[MATHCAD] Symbolic processor

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[MATHCAD] Symbolic processor
Author: Mark Smith    Posted: Thu, 9 Sep 1999 14:37:03 +0100
why is it that the symbolic engine seems so unable to simplify the
following:

sqrt(a/b).sqrt(b/a)

I seem to end up having to simplify results myself which defeats the object.

Does anyone have any tips on how to maximise the accuracy of rkfixed or
numerical integration as I am finding the numerical solution to a problem
diverging badly from the analytic solution? making TOL smaller seems not to
help. The function is a very smooth slowly changing one with no abrupt
surprises.

TIA Mark

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RE: [MATHCAD] Symbolic processor
Author: Diehl Ted-ETD012    Posted: Thu, 9 Sep 1999 11:31:29 -0400
Mark,

My experience is that Rkadapt is much better and more accurate than rkfixed.

Ted Diehl, Ph.D.
Principal Staff Engineer
MTC Advanced Drop & Structures Team
Motorola
8000 W. Sunrise Blvd
Fort Lauderdale, FL 33322
954 723-8024




-----Original Message-----
From: Mark Smith /> Sent: Thursday, September 09, 1999 9:37 AM
To: 'Mathcad
Subject: [MATHCAD] Symbolic processor


why is it that the symbolic engine seems so unable to simplify the
following:

sqrt(a/b).sqrt(b/a)

I seem to end up having to simplify results myself which defeats the object.

Does anyone have any tips on how to maximise the accuracy of rkfixed or
numerical integration as I am finding the numerical solution to a problem
diverging badly from the analytic solution? making TOL smaller seems not to
help. The function is a very smooth slowly changing one with no abrupt
surprises.

TIA Mark

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Re: [MATHCAD] Symbolic processor
Author: Chris Whitford    Posted: Thu, 09 Sep 1999 16:40:03 +0100
Integrating differential equations accurately is not automatic. There are
several solvers in Mathcad, for different types of problem and you may have
to experiment. A common problem is when an equation has 2 solutions - one
which is stable and one which is not. For example, consider

dy(x)/dx - k^2 y = 0

This has the solutions y = A exp(-k x) and y = B exp(k x). Even if the
solution which satisfies the initial conditions is stable, any numerical
error will excite the unstable solution, which then grows exponentially,
until it dominates. If the equation is linear, you can sometimes solve it
by integrating backwards from an assumed final state, then find the final
state which gives the known initial conditions.

Chris Whitford

At 14:37 09/09/99 +0100, you wrote:
>
>Does anyone have any tips on how to maximise the accuracy of rkfixed or
>numerical integration as I am finding the numerical solution to a problem
>diverging badly from the analytic solution? making TOL smaller seems not to
>help. The function is a very smooth slowly changing one with no abrupt
>surprises.
>
>TIA Mark


+----------------------------------------------------------------------+
+ Chris Whitford University of Leicester +
+ Tel: (44) 116 252 3496 Space Research Centre +
+ Fax: (44) 116 252 2464 Physics and Astronomy Department +
+ University Road +
+ http://www.star.le.ac.uk/ LEICESTER LE1 7RH +
+ UK +
+----------------------------------------------------------------------+

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Re: [MATHCAD] Symbolic processor
Author: Kenneth R Foster    Posted: Thu, 09 Sep 1999 11:49:58 -0400
At 02:37 PM 9/9/1999 +0100, you wrote:
>why is it that the symbolic engine seems so unable to simplify the
>following:
>
>sqrt(a/b).sqrt(b/a)
>
>I seem to end up having to simplify results myself which defeats the object.

but this can't be simplified unless you make assumptions about the domain
of a and b (e.g. a,b)

Mathcad 8 has an "assume" keyword that should let you simplify this
expression, but in few minutes I spent with it just now I did not figure
out how to use it correctly.


