This looks like a bug I have not seen before. Any one seen this before?

Error, (in Handlers:-TrigExpOnly) cannot determine if this expression is true or false: tr_is_cos

Can others reproduce it? I am using Maple 2023.2 on windows 10

btw, I found that by doing int(evala(integrand),t) instead of int(integrand,t) then the error goes away but not all the time. Below are two examples. The first where evala() fixes it, but the second it does not fix it. 

Download handler_trig_exp_only_nov_18_2023.mw

But the trick of using evala() to avoid this error does not always work. Here is an example below. So need to find another workaround for this.

Download handler_trig_exp_version_2.mw

ps. send to Maplesoft support.

Since C2=D1.D1inv should be equal to I. But return is just an expression (see attached). Further, how to obtain residue for a function C2?

residue.mw

There seems to be a consensus about using ListTools:-SearchAll to locate an item in a list. However, this subroutine does not work on other expressions; A simple instance is that “ListTools:-SearchAll(1, [[1], 1]);” only outputs  while what I need is  (because both “op([1, 1], [[1], 1])” and “op([2], [[1], 1])” are ). And actually, I hope that there is a more general version in Maple.
For example, I intend to do something like 

restart;
expr, elem := ToInert(eval(`print/Diff`)), '_Inert_NAME'("_syslib"):
SearchAll(elem, expr);

and 

List:=[[[[cS,[[[cS,cS],cS],[[[cS,cS],[[cK,cK],cS]],cS]]],cS],cS],[[[cS,[[cK,cS],cK]],cK],cS]]: 
items:=Or([[[identical(cS),anything],anything],anything],[[identical(cK),anything],anything]): 
SearchAll(items,List); 

In other words, I need all positions of an operand of an expression (cf. op).

It may be manually checked that the "indices" of  in  include [5,1,1,2,1,1,1,2,1,2,1,2], [5,1,2,2,1,1,1,1,2,1,2], and [5,2,2,1,1,3,1,2], since 

patmatch(op([5, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2], expr), elem);
 = 
                              true

patmatch(op([5, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2], expr), elem);
 = 
                              true

patmatch(op([5, 2, 2, 1, 1, 3, 1, 2], expr), elem);
 = 
                              true

Similarly, after some manual searchs, 

[[1], [1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 1, 1, 2, 2, 1, 2], [2], [2, 1, 1, 2]]:
convert(typematch~(map2(`?[]`, List, `%`), items), `and`);
 = 
                              true

It turns out that all "indices" in  of  are [1], [1,1,1,2], [1,1,1,2,2], [1,1,1,2,2,1,2], [2], and [2,1,1,2].
But isn't there such a  command that can eliminate the need to manually retrieve them?

When the original poster receives or finds the answer to the question he/she posed, should he/she

1. Reply to it
2. Answer to it?

I have seen "true answers" that were converted to a reply, despite addressing the initial answer correctly. In case there are no other answers, the question will still be listed under unanswered question which is incorrect.

What practice should be applied in MaplePrimes for "true answers"?

In an old question, @nm asked how to . While the answer in that question was almost up to the mark, there remains a regret. 

As the instance listed below shows, Maple, by default, draws arrows on a rectangular grid (rather than on a hexagonal mesh): 

  # Example of a three-dimensional vector field: 
vf__2d := VectorCalculus:-VectorField([sin(x)*(cos(x) + cos(y)), 
                                       sin(y)*(cos(x) - cos(y))], 'cartesian'[x, y]):
  # Example of a two-dimensional vector field: 
vf__3d := VectorCalculus:-VectorField([1 - (sin(u - v) + sin(u - w)), 
                                       1 - (sin(v - w) + sin(v - u)), 
                                       1 - (sin(w - u) + sin(w - v))], 'cartesian'[u, v, w]):
  # Phase portrait. 
Student:-VectorCalculus:-PlotVector(vf__2d, (x, y) =~ -Pi .. Pi, 
                                            'grid' = [`$`](25, 2), 
                                          'arrows' = 'THICK', 
                                   'fieldstrength' = log[63], 
                                           'color' = ColorTools:-Color("#0072BD"), 
                                            'axes' = "box"(*, …omitted…*));
= 

