RootOf(,,,,) Mathcad-MAPLE

[ptc-1368288]

Alvaro,

You had that question before, but recollect that I might have been dense or otherwise not clear how it works. Here is an example. It would be interesting 14 users try it and comment. You can argue the Given/Find will do, but my point was the Mathcad-Maple RootOf(,,,,).

Mona, this is not reverse engineering
or braking the code, just a "recast".

Jean

[AlvaroDíaz]

On 3/20/2009 1:13:30 PM, jmG wrote:
>Alvaro,
>
>You had that question before,
>but recollect that I might
>have been dense or otherwise
>not clear how it works. Here
>is an example.

Hi Jean. I see some other post from you (and I can't see all posts, so, I assume that probably there are a lot), exhibing the benefits of the use of root, whith susseffull, and I agree that they are elegants solutions and your use of root is powerfull.

Now you demonstrate a technique for discretizing a problem with the help of root and how to handle the RootOf' maple function, without using allvalues (anothe maple function), but using mathcad functions.

>It would be
>interesting 14 users try it
>and comment. You can argue the
>Given/Find will do, but my
>point was the Mathcad-Maple
>RootOf(,,,,).

I haven't mc14, but what I can see in a few momment was only that for simbolycall evaluations root need the complete set of arguments, or something like this. So, I think that there are chance to have goods results in mc14 also.

>Mona, this is not reverse
>engineering
>or braking the code, just a
>"recast".

To understand some questions (like how roots are implemented in mu-pad, and see their capabilities), I think that who are interested can read mu-pad help, which is free as chm somewhere in the web. (So, actually you don't need install anything. I remember that I point one direction in the collab, but can't found where). And this is not reverse engineering, only is reading how the programs are working reading their documentation.

The function that I found usefull for me in maple was isolate (a very simple function, but related with root). This avoid-me to make some simple keystrokes errors. But this is only in mc11 working model.



Regards. Alvaro

[ptc-1368288]

Alvaro,

The version is still in the oven.
There is a new problem in evaluating the Ridder derivative. Though the InverseFunction is analytical, the Ridder shows discontinuities. I have suspected that for years, but couldn't prove up until this very moment. Please have a look in your positive collaboration style so much appreciated.

Jean

[ptc-1368288]

... all repaired !

Thought the previous work sheet is all correct. The function needs the Maple instruction. The immediate interpretation is that Maple instruction installs a better "root" than the already glorious Ridder [Mathcad]. A most subtile detail that should interest PTC, as long as Maple is still alive in the house.

jmG

[AlvaroDíaz]

Hi Jean, thanks for your comments, but I guess that there are a lot of collabs that can be extract more juice from this technique, which looks quite more powerful rather than the original root function.

What make maples is: because I know that there are a root, but can't show this in explicit form, then take note that exist and maybe later someone want to eval this. And don't provide a numerical approach, because I (maple, the program) know about giving so many rationals approachs as the user wants (this is the idea of the vpa, variable precision arithmetic).

Congratulations, now you can handle this RootOf in a fashion way, so expected answers can be greats.

But, probably only for mc11. Or not. In http://collab.mathsoft.com/read?109117,11e#109117 there are a link to

http://www.math.utah.edu/pub/mupad/doc/pdf_help.zip

with the mupad documentation, where can found RootOf (with the same name) but mupad version. Even the access to the symbolic engine is broken, I don't know about how much time this could be true. Also this is absolutely true only for the 14 version. Some more sophisticated symbolic utilities are very welcomed.

The usual way to test any root function is first with polynomials of 4th, 5th or above degree, which have a very uncomfortable variations. And there are some ones that approach very closed to the x-axis, but don't touch him. Other step is testing functions defined with integrals. So, a lot of stuff.

I see also that you uses a limit in your development. Unfortunately, this maple version is very bad taking limits, and only in very recent releases one can see effectively some very usuals limits with a reasonable answer (this is true for mathematica also). Maybe because lim are see like a minor calculus auxiliar, wich isn't. So, don't worry if found reds there.

