using simplify twice in same symbolic command

[Ninetrees]

Curious. Until today, I don't recall thinking of using simplify twice in the same symbolic command. Don't know how this will appear in M11 because I wrote it in M14. (I'm still trolling for a copy of M11, but no joy to date.) I searched the collab for the keywords symbolic and twice but found no reference to this.

Rich
http://www.downeastengineering.com/

[RichardJ]

On 11/28/2009 5:05:42 PM, woodwise wrote:
>Curious. Until today, I don't recall
>thinking of using simplify twice in the
>same symbolic command.

Or me. It seems to behave the same as simplify,max. For this example, anyway.

>Don't know how
>this will appear in M11 because I wrote
>it in M14.

See the attached.

Richard

[ptc-1368288]

You are committing the same mistake many would. You are looking for a very particular integral function instead of a more generalized one, which more generalized integral might be more realistic and not further simplifiable than it can go.
Twice simplify:
if it means something in MuPad, don't know, but in Maple = no meaning.



What did you expect ?

jmG

[Ninetrees]

Well, yes. I /am/ looking at those specific limits because, well, those are the limits I am using! M14 gives the correct numerical answer if I choose = rather than ->, but I wanted a symbolic answer to this specific problem, so I did what I always do: I simply chose ->. Then I went through the steps in my original post. I simplified it, then noticed that the simplified answer could be simplified by hand pretty easily, and, on a whim, decided to see what would happen if I chose simplify twice. I liked the result, because it agreed with my hand calcs. Looks like MuPad does what I'd do when it applies the keywords as they appear to the result of each step. NOW it seems kinda intuitive, but there were many times in the past when I got a certain answer from M12/13/14 and simplified the result by hand. I'll certainly try this method in the future to save myself some work. I don't see that your solution is any better, though I understand your point. In fact, it introduces another variable, c, which you then set to pi. So that method requires me to go to the effort to set up another function and evaluate that. I'll keep the approach in mind for other cases, but here I like the double use of simplify. There might even be value to applying simplify several times.

Rich
http://www.downeastengineering.com/

[AlvaroDíaz]

On 11/28/2009 8:24:34 PM, woodwise wrote:
>... here I like the double use of simplify. There might even be value to applying simplify several times.

I think that have no effects, other than increase the algorithms that mupad apply before set the answer. In mupad there are two distinct simplify: undercase and uppercase simplify keyword, one of them have an optional second argument setting the number of steps to reduce the expression.

Mathcad implements "max" as second argument to set the maximun steps avaibles, and I think that this is the the best way to try to call simplify for complicated expression, but with better support from ptc, because it's an undocumented feature, like multiple simplify keywords.

A workaround could be mask the "max" keyword in simplify:



This prevents that if in other releases simplify,max isn't avaible or change the name (because isn't nothing happy) changing the meaning of one variable recompose syntax of another undocumented feature.

Regards. Alvaro.

[RichardJ]

On 11/29/2009 1:31:45 AM, adiaz wrote:

>changing the meaning of one variable
>recompose syntax of another undocumented
>feature.

"Simplify,max" is documented. "Simplify,min" on the other hand, isn't.

Richard

[AlvaroDíaz]

On 11/29/2009 8:22:57 AM, rijackson wrote:
>"Simplify,max" is documented.
>"Simplify,min" on the other hand, isn't.

You're right, thanks for the correction. Then, double simplify seems to be equivalent to simplify,max.

Regards. Alvaro.

[ptc-1368288]

On 11/29/2009 3:27:02 PM, adiaz wrote:
>On 11/29/2009 8:22:57 AM, rijackson
>wrote:
>>"Simplify,max" is documented.
>>"Simplify,min" on the other hand, isn't.
>
>You're right, thanks for the correction.
>Then, double simplify seems to be
>equivalent to simplify,max.
>
>Regards. Alvaro.
_________________________________________

How would you conceive a "Simplify,min". Would it be a non-sense ? Assuming max represents the last (or max) step in the process of equivalent algebraic transformation of an expression, past all the implemented steps, it should go back to the the entered step, then where would a "min" outputs something if any one is already displayed.

