export table with number written in scientific notation

Question

I am trying to write on a file the table generated in this way:

error = ConstantArray[0, 3];
error[[1]] = ScientificForm[Sqrt[CovMat[[1, 1]] /. out[[2]]]];
error[[2]] = ScientificForm[Sqrt[CovMat[[2, 2]] /. out[[2]]]];
error[[3]] = ScientificForm[Sqrt[CovMat[[3, 3]] /. out[[2]]]];
Ris = out[[2]] /. Rule -> (#2 &);
par = out[[2]] /. Rule -> (#1 &);
Finale = MapThread[{#1, ScientificForm[#2], #3} &, {par, Ris, 
    error}] // TableForm

CovMat anf out are generated in a previoous part of the code (a NMinimize). Typing Finale on the notebook I find:

M   4.35203*10^(10) 4.2566*10^(9)
\[Delta]    4.10847*10^(5)  2.12356*10^(4)
L   1.01689*10^(9)  1.30717*10^(16)

The problem is that in the file I find:

"M  ScientificForm[1.7467449664329874*^11]  \
ScientificForm[4.784135569792907*^9]

[\Delta]    ScientificForm[606745.0359163599]   \
ScientificForm[10326.21966853348]

L   ScientificForm[2.788541796939519*^10]   \
ScientificForm[1.5410843643505646*^18]"

I used Export and

file = OpenAppend["out.txt"]

string = ExportString[Finale,"Table"];

WriteString[file, string]
WriteString[file, "\n"];

Close[file]

(I thought that ExportString read the values as they are) but I cannot get rid of that ScientificForm.

I suspect that I should use something like:

Export["file.dat", {elem1->expr1, elem2->expr2, ...}, "Rules"]

but I cannot find a way to express the rule.

Answer 1

Why your file looks like that

As we can read at the end of of "Details and Options" section of ScientificForm documentation:

ScientificForm acts as a "wrapper", which affects printing, but not evaluation.

So although

In[1]:=  ScientificForm[410846.99999999994`]

is outputted as

Out[1]//ScientificForm=
          4.10847 x 10^5

under the hood it is still number 410846.99999999994` wrapped with ScientificForm:

In[2]:=  ScientificForm[410846.99999999994`] // FullForm
Out[2]//FullForm=
          ScientificForm[410846.99999999994`]

This number wrapped with ScientificForm when exported to "Table" format is somehow converted to a string:

In[3]:=  ExportString[ScientificForm[410846.99999999994`],"Table"]
Out[3]:= ScientificForm[410846.99999999994]

From simple experiment:

In[4]:=  Block[{ToString = toString}, ExportString[{{a, b}, {c, d}}, "Table"]]
Out[4]:= toString[a, InputForm]    toString[b, InputForm]
          toString[c, InputForm]    toString[d, InputForm]

we see that ToString[#, InputForm]& is used and, as one would expect, in input form we have:

In[5]:=  ToString[ScientificForm[410846.99999999994`], InputForm]
Out[5]:= ScientificForm[410846.99999999994`]

This is the reason behind output you're getting.

How to get what you want

What you want is to convert numbers wrapped with ScientificForm to strings in OutputForm not in InputForm. Since OutputForm is default form of ToString we don't specify any form:

In[6]:=  ScientificForm[410846.99999999994`] // ToString
Out[6]:=              5
          4.10847 x 10

It's not exactly what we want, but since "ordinary" *.dat file has no support for superscripts we need to change our scientific form a bit, to take that into account. We can do that using NumberFormat option:

In[7]:=  ScientificForm[410846.99999999994`, NumberFormat -> (#1 <> "*10^(" <> #3 <> ")" &)] // ToString
Out[7]:= "4.10847*10^(5)"

That's of course just an example you can customize it to suit your needs.

Going back to your particular case. Start with your table containing "raw" numbers not wrapped with any formating function:

In[8]:=  data = {
             {M, 4.35203*10^(10), 4.2566*10^(9)},
             {δ, 4.10847*10^(5), 2.12356*10^(4)},
             {L, 1.01689*10^(9), 1.30717*10^(16)}
          };

and make appropriate conversion just before exporting:

In[9]:=  Export[
              "file.dat"
              ,
              data /. a_?NumberQ :> 
                  ToString@ScientificForm[a, NumberFormat -> (#1 <> "*10^(" <> #3 <> ")" &)]
          ]
Out[9]:= file.dat

this produces following file.dat file:

M   4.35203*10^(10)  4.2566*10^(9)
δ   4.10847*10^(5)   2.12356*10^(4)
L   1.01689*10^(9)   1.30717*10^(16)