Given a function like f(x)=2*x

I can enter this in Flow 2022 like this ...  f := x -> 2*x;

1 - But how to enter the general case f(x) where the function is not defined beyond just f(x)?

2 - And ultimately how to enter the below?

In either case ...

Since f(x) is the general case and not defined as in my intial example above ...
I can't figure out how to enter this into Flow 2022

Thanks for any help.

System: Windows 10 Pro 64-bit

Maple Flow 2022

For an N'th order truncated multivariable Taylor series expansion for f(x,y) about (x₀,y₀), you can write

f := (x,y) -> 1/(2 + x*y^2):
P := (x,y,x0,y0,N) -> add(1/factorial(n)*add(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):

The procedure works well, but it is slow for large orders.

Comparing with Maple's mtaylor function:

temp.mw

The built-in mtaylor is ~1400 times faster at N=30, and increasing as N gets larger.

What is the easiest way to speed up my P procedure ?

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

Is it possible to write latex equations in MaplePrimes?

Googling for this and also searching here in MaplePrimes didn't turn up any obvious answers to this question. I am coming from using Math Stack Exchange, and I'd like to ask a question about how to write a particular function in Maple.

$f(x)=\begin{cases} 5, x \neq 0 \\  0, x=0 \end{cases} $

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?

Question 1 - How would you enter this in Maple Flow 2022?

I can create "i sub C" by pressing "space+ underbar" two times

but I can'g get (t) ... the "function of t" to go with C as part of the subscript.

So, how would you enter this into Flow 2022?

Question 2 - I watched this video ... Taking Derivatives in Maple 15 and he demonstrates right clicking to get a "Context Menu" ... I was unable to get this to work in Flow 2022 ... should it work or is that feature only avaible in Maple?

Thanks for any help.

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..