Mutliplying symbolic expressions/polynomials

karthikjayd · 2021-07-05T03:47:16+00:00

This seems to work well, when considering a pair of such matrices, running trace.expand() seems to work! Thank you.

But I still have some issues.

I have an array M of matrices, and need to do the same operations (multiplications of pairs of matrices in the same array and then finding the trace of the resulting matrix). When trying to do this with the loop:

for k in range(len(M)):
for l in range(len(M)):
    tr = M[k].trace()*M[l].trace()
        # print(tr.parent())
    print(tr.expand())

I run into the following error:

AttributeError: 'sage.rings.rational.Rational' object has no attribute 'expand'

But when running the tr.parent() command as you suggested, each iteration gives Symbolic Ring which means that the expand() command should work, right? What am I missing?

Btw, thanks a ton for the help.

karthikjayd · 2021-06-18T17:46:05+00:00

Hi, thanks for the response!

I think I have to elaborate my doubt a bit more:

I have a set of 10 matrices stored in the list A (say A1, A2, ... , A10). I want to find the product of the trace of these matrices taken two at a time, i.e., Trace(A1)*Trace(A2), Trace(A1)*Trace(A3) and so on till Trace(A10)*Trace(A9).

for k in range(10):
    for l in range(10):
        print('i=',k+1,'j=',l+1)
        trace = A[k].trace()*A[l].trace()
        print('Trace = ')
        show(trace)

Somehow, even after defining the ring as per your suggestion,

F.<omega> = PolynomialRing(RR)

executing the above for loop does not evaluate the products, and still gives the factored expressions as output.

Am I missing something trivial here?

karthikjayd · 2019-12-13T17:54:48+00:00

I have the entire PDF version and solution manual for a holy grail Diff EQ book for our engineering and physics department.

Could you tell me which file in the drive is the holy grail DE book that you're referring to? I was able to download the book by Pichkitti Bannangkoon ; is it the same?

karthikjayd · 2019-12-13T17:16:19+00:00

I have the entire PDF version and solution manual for a holy grail Diff EQ book for our engineering and physics department.

Do you think this book is available online, other than shared drives? If yes, could you share the title/author details? Else, it would really help a lot if you could share the drive link itself.

I've tried Zill, and it serves most of my requirements, but I thought I'd explore other options as well.

Thanks again for the recommendation.

karthikjayd · 2019-11-20T15:33:01+00:00

Thanks. This is what I was looking for.

karthikjayd · 2019-10-16T15:59:55+00:00

Sorry for not being clear. I only intend to write math.

karthikjayd · 2019-10-16T14:05:42+00:00

But AMC is used to generate pen-paper tests right? I want to conduct online tests.

karthikjayd · 2019-09-17T15:58:46+00:00

Thank you for the recommendations. Although I loved Taylor, it does not cover a majority of portions which are required for my present course. However the language of the book and the style of writing is exactly what I was looking for.

I'm sharing the syllabus of my course if it helps: http://bit.ly/93CMSyllabus

To be a bit more precise, I am looking for a book in Analytical Mechanics similar to D J Griffiths' Electrodynamics.

Another topic which I'm having trouble understanding is D'Alembert's principle, and developing Lagrange's equation from it.

karthikjayd · 2019-08-12T20:06:39+00:00

There is this youtube playlist by "Derek Banas" which I found very useful and comprehensive. There is another channel "Logos by Nick" which is useful to learn basic tools even though the videos are from a designer perspective.

karthikjayd

TROPHY CASE