Using StringReplace

Question

Here is my code. I have an equation that is given below. This code sorts through the terms and puts each term into a list and then each factor of the term into another list. I am able to call each factor in the equation.

eqn = Derivative[1][f1][y] . E^(I*x)*Derivative[1][f2][y] . 
     (2*I*E^(2*I*x)) + Derivative[1][f1][y] . 
     (I*E^(I*x))*Derivative[1][f2][y] . E^(2*I*x) + 
 Derivative[1][f3][y] . (3*I*E^(3*I*x)) + 
 Derivative[1][g3][y] . (I*E^(I*x)) + 
 (-f2[y]) . (2*I*E^(2*I*x))*Derivative[2][f1][y] . 
     E^(I*x) + (-f1[y]) . (I*E^(I*x))*
   Derivative[2][f2][y] . E^(2*I*x) + 
 Derivative[1][f1][y] . (I*E^(I*x))*
   Derivative[1][g2][y] + (-f1[y]) . (I*E^(I*x))*
   Derivative[2][g2][y];

Newlist = List @@ eqn;

For[i = 1, i < Length[Newlist] + 1, i++,


Terms = List @@ Newlist[[i]];
 Factor1 = Terms[[1]];
 Factor2 = Terms[[2]];

 Print[Factor1];
 Print[Factor2];

 ]

Here is my output from running this code

$\text{f1}'(y).e^{i x}$

$\text{f2}'(y).\left(2 i e^{2 i x}\right)$

$\text{f1}'(y).\left(i e^{i x}\right)$

and so on.

Most factors have a "." between the $f$ function and the $e^{m i x}$. I want to get rid of the period. I cannot get rid of the periods in the "eqn" definition as they are there for a specific reason. Here is what I have tried so far.

StringReplace["Factor1", "." -> ""]

Which outputs "Factor1" however, when I do this

StringReplace["f1'[y].e^{i x}","."->""]

It returns

$\text{f1}'(y)e^{i x}$

without the period how I want it.

My question is: How can I call Factor1 in the StringReplace without Mathematica thinking "Factor1" is the string and will replace it with the expression that it is equal to?

Thank you for any help

Answer 1

result = List @@@ List @@ eqn /. Dot -> Times

TeXForm @ Column @ result

$\begin{array}{l} \left\{e^{i x} \text{f1}'(y),2 i e^{2 i x} \text{f2}'(y)\right\} \\ \left\{i e^{i x} \text{f1}'(y),e^{2 i x} \text{f2}'(y)\right\} \\ \left\{\text{f3}'(y),3 i e^{3 i x}\right\} \\ \left\{\text{g3}'(y),i e^{i x}\right\} \\ \left\{-2 i e^{2 i x} \text{f2}(y),e^{i x} \text{f1}''(y)\right\} \\ \left\{-i e^{i x} \text{f1}(y),e^{2 i x} \text{f2}''(y)\right\} \\ \left\{i e^{i x} \text{f1}'(y),\text{g2}'(y)\right\} \\ \left\{-i e^{i x} \text{f1}(y),\text{g2}''(y)\right\} \\ \end{array}$