Kenneth R Foster
Department of Bioengineering
University of Pennsylvania
220 S. 33rd St.
Philadelphia PA 19104-6392
215-898-8534 (office)
fax (reflects to my email) 1-888-514-3577
Chair, EMBS Committee on Man and Radiation 1997-
*****************************************************************************
SSIT Website: http://www4.ncsu.edu/unity/users/j/jherkert/
COMAR website http://homepage.seas.upenn.edu/~kfoster/comar.htm
Blurb for latest book http://homepage.seas.upenn.edu/~kfoster/book.htm
Recent Papers http://homepage.seas.upenn.edu/~kfoster/papers.htm
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Re: [MATHCAD] Symbolic processor
Author: Ray Girvan    Posted: Thu, 9 Sep 1999 22:02:25 +0100

Kenneth R. Foster wrote:

> Mark Smith wrote:
>> why is it that the symbolic engine seems so unable to simplify
>> the following: sqrt(a/b).sqrt(b/a)

> but this can't be simplified unless you make assumptions about
> the domain of a and b (e.g. a,b)
> Mathcad 8 has an "assume" keyword that should let you simplify
> this expression, but in few minutes I spent with it just now I did
> not figure out how to use it correctly.

It *ought* to simplify as signum(a*b) for real a and b. But Mathcad
doesn't seem to like it, even though the syntax works on similar
problems, such as:

\x^2 simplify,assume=real -> signum(x)*x

(where \ is sqrt sign, "simplify,assume=real" is entered in the
symbolic equals placeholder, and "=" is the bold "Ctrl=").

Ray

--
+++ Technical Author +++ Topsham, Devon, UK
http://www.users.zetnet.co.uk/rgirvan/ +++ The Apothecary's Drawer


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Re: [MATHCAD] Symbolic processor
Author: Jonathan Armitage    Posted: Fri, 10 Sep 1999 09:32:51 +0100
In Mathcad 6.0 there appears to be no problem. It gives the answer 1 directly.

and sqrt(a/b)/sqrt(b/a) yields a/b as it should.



Jonathan Armitage


At 14:37 09/09/99 +0100, you wrote:
>why is it that the symbolic engine seems so unable to simplify the
>following:
>
>sqrt(a/b).sqrt(b/a)
>
>I seem to end up having to simplify results myself which defeats the object.
>
>Does anyone have any tips on how to maximise the accuracy of rkfixed or
>numerical integration as I am finding the numerical solution to a problem
>diverging badly from the analytic solution? making TOL smaller seems not to
>help. The function is a very smooth slowly changing one with no abrupt
>surprises.
>
>TIA Mark
>
>-------------------------------------------------------------
>The Mathcad List - Discussion, Support & News
> Contributions: /> >To unsubscribe: Send in the body: unsubscribe mathcad
> To: /> > Hosted by: Adept Scientific http://www.adeptscience.com
> List Archive: http://lists.adeptscience.co.uk/
>
>
Jonathan G M Armitage phone 01334 463110
ext 3110


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Re: [MATHCAD] Symbolic processor
Author: Kenneth R Foster    Posted: Fri, 10 Sep 1999 07:19:50 -0400
At 09:32 AM 9/10/1999 +0100, you wrote:
>In Mathcad 6.0 there appears to be no problem. It gives the answer 1 directly.
>
>and sqrt(a/b)/sqrt(b/a) yields a/b as it should.

If no limits are placed on a and b, this answer may be incorrect and that
is a very dangerous simplification
Kenneth R Foster
Department of Bioengineering
University of Pennsylvania
220 S. 33rd St.
Philadelphia PA 19104-6392
215-898-8534 (office)
fax (reflects to my email) 1-888-514-3577
Chair, EMBS Committee on Man and Radiation 1997-
*****************************************************************************
SSIT Website: http://www4.ncsu.edu/unity/users/j/jherkert/
COMAR website http://homepage.seas.upenn.edu/~kfoster/comar.htm
Blurb for latest book http://homepage.seas.upenn.edu/~kfoster/book.htm
Recent Papers http://homepage.seas.upenn.edu/~kfoster/papers.htm
-------------------------------------------------------------
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Re: [MATHCAD] Symbolic processor
Author: Jonathan Armitage    Posted: Fri, 10 Sep 1999 13:43:57 +0100
I humbly accept your comment.

