@adel-00 I will check your code soon. However, again it seems like you're apologizing for using loops. There's no problem with using loops, and I never said to not use them! What I don't want you to use are integration techniques, whether they be Maple's packaged routines or your own ad hoc method.

Now perhaps you can't produce a symbolic expression for the integrand; that is often the case. In that case, can you write a procedure that numerically evaluates the integrand for any real numeric w? That would be sufficient. Note that I said integrand, not integral.

@Earl Quotes are very often the key to a successful Google search. I think that without quotes you get something close to the intersection of the separate searches for "pedal" and "curve". This intersection is of course much too large to be of any practical value.

@mmcdara The reason that I said that I was editing rather than correcting is that your usage of contributor wasn't incorrect, and indeed contributor can be synonymous with contributing factor (however, this isn"t the most-usual usage). However, in this particular context, that led to the ambiguity mentioned by the OP; indeed, I had noticed exactly that same ambiguity immediately upon initially reading your sentence. I thought that it was possible, although unlikely, that you were referring to a human co-author of the worksheet as a contributor​​​​​. 

Googling "pedal surface" (with the quotes) turns up several useful hits (after ignoring numerous articles about the surfaces of mechanical pedals, of course), including JSTOR articles from 1863 and 1881.

It's surprising that this obvious generalization isn't at all mentioned in either the Wikipedia or MathWorld articles "Pedal curve". By the way, that Wikipedia article is quite detailed.

@ecterrab I think that you've misinterpreted Preben''s comment. He's not objecting to the RootOf. Rather, he's pointing out that this expression cannot be evaluated at x=0, thus one can't solve for the constants of integration in the normal way.

Hopefully Preben will verify my guess about his intended meaning. 

@mmcdara I wasn't correcting you--I was only editing--although I have no compunction against correcting (or elaborating on subtle ambiguities in) our contributors' English usage when it seems worthwhile to do so. Anyway, perhaps you realize at this point that contributor usually refers to a person who contributes, whereas the most-common term for a nonperson entity that contributes is contributing factor (even in nontechnical contexts where factor has no special meaning).

@adel-00 You claim that you want to "integrate L1 w.r.t. w from -infinity to infinity numerically." Well, then show me an expression L1 that depends on w. The end result of the worksheet that you just posted is a sequence of numbers L1[-10] ... L1[10]; that's not an expression that depends on w. Those numbers may be approximations to various parts of the integral; I can't tell for sure. So, I'm telling you again, for the time being, forget about integrating this expression. Instead, give me a worksheet that does nothing more than construct the expression L1(w) which is to be integrated. If you need to use loops to define that expression, that's totally fine. If the expression is too long to display, that's fine.

@dnaviaux I'd guess that in mmcdara's final sentence, "contributor" could be replaced by "factor that contributes to the error".

Before we can integrate the expression, we need to have the expression in Maple. So, forget about integrating for the time being. Concentrate on simply having this rather complicated expression entered into Maple such that it will display the expression in prettyprinted form. After that, we can discuss integrating it.

As it stands, it's difficult for me to distinguish the parts of your code that are for integrating from the parts that are for simply defining the integrand.

@mmcdara Okay, I now understand some things that were confusing you:

1. The categories of submissions to MaplePrimes: There are exactly five types of submissions to MaplePrimes---Posts, Comments, Questions, Answers, and Replies---organized like this:
(root)
    Post
        Comment
    Question
        Reply
        Answer
            Reply

When I use those words (or their inflected forms) capitalized, I am referring strictly to this MaplePrimes classification, not to what those words mean in English.

2. Definition of answer (note: lowercase): I checked several online English dictionaries, and I found to my great surprise that your translation software is correct: In every dictionary that I checked, the primary defintion of answer (noun) is synonymous with reply. So, under this defintion, anything at all said in response to a question is an answer (including nonsense, refusals, or requests for clarification). It was only in the fourth dictionary that I checked that I found a secondary definition akin to what I was thinking: "a solution to a problem". I think that this is the intended meaning of "answer" on the vast majority of the question-and-answer sites on the Internet.

3. What should be an Answer (note: uppercase): You wrote:

• You already said me something like  "an answer is the definitive and unique answer to a question while a reply is just one among many proposals to answer this problem". Is this right?

​​​​​​No, I didn't say anything like that, nor would I ever, because that statement is completely contrary to my way of thinking. Furthermore, I find the idea that the typical Maple question even has a "definitive and unique answer" ridiculous. So, I wonder where that statement comes from. 

I believe that a contribution here should be classified as an Answer if its author's primary intent is to present a solution to a problem posed in a Question. Note the emphasis on intent: It makes no difference to me if the contribution fails to fulfill this intent; it still should be an Answer. Thus, all of the following should be Answers:

1. Items that intend to present a solution but are incorrect.
2. Items that intend to present a solution to only one of several questions posed in the Question.
3. Items that intend to present a solution to a question that is implied by the Question but wasn't directly asked.
4. Items that intend to present a solution to another question that should have been asked in the Question but wasn't asked due to the OP's lack of knowledge.
5. Responses in the form of rhetorical questions if the intent is to make the solution occur to the OP.
6. Items that present information that by itself is useless to the OP but could be combined with a future response provided by an expert such that the combination is usable to the OP (perhaps, after a followup Reply that integrates the responses).
7. Responses that for pedagogical reasons are incomplete, such as those that avoid directly solving homework problems but instead give hints or examples.

@acer Expanding on your method, any Unicode "point" in "U+x" form (where x is a string of hex digits) can be converted to a symbol via

`convert/Unicode`:= 
    (U::And(
        string, 
        Not({0,1,2}) &under length,
        identical("U+") &under (index, ()..2),
        satisfies(
            U-> StringTools:-AndMap(StringTools:-IsHexDigit, U[3..])
        )
    ))->
    nprintf(`&#%ld;`, convert(U[3..], ':-decimal', 16))
:
convert("U+03A9", Unicode);
 

@acer Thanks for spotting that, and I have corrected the code above.

@dnaviaux By "style", I only meant with respect to word-processung features such as I mentioned. As shown in my other Answer, adding nonASCII characters to printf output is easy if you're content with fixed character width.

@dnaviaux If that style of report is "fine" with you, then it's trivial to do with printf, and I withdraw my statement about it being "nearly impossible". I was thinking of standard word-processing functionality: word wrapping, page breaks, bold and italics, sub- and superscripts, smoothing the right edges of paragraphs, and supporting non-fixed-width fonts.

I agree with acer: I've changed many of your Replies to Answers and usually given them a Vote Up in the process, all the while thinking "What was he thinking? This is obviously an Answer." But only the one who wrote the Question can select an Answer as Best.

So many of my good Answers don't get Voted Up. It does sadden me. Many users are completely unaware of those buttons.