData[
    \("N11 = "\)], "Print"],

Cell[BoxData[
    \(0\)], "Print"],

Cell[BoxData[
    \("N12 = "\)], "Print"],

Cell[BoxData[
    \(1\/\(\((beta2\ beta3 - beta1\^2\ k\^2)\)\ x\)\)], "Print"],

Cell[BoxData[
    \("N21 = "\)], "Print"],

Cell[BoxData[
    \(k\^2\/\(\((\(-beta2\)\ beta3 + beta1\^2\ k\^2)\)\ x\ x1\ x2\)\)], \
"Print"],

Cell[BoxData[
    \("N22 = "\)], "Print"],

Cell[BoxData[
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