I am trying to test types inside lists on the input to a procedure. Sometimes I can get this concept to work. 

This is a sample to show the problem. I need to know if the list has [ list[ $3] , Vector[column]($3) ] , or [ Vector[row]($3] , Vector [column]($3) ]

Download Q_2023-03-06_Proc_types_in_list_inputs.mw

This is second order ode solved using series method. This problem from textbook. The solution given by Maple does not match the book. I also solved this by hand and my hand solution agrees with the text book. I also solved this using Mathematica and its solution agrees with the book. 

Maple solution does not agree with the book for y2.  i.e. the general solution for this problem has the form 

    y= c_1 * y1 + c_2* (  y1 * ln(x)  +  y2 )

This is a Frobenius series method, since regular singular point and it falls into the hard case, where roots of indicial equation has difference of integer and where the second solution y2 can't be obtained using same method as y1 due to being undefined if using same method. So it require adjustment to the Frobenius series method.

This is ode

restart;
Order:=10;
ode:=x*diff(y(x),x$2)-3*diff(y(x),x)+x*y(x)=0;
dsolve(ode,y(x),'series')

Maple says that

   y2 = -144 - 36*x^2 + 1/2*x^6 - 25/1024*x^8 + ...)

First, it is missing x^4. And not able to make other coefficients match book. Book says y2 should be

   y2 = 1 + x^2/4 + x^4/64 - (11 x^6)/2304 + ....

And that is what I get and also Mathematica:

I do not have screen shot now of the page from the book to show. It is from an old textbook. Will try to make screen shot if needed.  This is problem 5, page 212 from SCHAUM's "differential equations" by Frank Ayers. 1952 edition. There is free PDF files on the net. Here is screen shot

My question is, why is Maple's series soluiton for the second basis solution y2 different? Could someone verify this? It also failes to verify it

restart;
ode:=x*diff(y(x),x$2)-3*diff(y(x),x)+x*y(x)=0;
Order:=10;
sol:=dsolve(ode,y(x),'series');
odetest(sol,ode,'series','point'=0)

Update

I've testsed few more problems, solved by hand and verified using Mathematica. All these problems give wrong solution by Maple for y_2. At least the solutions do not match the book and do not match my hand solution and do not match Mathematica. In all cases Mathematica's solution and my hand solution match the book. 

All these problem fall into the same difficult case of Frobenius series, where roots of indicial equation differ by integer and where y_2 can not be obtained directly using similar method used to obtain y_1. Other cases of Frobenius roots, Maple give complete correct general solutions. It is only this case where there seems to be something wrong.

In all of these problems below, y_1 solution is correct. It is the last series in y_2 shown which does not agree with book and it is this part which require using modifed method to obtain as explained on the book where these problems are solved from the above links. All the books used can be found online.

Please see attached worksheet.
 

Download series_solutions_Frob_difference_integer.mw

Download 1.mw

HI, I attach  a document (Pade_Approximants_for_alpha.mw) extract showing the errors (Error, (in Engine:-Dispatch) badly formed input to solve: not fully algebraic
).

Can any one help us please?

Thanks. Syed Asadullah Shah

Download shifting_index_in_sums.mw

Are there better ways?

Hi there,

i am working on an inverse z-transform in MAPLE. I would like to get the Impulse Response for a transferfunction with coefficients a, b, and c.

In maple, however I get the impulse response with sums over _alpha=RootOf(Z^2...). Through substitution of n = 0...end I get the right result, but for long impulse responses this takes quite a lot of time. With mathematica, however, the inverse z-transform is calculated to 1/(f(b,c)*(g(b,c,))^n+...), where f and g are functions of the coefficients. The function out of mathematica are quite faster to solve. How can I get Maple to solve this equation efficiently?

