Equiv Groups with 2 variant - Messages
#1 Posted: 6/8/2009 1:45:30 PM
How to solve:
x +y =7
x^2+y^2=25
i cant let the smath080 to solve it, and havnt searched the helpful q&a or samples.
x +y =7
x^2+y^2=25
i cant let the smath080 to solve it, and havnt searched the helpful q&a or samples.
#2 Posted: 6/8/2009 2:12:40 PM
How to solve:
x +y =7
x^2+y^2=25
Unfortunately, there is no ability to solve the equations set in the program. But it's for now...
#3 Posted: 6/8/2009 2:30:03 PM
How to solve:
x +y =7
x^2+y^2=25
Unfortunately, there is no ability to solve the equations set in the program. But it's for now...
Thanks for instant reply,
I found occasionally the SMath and then like it,
I had thought it was my own reason ,
hope SMath go far
#4 Posted: 6/18/2009 9:02:43 PM
Hi,
Appropriate to this problem I tried to write some simple Newton Algorithm to solve such nonlinear equation systems. During this I found a bug I guess.
I wanted to calculate the inverse of a 2x2 Matrix with is A^-1=1/det(A)*[A22,-A12;-A21,A11].
When I enter this equation and solve symbolically I get as result something like:
A^-1=[det(A)*A22,-det(A)*A12;-det(A)*A21,det(A)*A11]
so it seems there is some problem with Matrix calculations
.
By the way I not succeeded to write the algorithm, but I don't know why
Jakob
Appropriate to this problem I tried to write some simple Newton Algorithm to solve such nonlinear equation systems. During this I found a bug I guess.
I wanted to calculate the inverse of a 2x2 Matrix with is A^-1=1/det(A)*[A22,-A12;-A21,A11].
When I enter this equation and solve symbolically I get as result something like:
A^-1=[det(A)*A22,-det(A)*A12;-det(A)*A21,det(A)*A11]
so it seems there is some problem with Matrix calculations
.By the way I not succeeded to write the algorithm, but I don't know why
Jakob
#5 Posted: 6/18/2009 11:53:57 PM
Hello, Jakob.
I don't understand a problem.
[LIVE width=387 height=157]http://smath.info/live/?file=427[/LIVE]
Please, can you show an example with your finding?
I don't understand a problem.
[LIVE width=387 height=157]http://smath.info/live/?file=427[/LIVE]
Please, can you show an example with your finding?
#6 Posted: 6/19/2009 4:10:26 PM
Hello,
I tried to, and the Live Version seems not to have this Problem even if I upload my Problemfile directly into the live Version.
I uploaded the sm File to rapidshare, so you can check it. I use Version 0.8.
http://rapidshare.com/files/246329547/Problem.sm
Thanks!
Jakob
I tried to, and the Live Version seems not to have this Problem even if I upload my Problemfile directly into the live Version.
I uploaded the sm File to rapidshare, so you can check it. I use Version 0.8.
http://rapidshare.com/files/246329547/Problem.sm
Thanks!
Jakob
#7 Posted: 6/19/2009 5:36:37 PM
Thank you for the file. It's true, this error was already fixed in SMath Studio and fix will be included into the next release, soon. SMath Studio Live always has the last compiled assemblies, that's why you can't see described error there.
#8 Posted: 9/4/2010 10:37:10 AM
Is there still not a solution?
#9 Posted: 9/4/2010 5:35:06 PM
Hello,
Just testing.
[MATH=eng]A←mat(a11,a12,a21,a22,2,2)[/MATH]
[MATH=eng]invA←1/det(A)*mat(a22,-a12,-a21,a11,2,2)[/MATH]
[MATH=eng]A^{-1}*A—mat({-a22*a11+a12*a21}/{a12*a21-a11*a22},0,0,1,2,2)[/MATH]
[MATH=eng]A*A^{-1}—mat({-a22*a11+a12*a21}/{a12*a21-a11*a22},0,0,1,2,2)[/MATH]
[MATH=eng]invA*A—mat({a22*a11-a12*a21}/{a11*a22-a21*a12},0,0,1,2,2)[/MATH]
[MATH=eng]A*invA—mat({a22*a11-a21*a12}/{a11*a22-a21*a12},0,0,{-a12*a21+a11*a22}/{a11*a22-a21*a12},2,2)[/MATH]
Is there any explanation of these results? Why we do not get simply just identity matrices?