Regards. Alvaro.

[ptc-1368288]

On 3/20/2009 11:47:16 PM, adiaz wrote:
>Hi Jean, thanks for your
>comments, but I guess that
>there are a lot of collabs
>that can be extract more juice
>from this technique, which
>looks quite more powerful
>rather than the original root
>function.
>
>What make maples is: because I
>know that there are a root,
>but can't show this in
>explicit form, then take note
>that exist and maybe later
>someone want to eval this. And
>don't provide a numerical
>approach, because I (maple,
>the program) know about giving
>so many rationals approachs as
>the user wants (this is the
>idea of the vpa, variable
>precision arithmetic).
>
>Congratulations, now you can
>handle this RootOf in a
>fashion way, so expected
>answers can be greats.
>
>But, probably only for mc11.
>Or not. In
>http://collab.mathsoft.com/rea
>d?109117,11e#109117 there are
>a link to
>
>http://www.math.utah.edu/pub/m
>upad/doc/pdf_help.zip
>
>with the mupad documentation,
>where can found RootOf (with
>the same name) but mupad
>version. Even the access to
>the symbolic engine is broken,
>I don't know about how much
>time this could be true. Also
>this is absolutely true only
>for the 14 version. Some more
>sophisticated symbolic
>utilities are very welcomed.
>
>The usual way to test any root
>function is first with
>polynomials of 4th, 5th or
>above degree, which have a
>very uncomfortable variations.
>And there are some ones that
>approach very closed to the
>x-axis, but don't touch him.
>Other step is testing
>functions defined with
>integrals. So, a lot of stuff.
>
>I see also that you uses a
>limit in your development.
>Unfortunately, this maple
>version is very bad taking
>limits, and only in very
>recent releases one can see
>effectively some very usuals
>limits with a reasonable
>answer (this is true for
>mathematica also). Maybe
>because lim are see like a
>minor calculus auxiliar, wich
>isn't. So, don't worry if
>found reds there.
>
>Regards. Alvaro.
______________________________

Guess what Alvaro !

Not finished yet, It might be possible to automate the construct via program. But tomorrow is " La cabanne � sucre", maple sirup in "Qu�bec all styles", a tradition ... nearly a religion !

Jean

[AlvaroDíaz]

On 3/21/2009 2:25:21 AM, jmG wrote:
>Guess what Alvaro !

Hi! Guess nothing. I don't see the problem. Maybe this helps.

Alvaro.

[ptc-1368288]

On 3/21/2009 5:50:33 AM, adiaz wrote:
>On 3/21/2009 2:25:21 AM, jmG wrote:
>>Guess what Alvaro !
>
>Hi! Guess nothing. I don't see the
>problem. Maybe this helps.
>
>Alvaro.
>______________________________

Does not help, all red

The problem is NOT one of extracting the argument of RooOf [,,,,].
The argument being what is in the bracketed basket [,,,,].
The problem is to substitute _Z --> u
Is there a rename function in Mathcad/Maple ?
Or another dirty trick ?
There may still be a reconstruct problem not yet evidenced.

Jean

[AlvaroDíaz]

On 3/21/2009 9:09:32 AM, jmG wrote:
>Does not help, all red
>The problem is NOT one of extracting the
>argument of RooOf [,,,,].
>The argument being what is in the
>bracketed basket [,,,,].
>The problem is to substitute _Z --> u

For this you need to isolate _Z first. The problem with this is with the underscore at the beginin of the variable, which is broken. You need something that guives _Z in the answer and then isolate them. Because there are always enclosed insede a RootOf function, the obvious is use op repeteadly over some expression like root(Z^2+1)

>Is there a rename function in
>Mathcad/Maple ?

Yes, is subs (substitute in Mathcad), but also there are subsop, which substitute an operator. Sometimes limit works, and others algsubs. Also there are a chainging of variable, from pdetools in the small set of maple that have mathcad.

Regards. Alvaro.