## How to compare list in a if statement?...

I want to extract lists that are term by term smaller than a fix one.

To be clearer, I want to create something like

if a[i] <= b[i] for all i=1..min(nops(a),nops(b)) then ...

I tried with the forall call, but it doesn't work:

if forall( i=1..min(nops(a),nops(b)),a[i] <= b[i]) then ...

I also tried the assuming call with the is call. It works, but doesnt't give me the result I want:

if is(a[i] <= b[i]) assuming(1 <= i, i <= min(nops(a),nops(b))) then...

Is there a way to have a chain of conditions in a if statement like I am trying to do?

## Showing numbers in y-axis...

Hello,

How to show the y-axis numbers in the second plot ?   y is in [0,3].

I try the following but it shows a negative axis.

display(P, L, axis = [tickmarks = [5, subticks = 3], thickness = 2]);  this is not correct

The file is attached.

Thanks

## how to call exported proc inside a module?...

I do not understand why the following is not working. I have a package which has a module inside it. The module is exported by the package.

Inside that module, there is a proc, which is also exported by the module.

So why can't one call the proc from outside the package? What Am I doing wrong? and how to correct it? I'd like to be able to call the proc directly.

```A:=module()
option package;
export B;
B := module()
export foo;

foo:=proc()
print("in foo");
end proc;

end module;
end module;   ```

Now when typing (A::B):-foo() Maple is not happy and says Error, module does not export `foo`

I tried different syntax from the above, but can't get it to work. For example A::B:-foo() gives Error, `B` does not evaluate to a module

Maple 2019.1

## difficulty to plot an ellipse...

P; Q; lma; [3 -42] [-, ---] [2 25 ] [22649 -2304] [-----, -----] [5523 1841 ] 1.627112258 with(geometry); point(Pp, P[1], P[2]); point(Qp, Q[1], Q[2]); ellipse(p, ['foci' = [Pp, Qp], 'MajorAxis' = lma]); Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse; I can't understand this error

## How to get Maple 2018 settings in Maple 2019?...

Hi I’m a student, running Maple on a student license, and I have an issue with the way the Maple 2019 setup is.

I'm sorry if my answer is a bit hard to understand, I don't really know how to explain it.

My Maple 2018 expired and I was forced to upgrade to Maple 2019, however for me there is a huge difference in how the setup is in therms of “math” and “text” mode.

Before, I was able to easily switch between “text” and “math” mode in a paragraph (the red “>”) in my worksheet, by using “cmd+R” and “cmd+T”. So I would have paragraphs for text, where i could switch between “math” and “text” for writing, and then I would have paragraphs only for math for when I would calculate things. (I’ve tried to screenshot how it would typically look)

Mt problem with Maple 2019, is that when I switch a paragraph into text and start writing and want to switch to “math” by using “cmd+R”, Maple executes the formula whenever I press “enter”, and give me an output I don’t want.

How do I change the settings to get back to the way they were on Maple 2018 and the years before this?

(I know I can put a ":" after the "math" part in my text, but i don't wan't to do it every time)

## force keyword arguments to start only after positi...

When making a proc that accepts positional and keyword based arguments, Maple allows the caller to put the keyword arguments before or after the positional arguments, or in between.

Is there a way to force the keyword arguments (if they are used) to only be placed after the (required) positional arguments during the call?

An example will make it more clear. Given this proc

```foo := proc(a::integer, b::integer, {c::integer:= 1, d::integer:= 1},\$)
print("a=",a," b=",b," c=",c," d=",d);
end proc:
```

It can be called as any one of these cases