Regards,
Radovan
Just testing.
[MATH=eng]A←mat(a11,a12,a21,a22,2,2)[/MATH]
[MATH=eng]invA←1/det(A)*mat(a22,-a12,-a21,a11,2,2)[/MATH]
[MATH=eng]A^{-1}*A—mat({-a22*a11+a12*a21}/{a12*a21-a11*a22},0,0,1,2,2)[/MATH]
[MATH=eng]A*A^{-1}—mat({-a22*a11+a12*a21}/{a12*a21-a11*a22},0,0,1,2,2)[/MATH]
[MATH=eng]invA*A—mat({a22*a11-a12*a21}/{a11*a22-a21*a12},0,0,1,2,2)[/MATH]
[MATH=eng]A*invA—mat({a22*a11-a21*a12}/{a11*a22-a21*a12},0,0,{-a12*a21+a11*a22}/{a11*a22-a21*a12},2,2)[/MATH]
Is there any explanation of these results? Why we do not get simply just identity matrices?
Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#10 Posted: 9/4/2010 8:54:41 PM
Is there still not a solution?
Not yet.
Is there any explanation of these results? Why we do not get simply just identity matrices?
Hmm, good question... just for information: here is what I've got when compared a results with Mathcad:
This is due to imperfection of SMath Studio simplification engine (and Mathcad as well as I see :d)... will try to find the reason and fix it.
Regards.
#11 Posted: 9/5/2010 2:48:20 AM
Hello Andrey,
Here is a screenshot from an older Mathcad version (supported by Maple engine). I do not know the result from the recent Mcad versions (14,15).
It can simplify into identity matrix.
SMath will not simplify those expressions - they will remain the same.
Regards,
Radovan
P.S. Andrey, there's a long time since the Xcas plugin has been mentioned as a possibility for the alternative symbolic engine. As far as I know, some Xcas features are only implemented in the handheld systems. Could you please tell us how the things are going on regarding desktop systems and an alternative symbolic engine as a posibility.
Here is a screenshot from an older Mathcad version (supported by Maple engine). I do not know the result from the recent Mcad versions (14,15).
It can simplify into identity matrix.
SMath will not simplify those expressions - they will remain the same.
Regards,
Radovan
P.S. Andrey, there's a long time since the Xcas plugin has been mentioned as a possibility for the alternative symbolic engine. As far as I know, some Xcas features are only implemented in the handheld systems. Could you please tell us how the things are going on regarding desktop systems and an alternative symbolic engine as a posibility.
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#12 Posted: 9/5/2010 6:43:25 AM
Hello Radovan.
I'm adhere to the position that I am working on improving skills of SMath Studio. And I do not think, that spending my time on the any CAS plugin will improve the program (in fact, such plugin will even never be a part of distributive packages, because it will require for third-party libraries and will always have only support for one type of the program: Win PC, Linux PC, Win PPC). On the other hand I've made an ability to create plugins to extend calculation possibilities, so if it is really important someone can create such plugin.
Regards.
I'm adhere to the position that I am working on improving skills of SMath Studio. And I do not think, that spending my time on the any CAS plugin will improve the program (in fact, such plugin will even never be a part of distributive packages, because it will require for third-party libraries and will always have only support for one type of the program: Win PC, Linux PC, Win PPC). On the other hand I've made an ability to create plugins to extend calculation possibilities, so if it is really important someone can create such plugin.
Regards.
