how to create, print and use variables using a loop in Mathematica?

Question

I want to create, print and be able to use (i.e. do symbolic operations) variables in Mathematica using a for loop or equivalent.

So, I have a bunch of variables of this form:

$$dS_i = -\beta_i S_i$$ where $i$ is an index.

I would like to end up with the variables defined in the notebook like this:

$$dS_1 = -\beta_1 S_1$$ $$dS_2 = -\beta_2 S_2$$ $$dS_3 = -\beta_3 S_3$$

etc.

So that I can see each of them in my screen and I can actually perform symbolic operations with them (e.g. $dS_1 + dS_2$).

If I do:

Do[Print["dI", i, "= -beta", i, "*S"], {i, 4}]

then I get the printing part but they are not variables, just strings.

I have also tried:

Table[dI[i] = -beta[i]*S, {i, 4}]

which generates the variables but then I don't get to see them on the screen.

Any ideas? thanks in advance

Answer 1

You could do something like this:

expr[i_] := Defer[dS[i] = -β[i]*S]

Do[expr[i][[1]]; CellPrint@Cell[BoxData@ToBoxes@expr[i], "Output"], {i, 4}]

In the Do loop I evaluate the assignment and also create a cell with the definition. You could use "Input" instead of "Output" if you prefer.

Answer 2

You could try something like the following:

Table[dS[i] = -β[i]*S[i], {i, 4}];

To see the definitions for dS use the function Definition.

Definition[dS]
(* 
dS[1]=-S[1] β[1]

dS[2]=-S[2] β[2]

dS[3]=-S[3] β[3]

dS[4]=-S[4] β[4] 
*)

See that you can perform operations on dS.

dS[1] + dS[2]
(* -S[1] β[1] - S[2] β[2] *)

Answer 3

Dos this work

Do[dI[i] = -beta[i]*S; Print["dI", i, "= -beta", i, "*S"], {i, 4}]

Any method that can print what you want has to change the expression to a kid of String. At the end, the printed expression the way you what has to be kind of String

You can try Inactivate

Do[dI[i] = -beta[i]*S; Print[Inactivate[dI[i] = -beta[i]*S]], {i, 4}]