"There are many situations where you want to write a particular algebraic expression in the simplest possible form. Although it is difficult to know exactly what one means in all cases by the �simplest form�, a worthwhile practical procedure is to look at many different forms of an expression, and pick out the one that involves the smallest number of parts".

"You can often use Simplify to clean up complicated expressions that you get as the results of computations."

"Simplify is set up to try various standard algebraic transformations on the expressions you give. Sometimes, however, it can take more sophisticated transformations to make progress in finding the simplest form of an expression.
FullSimplify tries a much wider range of transformations, involving not only algebraic functions, but also many other kinds of functions."
"For fairly small expressions, FullSimplify will often succeed in making some remarkable simplifications. But for larger expressions, it often becomes unmanageably slow.
The reason for this is that to do its job, FullSimplify effectively has to try combining every part of an expression with every other, and for large expressions the number of cases that it has to consider can be astronomically large.
Simplify also has a difficult task to do, but it is set up to avoid some of the most time�consuming transformations that are tried by FullSimplify. For simple algebraic calculations, therefore, you may often find it convenient to apply Simplify quite routinely to your results.
In more complicated calculations, however, even Simplify, let alone FullSimplify, may end up needing to try a very large number of different forms, and therefore taking a long time. In such cases, you typically need to do more controlled simplification, and use your knowledge of the form you want to get to guide the process."
................................................

From the MuPad web demo and the simplified function illustrated. it does solve for the integral function but only as a symbolic algebraic expression. The same Integral plugged in Mathcad 11 simplifies to Psi(z), a lot more interesting result. I have recollection passing it back to Stuart. You can try same exercise with "Simplify,max" and check if it results in Psi(z).
Psi(z): Digamma function for complex z.

jmG

[PhilipOakley]

On 11/29/2009 8:22:57 AM, rijackson wrote:
>On 11/29/2009 1:31:45 AM, adiaz wrote:
>
>>changing the meaning of one variable
>>recompose syntax of another undocumented
>>feature.
>
>"Simplify,max" is documented.
>"Simplify,min" on the other hand, isn't.
>
>Richard
>
>
I have a vague recollection that somewhere in JS
Cohen's two books on "Computer Algebra and
Symbolic Calculation", there is a comment about
'min' being just the negative of 'max' so that may
be a reason.

However for most folk they will still want both
...


Philip Oakley

[ptc-1368288]

On 11/29/2009 7:12:10 PM, philipoakley wrote:
...
>I have a vague recollection that
>somewhere in JS Cohen's two books on "Computer >Algebra and Symbolic Calculation",
>there is a comment about
>'min' being just the negative of 'max'
>so that may be a reason.
>
>However for most folk they will still
>want both
>...
>Philip Oakley
_______________________________________

Not bad an idea to exercise 'max' & 'min'
Here are 6 equivalent forms for MuPad.



If 'max' is the max steps MuPad can equate,
then 'min' should reverse-recover.
Does it make sense ?
It would fix/illustrate and delight PTC
for the monthly news (fill a lot of hungry teeth).

jmG

[ptc-1368288]

... back to the given exercise,
Mathcad 11.2a recovers the original red form. It does go by some extra algebraic rules that maybe were not part of the Mathsoft-Maple subcontract.



Now, up to MuPad and those interested to demystify the process of their Mathcad 14. It might very well clear all questions as well as point out some eventual keywords left unexplained because not explored. A simple exercise worth the effort. Some form are preferred for good numerical reason and/or project oriented goal.

jmG

[ptc-1368288]

... hint to the exercise:

If MuPad has "parfrac & confrac", you should have no problem.

jmG

[ptc-1368288]

On 11/30/2009 2:27:50 AM, jmG wrote:
>... hint to the exercise:
>
>If MuPad has "parfrac &
>confrac", you should have no
>problem.
>
>jmG
______________________________

In fact MuPad just needs the right 'parfrac'.



It then needs a symbolic interpretative step.
Here is my point: the interpretative step may/myNOT be implemented in MuPad. Whether is is mathematically feasible ? If 'max' is implicit of 'parfrac', then what a stupid keyword ! and if 'min' is the "manual interpretative step", why not some examples, at least this one in 6 forms that can illustrate 'max' and 'min' if 'min' has any meaning.

jmG