PC-based supplement to the 50g?



#22

In the process of doing my homework (I'm attempting to obtain an AAS degree in Electronics Engineering Technology through home study), I have encountered some things that the 50g just won't do. For instance, I am currently trying to perform some matrix algebra with matrices containing complex numbers that contain symbolics (i.e. -j*(w/(w^2 - 4)). I have spent many hours trying to do this in many different ways and have come to the conclusion that I'm just asking too much of the 50g (I am middle-aged and don't have the time, skills or motivation to do the "dirty work" by hand). As a result, I am thinking of purchasing something like MATLAB or Maple. Please give me some advice.

Thanks,
Ken

Edited: 7 Dec 2006, 8:53 a.m. after one or more responses were posted


#23

I have never used Maple, so I'll leave it to others to comment on it.


MATLAB's strength is number crunching. It may have some support for symbolics these days -- when I was in college it didn't, unless you used the Maple plug-in, but then again, that was more than a decade ago.


One option you should also consider is Mathematica (http://www.wolfram.com/). When it comes to symbolics, it is extremely versatile. Expensive, too, but they do offer a cheaper student license.

Good luck!

- Thomas

#24

Quote:
In the process of doing my homework (I'm attempting to obtain an AAS degree in Electronics Engineering Technology through home study), I have encountered some things that the 50g just won't do. For instance, I am currently trying to perform some matrix algebra with matrices containing complex numbers that contain symbolics (i.e. -j*(w/(w^2 - 4)). I have spent many hours trying to do this in many different ways and have come to the conclusion that I'm just asking too much of the 50g (I am middle-aged and don't have the time, skills or motivation to to the "dirty work" by hand). As a result, I am thinking of purchasing something like MATLAB or Maple. Please give me some advice.

Thanks,
Ken


Hi Ken. Have you considered Freemat?

http://freemat.sourceforge.net/

Regards,

John

#25

Hi Ken. What are you wanting to do with the matrix? It should be able to handle a few things with that kind of matrix. I entered the following matrix in..

[[ 2  i+1           2  ]
[ i -i(w/(w^2-4)) 3 ]]

and it RREF'd just fine. Also, removing the third column, it was able to find the inverse and determinant. What it wasn't able to do was to find any of the LU or QR factoring. Mathematica (my choice for PC number crunching)had no problem finding the the QR decomposition.

Edited: 7 Dec 2006, 10:27 a.m.


#26

Hi Chuck,

I will try to described a specific example using this text format. Here we go:

I am trying to generate a transmission matrix. For this specific example the transmision matrix is obtained by multiplying 3 2nd order matrices.

For the first matrix the elements are:

-a11=1
-a12=Z1
-a21=0
-a22=1

For the second matrix the elements are:

-a11=1
-a12=0
-a21=1/Z2
-a22=1

For the third matrix the elements are:

-a11=1
-a12=Z3
-a21=0
-a22=1

The values of Z1, Z2 and Z3 are:

-Z1=i*.25*w
-Z2=-i*(w/(w^2-4))
-Z3=-i/w


#27

Hello Ken

I believe that the result is :

r11 = 2 - (w^2)/4
r12 = (0.5 w^2 - 2) i/w
r21 = w - 4/w
r22 = 2 - 4/w^2

(but I'm not sure at all)

The 50g seems unable to simplify (0.25 x^3)/x !!!
I had to remplace 0.25 by Q then I evaluated each member of the result matrix, and I substituted Q by its value.

Best regards


#28

r11 = 2 - (w^2)/4
r12 = (0.5 w^2 - 2) i/w
r21 = w - 4/w
r22 = 2 - 4/w^2

#29

WOW!

Thanks for your efforts in this matter!

How did you build the matrices? I assume you didn't use MTRW which is the way I was trying to do it.


#30

You should be able to use Matrix writer. I believe you need the first element to be a complex number to use complex in the matrix ie if the first element were real only, the matrix would then NOT accept complex numbers afterwards (maybe a bug? or convention?).

#31

I did use MRTW.

I put the expressions between ' ' in each cell and use i (left shift + TOOL) to create the 3 matrices.

i.e : ' i*0.25*w ' for a12.

But I replaced 0.25 by Q because of the bug.

Then I multiplied the 3 matrices.

Then, I put each of the four elements of the result matrix in the stack and evaluated them.

I can't believe the 50g is unable to simplify (0.25 x^3)/x to 0.25 x^2. This is very annoying.

Regards.


#32

Patrick,

I really appreciate your assistance. Because of your help I was able to complete my current lesson (Practical Matrix Theory for Engineers). Now, onto the next lesson....

Ken


#33

You're welcome Ken. Your problem gives me the opportunity to play with my 50g and to discover it. :O)

Best regards.

#34

Hi Ken,

Here's what worked for me...