Greetings

Let A:=[1,2,1,6,6,2,1,1,1,4,5,2,4,5,6,7,1] say

Then I want find the

1) number of times each of the each of the element occurs
2) To multiple the number by the number of times it occurs

3) Then to multple the all these that is in the above

(3*(2)) *(3*(6))*(3*(2))*(2*(4))*(2*(5))*(1*(7))*(5*(1)) = need this value

Here we can observe 3 is the number of times 2 occurs 

3 is the number of times 6 occurs

similiary 5 is the number of times 1 occurs so on

Kind help

From https://maplesoft.zoom.us/webinar/register/WN_qidPG4qHRWGiTyO65vnGpw?timezone_id=Europe%2FParis

Is the recording of  Sneak Peek at Maple 2023 made on march 1,  available anywhere to see on Maple website or somewhere else? 

Update

Recording is at https://www.maplesoft.com/webinars/recorded/featured.aspx?id=2100  but need to first register/login if you are memeber of maplesoft.com

"The recording will start immediately after filling out the form."

In graph theory, the lexicographic product  or graph composition G ∙ H of graphs G and H is a graph such that

 - the vertex set of G ∙ H is the cartesian product V(G) × V(H); 
 - and any two vertices (u,v) and (x,y) are adjacent in G ∙ H if and only if either u is adjacent with x in G or u = x and v is adjacent with y in H.

Given two graphs, it is easy to obtain their lexicographic product. However the inverse process does not look so easy. 

I read the book "Handbook of product graphs" and wiki, that say that the recognition complexity of lexicographic products is polynomially equivalent to the graph isomorphism problem. 

For the lexicographic product, I know that there is some algorithm without codes to implement the decomposition of the lexicographic products of a graph.

• Feigenbaum, J.; Schäffer, A. A. (1986), "Recognizing composite graphs is equivalent to testing graph isomorphism", SIAM Journal on Computing, 15 (2): 619–627, doi:10.1137/0215045 (https://www.cs.yale.edu/homes/jf/FS-SICOMP86.pdf)

However, I did not understand the algorithm process mentioned in the article, nor did I see the program implementation of this algorithm. About 5 months ago, I asked similar questions on multiple platforms, but did not receive any feedback.

The potential algorithm can help us discover some theorems, so I am very interested in the implementation of the algorithm in the above article.

PS:We also know that there are already polynomial algorithms for the decomposition of the cartesian product of a graph. A polynomial time algorithm for finding the prime factors of Cartesian-product graphs", Discrete Applied Mathematics, 12 (2): 123–138, doi:10.1016/0166-218X(85)90066-6, MR 0808453 and we can find the java codes for implementation of finding the prime factors of Cartesian-product graphs.

Given a Graph G kind help to write a function F to compute values Based on Neighboorhood

Another_type_using_neighborhood.pdf

Your help will be greatly acknowleged greatly

looking for a simple code kind help

Looking to write a function f which takes a weighted graph g and returns values with are distance based

Kind help please your help will be acknowleged

Try_code_based_with_distance.pdf

Please kind help

Looking for simple code

 I am looking to program to create a function which can take a weighted Graph G and output me a array of computed values as an list 

I have around 15 values to be found 

say a function

Compute(graph::g)

I am mainly look for a simple way to code all these in fewer number of lines kind help in that

I attach a PDF file on what i require     Trying_to_code_1.pdf

Kind help

The main ideas i need are

1) How to do sum over edges of a graph G in a simple line of code

2) How to Product sum  over edges of a graph G in a simple line of code

Each one of your help will be greatly apprieciated Please kind help and it will be acknowleged too

What is the reason Maple likes to do this

arccos(sin(x));

         Pi/2 - arcsin(sin(x))

Both are correct, but the first has leaf count of only 3 and the second expression has leaf count of 11.

Surely the first is simpler to look at and read so the second form is not simpler.

What is the logic behind this automatic transformation? And did Maple always do this?

Convert undirected graph unweighted graph to a weighted graph even though all the weights are 1

as i want to check how my function works on weighted graph as I know it works unweighted

I teach high school math where we use Maple. Some times some students who use Maple 2022 on Mac computers both older and new version of the OS, experience that the document won't react to simple things like plot, solve of loading packages with the "with" command. 

Any idea could be causing this? Because the error goes away if we load a new document within Maple or restart the program.