At 07:19 10/09/99 -0400, you wrote:
>At 09:32 AM 9/10/1999 +0100, you wrote:
>>In Mathcad 6.0 there appears to be no problem. It gives the answer 1
directly.
>>
>>and sqrt(a/b)/sqrt(b/a) yields a/b as it should.
>
>If no limits are placed on a and b, this answer may be incorrect and that
>is a very dangerous simplification
>Kenneth R Foster
>Department of Bioengineering
>University of Pennsylvania
>220 S. 33rd St.
>Philadelphia PA 19104-6392
>215-898-8534 (office)
>fax (reflects to my email) 1-888-514-3577
>Chair, EMBS Committee on Man and Radiation 1997-
>*****************************************************************************
>SSIT Website: http://www4.ncsu.edu/unity/users/j/jherkert/
>COMAR website http://homepage.seas.upenn.edu/~kfoster/comar.htm
>Blurb for latest book http://homepage.seas.upenn.edu/~kfoster/book.htm
>Recent Papers http://homepage.seas.upenn.edu/~kfoster/papers.htm
>-------------------------------------------------------------
>The Mathcad List - Discussion, Support & News
> Contributions: /> >To unsubscribe: Send in the body: unsubscribe mathcad
> To: /> > Hosted by: Adept Scientific http://www.adeptscience.com
> List Archive: http://lists.adeptscience.co.uk/
>
>
Jonathan G M Armitage phone 01334 463110
ext 3110


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RE: [MATHCAD] Symbolic processor
Author: Mark Smith    Posted: Mon, 13 Sep 1999 10:27:13 +0100
Thanks for all the hints, I have finally tracked down my problem as a bug in
version 8 symbolic processor see attached mathcad document, Version 6 give
the correct answer. My problem with rkfixed result diverging from the
analytic one is entirely due to the analytic result as given by the symbolic
engine being wrong. I am now loosing even more faith in version 8, why did I
ever desert version 6 I will now have doubts about any results!!!

Mathsoft: What are you doing to your customers?

Regards Mark

> -----Original Message-----
> From: /> > Behalf Of Jonathan
> Armitage
> Sent: Friday, September 10, 1999 9:33 AM
> To: /> > Subject: Re: [MATHCAD] Symbolic processor
>
>
> In Mathcad 6.0 there appears to be no problem. It gives the
> answer 1 directly.
>
> and sqrt(a/b)/sqrt(b/a) yields a/b as it should.
>
>
>
> Jonathan Armitage
>
>
> At 14:37 09/09/99 +0100, you wrote:
> >why is it that the symbolic engine seems so unable to simplify the
> >following:
> >
> >sqrt(a/b).sqrt(b/a)
> >
> >I seem to end up having to simplify results myself which defeats
> the object.
> >
> >Does anyone have any tips on how to maximise the accuracy of rkfixed or
> >numerical integration as I am finding the numerical solution to a problem
> >diverging badly from the analytic solution? making TOL smaller
> seems not to
> >help. The function is a very smooth slowly changing one with no abrupt
> >surprises.
> >
> >TIA Mark
> >
> >-------------------------------------------------------------
> >The Mathcad List - Discussion, Support & News
> > Contributions: /> > >To unsubscribe: Send in the body: unsubscribe mathcad
> > To: /> > > Hosted by: Adept Scientific http://www.adeptscience.com
> > List Archive: http://lists.adeptscience.co.uk/
> >
> >
> Jonathan G M Armitage phone 01334 463110
> ext 3110
>
>
> -------------------------------------------------------------
> The Mathcad List - Discussion, Support & News
> Contributions: /> > To unsubscribe: Send in the body: unsubscribe mathcad
> To: /> > Hosted by: Adept Scientific http://www.adeptscience.com
> List Archive: http://lists.adeptscience.co.uk/
>

 Attachments:
 symbolic bug.mcd


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