@Ronan You haven't given any explanation as to why a clash (such as `print`) would cause a problem. What problem would it cause, that you don't know how to overcome?

Why precisely do you need to avoid any "clash"? Can you give an example of such a "clash", for which you believe that you could not utilize your procedure successfully?

The worksheet you've shown doesn't make your purported problem clear, IMO. You used Line as the procedure's parameter name, yet then passed it line=... as an argument, so naturally that doesn't do much. What were you trying to illustrate (apart from your using the wrong name when calling it...)?

Why do you think that you cannot/oughtn't use the lowercase name line for your keyword parameter name in the definition of your procedure?

Please be very explicit, because I really don't understand what you're trying to convey. Thanks.

ps. There are lots of Library procedures that use some other Library procedure name as one of its keyword parameters. An example of such a keyword is value, which is also the name of a top-level command. That doesn't prevent such procedures from being used properly.

I forgot to mention, your (mixed Vector/list) elementwise arithmetic can also be done using infix notation, which I think looks tidier here than the prefix form. Eg,

Download Perpendicular_3D_lines_acc.mw

@mmcdara The whole top-level local declaration thing seems like a bad idea to me. I would never use it in my own work.

I simply use another name, instead of one with a special meaning to Maple.

Is it deliberate to have sigma__nu in M, etc, while having sigma__v in sigma__Y, etc?

@vv Thanks!

That is consistent with the cited Documentation sentence, which mentions, "...as if it had been entered or read from a file".  If one enters the name (eg. manually types it in at the top-level) then any top-level locally-declared name is what one would then get, naturally.

But by default (ie. with no special top-level local declaration of it) entering a name at the top-level gets the global name. I don't know whether in future I'll always qualify my own personal description of this issue, to cover the special situation of a local declaration. Maybe. If I remember. (I'm not a huge fan of the top-level local declarations, btw.)

Download parse_ex4.mw

@Anthrazit See also the first paragraph of the Description section of the Help page for the parse command,

"The parse command takes a Maple string and parses the string into a Maple expression as if it had been entered or read from a file."

Another example, where I have a file names file.mpl in my home directory, whose contents are just the single line,
   a;

Download parse_ex3.mw

@mmcdara I had written it at first with convert,base .

Then I did some perfomance stress testing and noticed that Explode was slightly faster (for the sizes I considered).

@jasser 

Download fl_op.mw

Note that in your earlier examples the log10 of the repeating part can be used to indicate which is the last decimal position occupied by the non-repeating part. So trailing zeroes needn't get in your way there.

So, for example, if you wanted the number of decimal places (to the right of the dot, including zeroes to its left) taken up by the fractional part of the non-repeating part, then you could compute that as 1 less than the decimal place in which the repeating part started.

Download rep_dec_2.mw

Please put your close followup queries here, instead of spawning wholly separate new Question threads for such.

The dsolve command expects its first argument to be a list or set of both the differential equations and the initial conditions, together in a single list. But your attempt is passing those as two separate lists.

Instead, try something like this:

   SOL := dsolve({EL[V][], IC[V][]}, [r[V](t), theta[V](t)], numeric, output = listprocedure):

ps. Are polar coordinates best here? By what proportion might you expect r to vary? (If varying by only a very small proportion, would extra working precision be necessary?)

@MaPal93 Please don't start another thread for this.

@ceeeb It wasn't just a hint, IMO. I explicitly explained that the 2D Input sigma' instances were different (and how).

ps. I deleted the eight extra copies of your response.

Please stop posting multiple Question threads on this.

If you have followup queries then please put them here, instead of spawning wholly separate new Question threads on this.

@Jack D Well, the first thing is that I used fsolve instead of solve.

The maxsols option of fsolve currently works for a finite range, so I supplied such, admittedly based on a visual plot. (I could also have used m=-100..100. It's generally faster if it's not unnecessarily wide. Seems I could have used -10^6..10^6 as well.)

No, I didn't specify a starting point.