Note that I have changed some of the options in order to make the layout of arrows more prominent.
However, according to the help page of Mma's VectorPoints, among the following methods of location generation, Mma by default uses Hexagonal for 2D field vectors and FaceCenteredCubic for 3D field vector: 

, 

Here is a collection of different settings available in Mma:

So if the requirement is to get the Maple's output looking like Mathematica's (see the beginning), the number and placement of vectors to plot should be thought of as well. In Maple, “the number of vectors” can be controlled by the plot (or plot3d) opinion , but how do I specify “the placement of vectors” (e.g., Mma's "Hexagonal" and "Mesh")?

Although there exists an  chapter in the documentation, randomly positioned arrows do not fit the bill. Is there any workaround?

This is linear ode, third order, Euler type and inhomogeneous ode.

If I solve the homogeneous ode only, then ask Maple to give me a particular solution, then add these, I get much much smaller solution which Maple verifies is correct.

Now when asking Maple to solve the original inhomogeneous ode as is, the solution is much more complicated and much longer with unresolved integrals.

Why does not Maple give the simpler solution? Both are verified to be correct.

This is my theory: When asking maple to find only the particular solution, it seems to have used a different and advanced method to find yp. Which is new to me and trying to learn it. It is based on paper "D'Alembertian Solutions of Inhomogeneous Equations (differential, difference, and some other).

Undetermined coefficients method can't really be used on ode's such as this because its coefficients are not constant.

Now, when asking Maple to solve the inhomogeneous ode, it seems to have used variation of parameters method, which results in integrals, which can be hard to solve.

My question is: Why does not Maple give the same much shorter answer when asked to solve the ode as is? Should it not have done so? Any thoughts on why such large difference in answer? Why it did not use the same method to find yp when asked to solve the whole ode as that leads to much smaller and more elegant solution.

ps. debugging this, it uses LinearOperators:-dAsolver:-dAlembertianSolver which is called from ODEtools/particularsol/linear to find yp when calling DETools:-particularsol(ode); but for some reason, it does not do this when asking it to solve the whole ode directly (if it did, then one will expect same answer to result, right?)

Maple 2023.2 on windows 10.
 

Download why_such_difference_in_dsolve_answer.mw

Hi i study as an marine engenieer and use phasors alot.

I came across Acers startup code to use. 

At the moment i have been been using the gym package for my calculations. Is there a way to setup this startup code to function every time when i load maple? Also how does it go about using units in general? 

I currently have an issue where it outputs some strange format i can not understand 

I do not know why there is added so many decimals. I work on a macOS computer and have thought about using mathCAD for the ease of use instead of all of this. I am hoping for a helping hand to stay with maple because this is what i know and have used the last 3 years. 

Hi,

I would like to calculate Laplacian(1/r) in spherical coordinates

Considering that 1/r in spherical coordinates defines a distribution function (understood in Laurent Schwartz meaning) , the result has to be -4πDirac(r)

I tried to establish this result on Maple but that doesn't work. The result given is -Dirac(r)/r²  (see below)

What is the mistake I made?

Thanks

with(Physics[Vectors]);

SetCoordinates(spherical[r, phi, theta]);

F := Laplacian(1/r);
                               Dirac(r)
                        F := - --------
                                    r²  

Perhaps a stupid question but I fail to convert 2^1/4a^1/4/pi^1/4 (a result of a calculation performed by maple) into (2a/pi)^1/4.

I tried simplify, combine, collect, ... with options. None of them work.

Thank you. 

Could you please help me to solve this error.

my code is here.

CR-C.mw

This question is an expansion of my previous reply. 

There exist sixty kinds of statements in Maple, whose major ​​​​portion can be used as an expression or within an expression (e.g., assignment, loop, and condition). But why is use an exception?

Moreover, since it is reasonable to think of use as a (partial) generalization (see below) of the subs function, shouldn't the behaviour of use be consistent with do/if?

