Bxdty

I want to produce a table (or a grid) from my list of data, as follows:

eq01={0.01,1.02};

ev01={{1,3},{2,4}};

ev02={{5,5},{6,1}};

 data1 = {{"", "Equilibrium points", "Eigenvalues", 

   "Eigenvectors"}, {"A = 0",eq01,ev01,ev02}};



Grid[data1, Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 

 ItemStyle -> "Text"]

And what I obtain is the following:

Is there a way to:
1) flatten the lists under "Eigenvalues" and "Eigenvectors" without using flatten for every definition of list in the beginning? Because I have many eigenvalues and eigenvectors and it would be very long;
2) substitute the curly brackets with round brackets, to have for example, in the second column and second row, (0.01,1.02)?

I hope the question is clear, thanks in advance!

Edit

this works exactly as OP asked in the comments below

also for many rows

eq01={0.01,1.02};

ev01={{1,3},{2,4}};

ev02={{5,5},{6,1}};

data1=StringReplace[#,{"{{"->"(","}}"->")","{"->"(","}"->")"}]&/@

ToString/@#&/@{{"","Equilibrium points","Eigenvalues","Eigenvectors"},{"A = 0",eq01,ev01,ev02}};



Grid[data1,Alignment->Left,Spacings->{2,1},Frame->All,ItemStyle->"Text"]

I think you have to use a custom formatting utility of some sort:

vectorForm[v_?VectorQ] := Row[{"(", Row[v, ","], ")"}];



Grid[data1 /. {

   m_?(MatrixQ[#, NumericQ] &) :> Row[vectorForm /@ m, ","], 

   v_?(VectorQ[#, NumericQ] &) :> vectorForm[v]},

 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 

 ItemStyle -> "Text"]

One distinct advantage of this approach is that it leverages Mathematica's expression formatting capabilities and avoids the lack of robustness of ToString. Compare the above method with @J42161217's on normalized eigenvectors:

eq01 = {0.01, 1.02};

ev01 = {{1, 3}, {2, 4}};

ev02 = Normalize /@ {{5, 5}, {6, 1}};



(* @MichaelE2 *)

data2 = {{"", "Equilibrium points", "Eigenvalues", 

    "Eigenvectors"}, {"A = 0", eq01, ev01, ev02}};

Grid[data2 /. {

   m_?(MatrixQ[#, NumericQ] &) :> Row[vectorForm /@ m, ","], 

   v_?(VectorQ[#, NumericQ] &) :> vectorForm[v]},

 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 

 ItemStyle -> "Text"]

(* @J42161217 *)

data2 = StringReplace[#, {"{{" -> "(", "}}" -> ")", "{" -> "(", 

        "}" -> ")"}] & /@ ToString /@ # & /@ {{"", 

     "Equilibrium points", "Eigenvalues", "Eigenvectors"}, {"A = 0", 

     eq01, ev01, ev02}};

Grid[data2, Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 

 ItemStyle -> "Text"]

Something similar happens with ordinary fractions and square roots.

Original formatting, in which a set appears in set notation:

Grid[data1 /. v_?(VectorQ[#, NumericQ] &) :> vectorForm[v], 

 Alignment -> Left, Spacings -> {2, 1}, Frame -> All, 

 ItemStyle -> "Text"]

Another possibility is to define a form that automatically formats numeric vectors and numeric matrices as desired:

MakeBoxes[EigenForm[e_], StandardForm] ^:= Internal`InheritedBlock[

    {MakeBoxes},

    MakeBoxes[m_List?numericVectorQ, StandardForm] := RowBox[

        {"(", MakeBoxes[Row[m, ","], StandardForm], ")"}

    ];

    MakeBoxes[m_List?numericMatrixQ, StandardForm] := RowBox[

        BoxForm`AddCommas @ BoxForm`ListMakeBoxes[m, StandardForm]

    ];

    MakeBoxes[e, StandardForm]

]



SetAttributes[{numericMatrixQ, numericVectorQ}, HoldAll];



numericMatrixQ[e_]:=MatrixQ[Unevaluated[e], System`Dump`HeldNumericQ]

numericVectorQ[e_]:=VectorQ[Unevaluated[e], System`Dump`HeldNumericQ]

Michael's example:

eq01 = {0.01,1.02};

ev01 = {{1,3},{2,4}};

ev02 = Normalize/@{{5,5},{6,1}};



data2={{"","Equilibrium points","Eigenvalues","Eigenvectors"},{"A = 0",eq01,ev01,ev02}};

Grid[

    data2,

    Alignment -> Left, Spacings -> {2, 1}, Frame -> All, ItemStyle -> "Text"

] //EigenForm