I want to explore multivariable function approximations using truncated Taylor series.

Mathematically, for a function f(x,y) and using operator notation for the partial derivatives, where e.g. D_x² f(x,y) denotes the second partial derivative of f wrt x evaluated at (x,y), we can write the N'th order truncated Taylor series for f around (x₀,y₀) as

I want to make a Maple-function for this expression, and try

P := (x,y,x0,y0,N) -> sum(1/factorial(n)*sum(binomial(n,k)*
D[1$(n-k), 2$k](f)(x0,y0)*(x-x0)^(n-k)*(y-y0)^k, k=0..n), n=0..N):

where f(x,y) is a previosly defined Maple-function.

My P function fails, and the reason why it fails is related to the "D" operator in the "sum".

Please take a look at the following code-snippet:

Output (9) is as expected, but output (8) is not !!
I would expect output (8) to be equal to the sum of output (9), i.e. to be equal to (-1/2).

Please illuminate why I don't get the sum of the sequence (9) as my output (8).

Hellow, 

I am unable to combine the graphs. I have a plot structure as

P1:=plots[odeplot](dsol, [x, F(x)], 0 .. 5, color = red);

P2:=plot(eval(F(x), p = 1), x = 0 .. 5, color = blue);

I want to combine two structure and display in same plot

display (P1,P2);

 thank in advance

I can get a group like this:

g := SmallGroup(48, 8)

But I want to get the PermutationGroup form like PermutationGroup({[[...]], [[...], [...]]}). Can we change it into this form?

Switching font to Arial apparently makes the sign disappear in MathContainers.

Vorzeichen.mw

If i want to do mathematical modelling for planetary motion, how can maple help me with it?

 I want to plot phase portrait but i get some errors. I didn't understand errors? Can anyone help me? zuhal_faz_portresi.mw

Dear power users, I probably have 2 dummy questions, which I show in the attached worksheet. 

1. it looks to me that the equation can be further simplified than done by maple

2. is there a quick way in cleaning up the array by replacing the strings by something as NaN (not a number) so that I can use the array for numeric calculations?

Thank you for helping me out     Download Questions.mw

Download Questions.mw

As we know, since the order about the element Perm([[1, 2], [3, 4, 5]]) of S₅ is 6. Then  the C₆ is a subgroup of S₅, but why IsSubgroup(CyclicGroup(6), SymmetricGroup(5)) return false? Is it a bug?

Of course, we know the A₅ of 60 order is an unsolvable group, but as the wiki here, There are also some solvable groups in the same 60 order. Similarly, although map(IsSolubleNumber, [60, 120, 168, 180]) will give false, there are some solvable groups in orders 60, 120, order 168, and order 180. But how to find these corresponding solvable polynomials by maple? I tried to generate them using random polynomials like this:

with(GroupTheory);
do
    do poly := randpoly(x, degree = rand(6 .. 8)()); until irreduc(poly);
    G := GaloisGroup(poly, x);
until IsSoluble(G) and is(GroupOrder(G) in {60, 120, 168, 180});
poly;
galois(poly, x);

But I didn't get any result even after one night..

We are holding another Maple Conference this year, and I am pleased to announce that we have just opened the Call for Participation!

This year’s conference will be held Nov. 2 – Nov. 3, 2022. It will be a free virtual event again this year, and it will be an excellent opportunity to meet other members of the Maple community and share your work.

We are inviting submissions of presentation proposals on a range of topics related to Maple, including Maple in education, algorithms and software, and applications. We also encourage submission of proposals related to Maple Learn. This year, we are not requiring recorded videos, and we hope to see more interaction between presenters and audience members in our live sessions.

You can find more information about the themes of the conference and how to submit a presentation proposal at the Call for Participation page. Proposals are due July 18, 2022.

Presenters will have the option to submit papers and articles to a special Maple Conference issue of the Maple Transactions journal after the conference.

Registration for attending the conference will open in June. We will also be featuring an art gallery again at the conference. Watch for further announcements in the coming weeks.

I sincerely hope that all of you here in the Maple Primes community will consider joining us for this event, whether as a presenter or attendee!

Hi folks

If you try this simple integral 

simplify(int(P(q)*(Dirac(k-q)+ Heaviside(k-q)),q = 0..infinity)) assuming k>0; 

it returns int(P(q), q = 0 .. k), completely ignoring the delta function. However, if you expand the integral first:

simplify(value(IntegrationTools[Expand](Int(P(q)*(Dirac(k-q)+ Heaviside(k-q)),q = 0..infinity)))) assuming k>0;

 it gives the correct answer 

P(k) + int(P(q), q = 0 .. k)

Looks like a bug to me?

Cheers!

I've been asking a similar question：

How does Maple call external programs such as nauty?

Recently I used Mathematica to call these gadgets very succinctly, so I revisit the topic, and maybe Maple can do it as well, but I just didn't do it the right way.

• nauty and Traces are programs for computing automorphism groups of graphs and digraphs. There is a small suite of programs called gtools included in the package. For example, geng can generate non-isomorphic graphs very quickly. 
• plantri and fullgen are programs for generation of certain types of planar graph.

We note that binary executables of above two programs for Windows are not officially available. Fortunately, I recently compiled them by cygwin.  Of course, other operating systems can make it easier to use them. See attached two compressed files of compiled nauty and plantri programs for Windows.

The official websites of the two programs are listed below.

• https://pallini.di.uniroma1.it/
• https://users.cecs.anu.edu.au/~bdm/plantri/

So, I found that Mathematica works very well for running these programs by Import. We list the following two examples: first example is to get all non-isomorphic 10-order 2-partite connected graph, and the second example is to get all 14-order non-isomorphic  quadrilateral graphs (the planar graphs in which any face is 4-face).

glist10 = Import["!D:/nauty27r3/geng -c -b 10", "Graph6"]; // AbsoluteTiming
Length[glist10]

g14 = Import["!D:/plantri52/plantri 14 -q -g ", "Graph6"] // AbsoluteTiming

I tried maple's Import or ImportGraph functions, but both failed.

restart: 
with(GraphTheory):
L:=ImportGraph("!D:/nauty27r3/geng -c -b 10 -g",output=list):
L2:=Import("!D:/nauty27r3/geng -c -b 10 -g"):

Error, invalid input: GraphTheory:-ImportGraph uses a 2nd argument, format (of type {string, symbol}), which is missing
Error, (in Import) must specify format for this input

The problem seems to be not recognizing compilations symbols " !".  I don't know if Maple can do this like mathematica.

Dear all

I need to  `Put markers to emphasize the point of intersection between f, and g

iteration.mw

thank you

Given a polynomial, e.g. 3*x^2 + a*x*y + b*y^2, is there some built-in function which can give me a list of monomials, with each monomial represented as [coefficient, [exponent_of_x, exponent_of_y]] ? The above polynomial would turn into something like [ [3, [2,0]], [a, [1,1]], [b, [0,2]] ].

It's not difficult to write this procedure from scratch. The procedure would require two arguments: (1) the polynomial itself, (2) which symbols are considered variables (in the above case, x and y). The remaining variables, a and b, would then be treated as constants that appear as coefficients. But I'm wondering if there's a built-in function I can just use.

Hi everyone, Could you help me to get a general solution to the following ode? Here rho and z are constants.

Thanks.

Download ode_rlmt.mw