## How to generate a ColumnGraph with bars centered o...

Hello,

I would like to generate a ColumnGraph such that the bars are centered over 1, 2, and 3. For example, I have a vector:

x:= Vector([1,2,3]);

When you execute ColumnGraph(x), you a get the first bar centered over 0.375, instead of 1, second bar centered over 1.375, instead of 2, and so on.

## What causes multiple ">" symbols in one block...

I have seen this quite a bit in blocks of code. The `>` symbol seems to appear erratically. I don't know how to specifically reproduce this. Does it mean something? I would post the worksheet but it will not run without the package.

## system ode plot not working...

 >
 (1)
 > #  plot  solutions to a system  of DEs
 >
 > sys := {diff(x(t), t) = y(t), diff(y(t), t) = -x(t) - 1/2*y(t)}
 (2)
 > DEplot(sys, [x(t), y(t)], t = 0 .. 15, [[x(0) = 1, y(0) = 0]])
 > ;

This is not working, seems to be simple ...
Have made an attempt to create a procedure from these two commands, but no success
Apparently, I need to learn to use a debugger to determine what is wrong, then?

 > dv_systeemplot:= proc ( DV1,DV2 ,RV1,RV2 )                  local t, sys,systeemplot;                    sys := {DV1 , DV2 }:                  systeemplot:= DEplot(sys, [x(t), y(t)], t = 0 .. 15, [[RV1 , RV2]]);                  return systeemplot; end proc;
 (3)

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 > dv_systeemplot( DV1,DV2 ,RV1,RV2 );
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Ask AI to get some code: never i got the right Maple code ! :)

 >
 (8)
 > restart; systeem := proc(eq1, eq2, beginwaarden)   local x, y, oplossing;   x := unapply(rhs(dsolve({eq1, eq2, beginwaarden}, {x(t), y(t)})), t);   y := unapply(rhs(dsolve({eq1, eq2, beginwaarden}, {x(t), y(t)})), t);   oplossing := DEplot([x(t), y(t)], t = 0 .. 10, beginwaarden);   oplossing; end proc; # Definieer de differentiaalvergelijkingen eq1 := diff(x(t), t) = y(t); eq2 := diff(y(t), t) = -x(t); # Geef de beginwaarden op beginwaarden := [x(0) = 1, y(0) = 0]; # Roep de procedure aan met de differentiaalvergelijkingen en beginwaarden systeem(eq1, eq2, beginwaarden);

Probably i do need to work with a debugger here?

## Why do we need to assume abs(z)<1 for evaluating...

If we write

restart: alias(po=pochhammer):

assume(abs(z)<1);  F:=z->sum(po(1,n)^2/po(1/2,n)^2*z^n/(n+1),n=1..infinity);

Then the output of F(z) is a hypergeometric series, and

A=subs(z=4, F(z);

evalf(A)

gives the correct output. But, why do we need to assume that abs(z)<1 if we are evaluating at abs(z)>1?. Observe that if we do not assume it, then the output we get is wrong, why?

## Probably just mathematical entertainment...

I recently watched a video in which the speaker asked the following question: "How many seconds are there in 42 days?".
I think I've done what anyone would do: trying to quickly find an order of magnitude for this number.
But the speaker's answer was both remarkable and obvious when you think of it: "Exactly 10! seconds".

So my question: Given the number 3628800, is there a way to identify it (in the  identify's sense) to 10!  ?
Or maybe some trick to force identify to answer 10! ?

## Drawing a line element field using a procedure...

Well , honestly I can't make sense of how to do this.

Interactive can be done step by step , but now generalize via a procedure , but can't get a handle on it
How to get the right procedure ?

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 > DVplot:=proc(DVA,RV1A,RV2A)           local DV;RV1;RV2;opl_1;opl_2;opl;lijnelement;           DV:           RV1:           RV2:           opl_1 := dsolve({DV, RV1}, y(x)):           opl_2 := dsolve({DV, RV2}, y(x)):           opl:= plot({rhs(opl_1), rhs(opl_2)}, x = 0 .. 5, y = -10 .. 10, thickness = 3):           lijnelement:=dfieldplot(DV, y(x), x = 0 .. 5, y = -10 .. 10, title = "lijnelementveld met                intergaalkromme door (1,1)(1,-1)"):           display({opl, lijnelement}); end proc:
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## How to make this inline assignment work...

I want to make from a procedure call a single argument function that can be used in function composition.

To illustrate this with a simple example, below the function pow[3] performs a cube operation

```pow[3]:=x-> `^`(x,3):
(evalf[4]@pow[3]@sin)(Pi/6)
0.1250

```

To make the use of pow a bit more generic, I though about doing definitions for other powers in a loop with an inline assignement

```for i from -1/2 to 5 by 1/2 do (power[i]:=x-> `^`(x,i)) end do;
```

This does not work because the i in the rigthhand side of power[i]:=x-> `^`(x,i) does not evaluate to the acutal value of the loop counter. I tried eval and evaln without success. How do I get full evaluation of the inline assignement?

