[MATHCAD] Symbolic processor
[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  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/ 
RE: [MATHCAD] Symbolic processor 

Author: Diehl TedETD012
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 7238024 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  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/  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/ 
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 + ++  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/ 
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 191046392 2158988534 (office) fax (reflects to my email) 18885143577 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/ 
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  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/ 
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  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/ 
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 191046392 2158988534 (office) fax (reflects to my email) 18885143577 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/ 
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 191046392 >2158988534 (office) >fax (reflects to my email) 18885143577 >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  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/ 
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/ > 
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