vv

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These are replies submitted by vv

@_Maxim_ 

In my answer (after edit) it also works if expressions are used instead of functions.
It would be interesting to investigate the source of the bug.

Added later.
The RootOf obtained by solve is a bit simpler.
For the OP's RootOf, Maple enters somehow in an infinite loop of simplifications/conversions.

 

@Axel Vogt 

Yes, the picture is the geometric interpretation.

I am a mathematician, not a physicist and I do not use the Physics package (except a few commands, very seldom).
I'd like to ask a few principial questions.
The Physics package looks to me like a "state within a state" with those Setups, redefined basic commands and operators (including *, .), special typesetting etc.
So, the questions.
- Is Maple going to evolve in these directions?
- Why in Maple is missing an AbstractLinearAlgebra or a Rings package (similar to the GroupTheory package)? Many of their commands could be used by Physics and would have a larger audience.
- Are the basic commands in Physics (such as Assume) going to be merged/unified with the existing ones (assume in this case)?

@Cryme 

The procedure uses the general solution obtained by solve (actually SemiAlgebraic).
E.g.
if the solution is  a<x<b, c<y<d then ==>  x = (a+b)/2, y = (c+d)/2
if the solution is  a<x, c<y<x then ==>  x = a+1, y = (c+a+1)/2
etc.

@jnjn0291 

Yes, provided that the eigenvalues are real. Otherwise take the real (or imaginary or both) parts. E.g.

plot3d([seq(Re(R(i)),i=7..8)], x=0..2*Pi,y=0..2*Pi);

@Markiyan Hirnyk 
Just use:
printlevel:=40;  # typesetting=standard

@Carl Love 

The user has m(R+x) (missing `*`). The main problem is using c[1],...,c[4]  and c  followed by  c := ...

@tsunamiBTP 
Yes.
If you just want sinc ant not the DynamicSystems package then define e.g.

sinc := x -> piecewise(x=0, 1, sin(x)/x);

 

@_Maxim_ 

I totally agree that an epsilon parameter would be nice, but not essential. Note that the epsilon in evalf/Int was also absent in the past. The main problem is the lack of methods.

BTW, the eulermac implementation is far from perfect, see here.

@_Maxim_ 

I don't think that such options are really necessary. Why use an epsilon when Digits should be enough? evalf/Sum usually increases internally Digits.

In your example Maple probably does not have a suitable convergence accelerator.
[The acceleration is usually more efficient for alternating series].

In such cases I think that a combination of symbolic+numeric methods should be used; of course here the symbolic one is sufficient, but take e.g.
evalf(Sum((1-10^(-3))^k/(k+ln(k)), k = 1 .. infinity));

The number of beginning terms is also superfluous because one may use
add(f(n),n=1..N) + Sum(f(n),n=N+1..infinity).

 

@jacobBN 

With uses in a procedure, the package is not loaded in memory; instead, the necessary functions are invoked by their long names.
with(packagename) can be used only at top-level (i.e. not inside a procedure).

@Markiyan Hirnyk 

Have you read the question or the answer?

restart;

Oper:= proc (F::list, G::algebraic, X::list)
local J,dG;
uses VectorCalculus;
if nops(F)<>nops(X) then return FAIL fi;
J := Jacobian(F,X);
dG := Matrix(Gradient(G,X));
J^+ . dG
end proc:

Oper([X^2*Y, X^3*Y, Z], G(X,Y,Z), [X, Y, Z]);

_rtable[18446744074328897526]

(1)

Oper([X^2*Y, X^3*Y, Z, Z*T], G(X,Y,Z,T), [X,Y,Z,T]);

_rtable[18446744074328908014]

(2)

 

@Robert Israel 

Unfortunately there are much simpler expressions for which testeq fails, e.g.

sin((3/7)*Pi)-sin((1/7)*Pi)+sin((2/7)*Pi)-sqrt(7)/2;

 

@_Maxim_ 

Unfortunately; probably branch problem due to the complex arguments of the elliptics.
MultiSeries seems to be still experimental, so maybe it will be corrected.
 

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