Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Hello,

I have viewed on youtube the video "A Swift Introduction to Geometric Algebra" and i would like to start on the same subject with Maple but i don't even know to start !!

Do you have an idea how to start doing simple things like the "geometric product", operations on bivectors, trivectors....

Thanks

ps:  link to the video

https://www.youtube.com/watch?v=60z_hpEAtD8&ab_channel=sudgylacmoe

Dear maple user,

I have codes for Differential equations while applying one do and end loop i am able to plot the graph of G(x) while same problem with other way of applying do and end loop i am unable to plot. whats wrong with do and end loop. These are codes available in maple primes . while combining i am unable to plot .

any one resolve it.

Thanks in advance . 

 

restart:
with(DETools):
with(plots):
with(IntegrationTools):
de0 := {
    (1-p)*(diff(f(x),x,x,x))+p*(diff(f(x),x,x,x)+(1/2)*f(x)*(diff(f(x),x,x))),
    (1-p)*(diff(g(x),x$2))/Pr+p*((diff(g(x),x$2))/Pr+(1/2)*f(x)*(diff(g(x),x)))}:

ibvc0 := {f(0),(D(f))(0),(D(f))(5)-1,g(0)-1,g(5)}:
n:=2:

F := unapply( add(b[k](x)*p^k,k=0..n), x ):
G := unapply( add(c[k](x)*p^k,k=0..n), x ):

de := map( series, eval( de0, {f=F,g=G} ), p=0, n+1 ):

for k from 0 to n do

    if k = 0 then
        ibvc := expand( eval[recurse]( ibvc0, {f=F,g=G,p=0} ) ):
    else
        ibvc := { b[k](0), D(b[k])(0), (D@@2)(b[k])(0), c[k](0), D(c[k])(0) }:
    end if:

    sys := simplify( map( coeff, de, p, k ) ) union ibvc:
    soln := dsolve( sys ):
    
    b[k] := unapply( eval( b[k](x), soln ), x ):
    c[k] := unapply( eval( c[k](x), soln ), x ): 

end do:

'F(x)' = F(x)+O(p^(n+1)):
'G(x)' = G(x)+O(p^(n+1)):

Pr:=1:
plot(eval(G(x), p = 1), x = 0 .. 5, color = blue):
###### Same problem with other  way of do and and end loop unable to plot with G(x)
restart:
with(DETools):
with(plots):
with(IntegrationTools):
Pr:=1:
de1 := (1-p)*(diff(f(x), `$`(x, 3)))+p*(diff(f(x), `$`(x, 3))+(1/2)*f(x)*(diff(f(x), `$`(x, 2))));
de2 := (1-p)*(diff(g(x), `$`(x, 2)))/Pr+p*((diff(g(x), `$`(x, 2)))/Pr+(1/2)*f(x)*(diff(g(x), x)));
ibvc := f(0), (D(f))(0), (D(f))(5)-1, g(0)-1, g(5); n := 2; F := unapply(add(b[k](x)*p^k, k = 0 .. n), x); G := unapply(add(c[k](x)*p^k, k = 0 .. n), x);
DE1 := series(eval(de1, f = F), p = 0, n+1);
DE2 := series(eval(de2, g = G), p = 0, n+1);
CO := map(coeffs, eval([ibvc], f = F), p); CT := map(coeffs, eval([ibvc], g = G), p);

for k from 0 to n do IBVC1 := select(has, C*T, c[k]); slv := dsolve({coeff(DE2, p, k), op(IBVC1)}); c[k] := unapply(rhs(slv), x) end do;
G(x) = G(x)+O(p^(n+1));
plot(eval(G(x), p = 1), x = 0 .. 5);
 

Hi, Maple users 

I hope you are doing well.
Here I solved one of the ode problems by dsolve.
But I am getting  "Error, invalid subscript selector" error.
Kindly do the needful to find a solution.
Thank you.

JVB.mw

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. Dx2 f(x,y) denotes the second partial derivative of f wrt 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

simplify((x^2-2)/(x-sqrt(2)))

(x^2-2)/(x-2^(1/2))

(1)

why is the above not simplifying to x+sqrt(2)

x+2^(1/2)

(2)

``

How can I replace the strings in the matrix below by something like NaN (not a number) so I can use it for further numeric calculations?

 

Error, invalid assignment

"dat:=[[124.0,124.0,22.0,2.2],[130.0,160.0,20.0,4.4],[130.0,129.0,26.0,4.3],[119.0,115.0,21.0,">2,6"],[136.0,129.0,30.0,4.9],[118.0,126.0,24.0,2.9],["NA / 101",115.0,20.0,3.0],[130.0,118.0,21.0,2.4],[95.0,94.0,25.0,3.4]]"

 

``

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!

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