Edit. Besides that, is there some workaround to do something like

  # If use can be used as an expression or within an expression, 
use x = 2 + y in 'use y = 4 in x + y end' end;
  # should return “use y~ = 4 in (2 + y) + y~ end use;” and 
(use y = 2 + x in x -> x + y end);
  # should output “x~ -> x~ + (2 + x);”. 
  # Unfortunately, I cannot find a workaround to stimulate them.

 at present? Note that the `subs` function is unable to do so, so in my opinion, only when the use of `use` is no longer limited to statements will it become a sweeping generalization of `subs`.

I was wondering whether the rendering of bars

looks also dot like on other computers

Looks like Newtonian notation

long time ago I asked about automatic spacing to improve latex for sqrt. A nice solution was provided in https://www.mapleprimes.com/questions/231062-Adding-Space-After-Sqrt-To-Improve-The-Latex

The above is activatived using spaceaftersqrt = true option for latex:-Settings

There is a similar issue for inert integration where a space is typically added before the final dx This is done similar to the above fix using \, See for example this Latex web site giving many examples.

But there is no option I could see to tell Maple to do this automatically for integration.

So all my inert integrals now look not too good as the dx is too close to the integrand. Here are 2 examples with the settings I am using

restart;

latex:-Settings(useimaginaryunit=i,
      usecolor = false,
      powersoftrigonometricfunctions= mixed, ## computernotation,
      leavespaceafterfunctionname = true,
      cacheresults = false,
      spaceaftersqrt = true,
      usetypesettingcurrentsettings=true,
      linelength=10000      
);

sol:=sqrt(4*y^3-a*y-b)*a;
Intat( subs(y=a,1/sol),a=y(x));
latex(%);

Int(sol,y);
latex(%);

I copied the latex and compiled it, and this is the result

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}d a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a d y
\]

\end{document}

Which gives

Compare the output when adding \, by hand to the latex

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}\, d a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a \, d y
\]

\end{document}

Which now gives much better result

Actually, what would be nice if the "d" in "dx" was mathrm which becomes

\documentclass[12pt]{book}
\usepackage{amsmath}
\begin{document}

\[
\int_{}^{y \left(x \right)}\frac{1}{\sqrt{4 a^{3}-a^{2}-b}\, a}\, \mathrm{d} a
\]

\[
\int \sqrt{4 y^{3}-a y -b}\, a \, \mathrm{d} y
\]

\end{document}

But may be I am asking for too much here. But having an option to add \, only for inert integration will be good to have.

Does there exist an option to do this that may be I overlooked?

Maple 2023.2

I recently answered a question concerning the Lane-Emden equation (see here LaneEmden) where the main topic was about finding its numerical solution.

The generic form of the Lane-Emden equation with parameter n is

LaneEmden := n -> (Diff(xi^2*(Diff(theta(xi), xi)), xi)) = -theta(xi)^n * xi^2

      d   /  2 / d            \\             n   2
n -> ---- |xi  |---- theta(xi)|| = -theta(xi)  xi 
      dxi \    \ dxi          //                  

I have just realized that I missed a "small" point in the original question: the OP ( @shashi598 ) wrote
"[...] Maple never comes out of evaluating [the] analytical solution when n=5 [...] ".
The important point here is that this solution (at least for some initial conditions) is known and simple (in the sense it doen't involve any special function).

So I tried for a few hours to verify this claim, and ended wondering myself if it might not be right?

Could you please tell me (I guess @shashi598 would be interested too in your return) if the differential equation LaneEmden(5) can be solved formally?
TIA.

Emden_equation.mw


EDITED:
After a little research it seems that very specigic method are used to build the analytic solution of the LaneEmden(n) (n not equal to 0, 1 and 5): serie expansions, homotopy, Adomian decomposition for instance.
I wasn't capable to find how the solution for LaneEmden(5) have been got for the first time (iseems to be atthe end of the 19th century).

How to apply the following relationship in maple commands? In this physics this relation it's utilized in effective field theory