## How can I find a relation of a, b, c, d, t so that...

How can I find a relation of a, b, c, d, t (a d <> 0) so that the function f(x) = (a x^2 + b x + c)/(d x +t) is a increasing function on the interval (m, n)? I know that, we have the conditions
f'(x) >=0 forall x in (m, n) and -t/d not in (m, n)

## How to make (if possible) this procedure ThreadSaf...

Hello

I have the following procedure that uses the Lie Derivatives of a vector field to build a set of equations.

```LieDerList:=proc(h::symbol,f::list,vars::list)
description "This function returns the system of equations based on the Lie derivative.":
local i,n:=numelems(vars),L:=Array(0..n):
L[0]:=h:
for i from 1 to n do
L[i]:=inner(f,map((a,b) -> diff(b,a),vars,L[i-1])):
end do:
return(zip((w,v)->simplify(w-v),[seq(L)],[seq](cat(h,i),i=0..n))):
end proc:
```

Below it is an example on how to call the procedure.

I used CodeTools:-ThreadSafetyCheck to check all the procedures used within LieDerList and LieDerList itself, but nothing wrong came out. However when I try to run

`LieEq4:=Threads:-Map(w->LieDerList(x,w,[x,y,z]),models4):`

where models4 is a list of 1765 elements, maple returns "Error, (in factors) attempting to assign to `LinearAlgebra:-Modular:-Create` which is protected". If I change Threads to Grid, there is no problem at all.

What am I overlooking? Is there a method to ensure the procedure is thread-safe?

Many thanks.

PS.  I found one problem - inner, which is related to LinearAlgebra package, is not thread-safe.

## reproducible server crash (Kernel connection has ...

This is not new in Maple 2024, and also happens in Maple 2023. But it causes the famous "kernel connection has been lost" each time.

I think many of the kernel connection has been lost problems I see might be related. It could be memory problem in this case. I wonder if someone will be able to track what causes it. Is it expected that server.exe crash on such input?

ps. Reported to Maplesoft support.

 > interface(version);

 > Physics:-Version();

 > restart;

 > integrand:=(2*x^2022+1)/(x^2023+x);

 > int(integrand,x);

For reference, another software give this result instantly and with no crash:

My PC is windows 10, with 128 GB RAM.

## new error (in int/gparse/gmon) too many levels of ...

May be someone could find what causes this new internal error in Maple 2024.

I did report it already to Maplesoft. It does not happen in Maple 2023. Attached both worksheets.

 > interface(version);

 > Physics:-Version();

 > integrand:=(d*x)^m/(a+b*arctanh(c*x^n))^2;

 > int(integrand,x);

Error, (in int/gparse/gmon) too many levels of recursion

 > interface(version);

 > integrand:=(d*x)^m/(a+b*arctanh(c*x^n))^2;

 > int(integrand,x);

## Option to display or not display a default message...

I setup my package to display the a message when it is loaded. It is quiet convienent but I don't need it all the time. Obviously I can "#" in the code to hide it premanently. I was wondering if there is away to optionally turn it off/on. Something along the lines.

with(RationalTrigonometry,false) or with(RationalTrigonometry)[false]....

Or put something in the .ini flie to set the default behaviour.

```restart:with(RationalTrigonometry):
"Default global settings:-

GeomClr = "Blue",

Prntmsg = true,

Prjpsn = 3 can be set to 1,

Normalgpt = 1 or set to 0,

Metric is a 3 x3 symmetric matrix defaults to the Identity

matrix "

```

## Why does Statistics:-Mean fails computing the mean...

For a lesson I'm preparing, I want to illustrate some probability concepts using Maple.
In particular, I need to use the fact that the Expectation operator(let say the Mean operator) is a linear operator with respect to random variables.
However, I don't want to particularize my demonstration by using this or that statistical distribution but simply the notion of random variable.
I have therefore created a specific Distribution named  MinimalAbstractDistribution in which only the mean and variance are defined.

When Statistics:-Mean is applied to the expression (A*p+q) where p and q are names and A is a random variable with distribution MinimalAbstractDistribution, linearity is effectively used.
But not when it is applied to A/p or A-q.

Why that?
Is there a way of defining a statistical distribution so that Mean behaves as expected?

(You will easily understand that no workaround of the form

```Mean(A+q);
eval(%, q=-q);

# or
```

can be accepted in a lesson).

 > restart
 > with(Statistics):

 > MinimalAbstractDistribution := proc(i)   Distribution(Mean=mu[i], Variance=sigma[i]^2) end proc:
 > A := RandomVariable(MinimalAbstractDistribution(1))
 (1)
 > [Mean, Variance](A);
 (2)
 > Mean(p*A+q); Mean(p*(A+q))
 (3)
 > # But Mean(A-q); Mean(A/p)
 (4)

## How to define a matrix of partial differential ope...

How do we define a matrix or a vector of the partial differential operator?

## Has evalf(...,n) been deprecated...

```evalf(Pi, 20);