#13 Posted: 9/5/2010 12:12:44 PM
Hej Andrey,
Sorry, did not make myself clear. I did not think about you, about making these plugins by yourself. It is mentioned many times that SMath can be expanded by using plugins. Just interested if you, or someone else, have the information that anyone is going to prepare such a plugin for desktop systems, or something symilar.
As I understood - correct me if I am wrong - Xcas plugin for Handheld PC has been made just as a test that this is possible. I think I was wrong having the impression that Xcas for desktop systems is in the developing stage .
Regards,
Radovan
Sorry, did not make myself clear. I did not think about you, about making these plugins by yourself. It is mentioned many times that SMath can be expanded by using plugins. Just interested if you, or someone else, have the information that anyone is going to prepare such a plugin for desktop systems, or something symilar.
As I understood - correct me if I am wrong - Xcas plugin for Handheld PC has been made just as a test that this is possible. I think I was wrong having the impression that Xcas for desktop systems is in the developing stage
.Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#14 Posted: 9/5/2010 1:02:46 PM
Unfortunately I have no any information about CAS for desktop version of SMath Studio. And I've never started this work by myself. This is a bad news... but I have a good one:
This will be available for SMath Studio 0.90 (will think about possibility to create a plugin for 0.89 as well).
Regards.
This will be available for SMath Studio 0.90 (will think about possibility to create a plugin for 0.89 as well).
Regards.
#15 Posted: 9/5/2010 2:50:28 PM
Hej Andrej
As mentioned many times - function for solving systems of nonlinear equations numerically is always welcome .
Btw., frome the previous screenshot - does the variable "vars" need to be here? Don't we just need "f(x)" as a function with vector "x" as argument returning a vector, and a vector of initial guess?. I suppose there is a simple explanation on this - f.e. to point out by "vars" which variables are "unknown", or something like that. Andrey, could you please put few words of explanation here as it is very important - just for my curiosity .
Regards,
Radovan
As mentioned many times - function for solving systems of nonlinear equations numerically is always welcome
.Btw., frome the previous screenshot - does the variable "vars" need to be here? Don't we just need "f(x)" as a function with vector "x" as argument returning a vector, and a vector of initial guess?. I suppose there is a simple explanation on this - f.e. to point out by "vars" which variables are "unknown", or something like that. Andrey, could you please put few words of explanation here as it is very important - just for my curiosity
.Regards,
Radovan
When Sisyphus climbed to the top of a hill, they said: "Wrong boulder!"
#16 Posted: 9/5/2010 4:40:19 PM
Using of "vars" vector showing a common use case. Not only indexed variables can be used as a functions variables. One can use "a" and "b" instead of indexed "x", so that's why second argument is required.
Updated: "vars" also makes it possible to reorder roots in the vector-answer manually.
Regards.
Updated: "vars" also makes it possible to reorder roots in the vector-answer manually.
Regards.
#17 Posted: 9/5/2010 8:13:56 PM
SMath Studio 0.89.6 Beta version available to test roots(..) and Jacob(..) functions.
Desktop Windows (desktop computer with Windows OS):
SMathStudioDesktop.0_89.6.Setup.msi (Date: 06.09.2010. File size: 1.39MB)
SMathStudioDesktop.0_89.6.Portable.exe (Date: 06.09.2010. File size: 17.34MB) - .Net Framework 2.0 doesn't required
Warning! Before installing SMathStudioDesktop.0_89.6.Setup.msi previous version of SMath Studio must be removed!
Best regards.
Desktop Windows (desktop computer with Windows OS):
SMathStudioDesktop.0_89.6.Setup.msi (Date: 06.09.2010. File size: 1.39MB) SMathStudioDesktop.0_89.6.Portable.exe (Date: 06.09.2010. File size: 17.34MB) - .Net Framework 2.0 doesn't requiredWarning! Before installing SMathStudioDesktop.0_89.6.Setup.msi previous version of SMath Studio must be removed!
Best regards.
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