1)  create all the matrices and Z variables
2) change the CAS variable to 'W' (not sure if this is necessary)
3) Multiply the matrices, and OBJ-> the matrix to the stack.
4) EVAL each element and apply the ->Q and PARTFRAC (in that order) to each element.
VOILA. Perfect simplification.

My only concern is I keep getting a different r21 element from the others. I get

wi - 4i/w

Can't for the life of me figure why (maybe Patrick missed the i).
CHEERS


EDIT
The ->Q is under [CONVERT] [REWRITE] [NXT]
and PARTFRAC is under [ALG]

Edited: 7 Dec 2006, 7:37 p.m.


#35

Hi Chuck,

You're correct. I forgot i in r21.

I did not have the idea to use the ->Q function of which it is necessary to be wary because it produces an approximate fraction if the number is not a rational.

Beautiful craftiness nevertheless, without any risk in that case.

Best regards


#36

Hi Patrick. The ->Q discovery also fixed the annoying problem I was having with "i" displaying as (0,1), and also converting a real number, i.e., (4,0), back to 4. It was more luck than know-how. ;)

#37

Chuck,

Thanks a million for your efforts. I will study your methods and try to understand them. All in all, solving the problem at hand with the 50g has been a great learning experience for me.

Ken

#38

Well, I'm loaded for bear now. If I can't get through my lessons with these 3 tools, I might as well throw in the towel.

BTW My initial impression of Maple 10 is ... "LEAPIN' LIZARDS. This is almost fun!"

My thanks to you all,
Ken

#39

I, too, am a student. Physics major @ UNH. (I have been busy making converts to RPN there. <smile>) I /really/ appreciate this thread because I have had the same sorts of questions about complex matrices with variables. Now I'll review this thread to see how it is done. Thanks to all!

I am a heavy user of MathCAD, and recommend it. It is an industrial strength product, but is /most/ convenient for producing documents that contain live mathematics. UNH is largely MATLAB-centric, but I often have MATLAB users comment on how easily I can create documents. I often just fire it up to do stuff like these complex matrix calcs, but I have to admit that it would be more convenient many times to use my 50g.

I also use MATLAB regularly and Maple 10. Of the 3, I recommmend MathCAD first for the undergrad and for it's ease of documenting. Next, MATLAB, which is more difficult to use overall, but easier for some things once you learn how to use it and how to configure the desktop. It is also more powerful in some ways than MathCAD, but not in ways that are as important to the casual user. Last, I recommend Maple 10. Though it has a few attibutes that I prefer over MathCAD, I don't use it very often because it doesn't do as good a job at producing the sorts of documents that I want to produce, and it doesn't handle units the way I want to see them handled.

I'll be happy to post a pdf file of a MathCad project and let folks know where it can be found, if there is interest. Other than that, browse the web for MathCAD and other keywords, or visit the MathCAD website.

Rich


#40

Greetings,

I am very interested in seeing a .pdf of a MathCAD project. I just recently purchased the student version of Maple 10. My first impression was very positive but I soon became disenchanted with it because trying to work with complex numbers using polar representation and using angles measured in degrees rather than radians is a royal pain in the butt. I am currently trying to get a refund from mathsoft and use the money to get the acedemic version of MathCAD.

Ken


#41

Sorry that I don't have more time for something fancier or more detailed, but final exams are upon us!

Please try to download

www.DownEastEngineering.com/physics/Lobster Tracking Project v4.0.7.pdf

Yours,
Rich

#42

Ken, I support other suggestions for MATHCAD which uses some of MAPLE'S ALGORITHMS. When you balance all features of MATHCAD 13 with the additions of the Data Analysis Extension and the Excell add-in, you should have most of the desktop you'll need as a student of physics. Be sure you are comparing version 13 with its many improvements.

Go on line with mathcad.com and look at the forum for a glimpse at part of the HELP facility. there is also considerable help in other areas.

Documentation is lacking. Try to find a copy of version 11 User Manual. Be prepared to pay a little premium for .pdf copies of some of the manuals if you need hard copy.

Mathcad is not an emulator, does not use RPN, more like algebraic mode in g50. G50 is better at step by step solution of integrals in symbolic mode, but Mathcad will symbolically solve most equations. Mathcad much friendlier with differential equations.

A frustrating short coming of MATHCAD prior to version 13 was the lack of direct control over such things as solve blocks in a reiterative environment to handle specific solutions to certain differential equations under program control. Programmed loops can be very tricky because of positioning of variables, both global and local.

There is some excelent help on the forum with the qualifications of some of the best talent on this one for HP. Unless you have lots of time to learn a new system altogether like Maple and you have lots of money, do yourself the favor of looking at mathcad along with the others. If you expect to write lots of papers with math symbols, especially live math, it's a no-brainer.

Regards,

Ron

Edited: 9 Dec 2006, 7:40 p.m.


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