```foo(1,2);                                #case 1
foo(1, 2,'c' = 1, 'd' = 2);              #case 2
foo('c' = 1, 1, 'd' = 2, 2);             #case 3
foo('c' = 1, 1, 2);                      #case 4
foo(1, 'c'=1, 2);                        #case 5
#more combinations possible
```

Is it possible to change how proc is defined, so that Maple will accept case1, and case 2 only in the above when the call is made and give an error otherwise?

i.e. only allow keyword arguments after all positional arguments.  I read https://www.maplesoft.com/support/help/Maple/view.aspx?path=argument_processing  and it says

After all arguments matching keyword parameters have been processed, matching of required positional and optional or expected ordered parameters is carried out

So from above, it looks like what I am asking for is not really possible. But I thought to ask, in case there is some way.

I find ability to put keyword arguments in the call anywhere and in-between required positional arguments confusing that is all.

Maple 2019.1

## Problems with series expansion...

I am trying to expand a multivariable (more specifically 4 variables) function in powers of one of its variables when it goes to infinity.

However, the result I get is always zero, even if I input (or not) values for some of the other variables.

Can anybody help?

series_expansion.mw

P.s.: I want to do the same for the other two functions I defined in the worksheet as well.

## how to obtain list of protected names in Maple?...

Is there a command or method in Maple to list all initially protected names?

But what about a list of all protected names? sin,cos, eval, uneval, etc.. any name that can't be assigned to. In my search so far, I could not find how to find these names. There are 100's of such names. Can one get them all in a list to look at?

Using Maple 2019.1

## How to solve system of PDEs in maple?...

I want to solve the following system using PDE Solve command but finding an error. Please help me in this regard. Thanks!

restart; d1 := 1; d2 := 1; AA := 0.2e-2; BB := 0.79e-1; L := 1;
with(PDEtools, casesplit, declare);
PDE1 := diff(u(x, t), t) = d1*(diff(u(x, t), x, x))-u(x, t)*v(x, t)^2+AA*(1-u(x, t)); PDE2 := diff(v(x, t), t) = d1*(diff(v(x, t), x, x))+u(x, t)*v(x, t)^2-BB*v(x, t);
/  2         \
d            | d          |                  2
PDE1 := --- u(x, t) = |---- u(x, t)| - u(x, t) v(x, t)  + 0.002
dt           |   2        |
\ dx         /

- 0.002 u(x, t)
/  2         \
d            | d          |                  2
PDE2 := --- v(x, t) = |---- v(x, t)| + u(x, t) v(x, t)
dt           |   2        |
\ dx         /

- 0.079 v(x, t)
IBC1 := {u(0, t) = 1, u(1, t) = 1, u(x, 0) = 1-(1/2)*sin(Pi*(x-L)/(2*L))^100}; IBC2 := {v(0, t) = 0, v(1, t) = 0, v(x, 0) = (1/4)*sin(Pi*(x-L)/(2*L))^100}; dys1 := {IBC1, IBC2, PDE1, PDE2};
/              /  2         \
| d            | d          |                  2
dys1 := < --- u(x, t) = |---- u(x, t)| - u(x, t) v(x, t)  + 0.002
| dt           |   2        |
\              \ dx         /

- 0.002 u(x, t),

/  2         \
d            | d          |                  2
--- v(x, t) = |---- v(x, t)| + u(x, t) v(x, t)  - 0.079 v(x, t),
dt           |   2        |
\ dx         /

/                                                           100
|                                        1    /1           \
< u(0, t) = 1, u(1, t) = 1, u(x, 0) = 1 - - sin|- Pi (x - 1)|
|                                        2    \2           /
\

\
|
>,
|
/

/                                                       100\
|                                    1    /1           \   |
< v(0, t) = 0, v(1, t) = 0, v(x, 0) = - sin|- Pi (x - 1)|    >
|                                    4    \2           /   |
\                                                          /

\
|
>
|
/
pds := pdsolve(dys1, numeric, time = t, range = 0 .. 1);
Error, (in pdsolve) invalid input: `pdsolve/numeric` expects its 2nd argument, IBCs, to be of type {list, set}, but received time = t
p1 := pds:-plot(t = 0, numpoints = 50);

p2 := pds:-plot(t = 1/8, numpoints = 50, color = blue);

p3 := pds:-plot(t = 1/4, numpoints = 50, color = green);

plots[display]({p1, p2, p3});
Error, `pds` does not evaluate to a module
Error, `pds` does not evaluate to a module
Error, `pds` does not evaluate to a module
Error, (in plots:-display) expecting plot structures but received: {p1, p2, p3}

## How do I solve Optimal control in Maple?...

Hi, Is there a way in which i can solve the following optimal control problem numerically with Maple ??

where P(t)=N(t)+S(t)+A(t) and N(0)=0.4897, S(0)=0.4018, A(0)=0.1085.

μ=0.000833, d=0.000666, ε1=0.0020, ε2=0.000634, β1=0.002453, β2=0.25*0.02, γ1=0.0048, γ2=0.25*0.02+0.00013, k1=1, k2=0.001, k3=0.99.

where

p1,p2,p3 are transversality conditions

p1(60)=0
p2(60)=0
p3(60)=0

Benz.

## How do I animate a plot-based procedure or functio...

Hi MaplePrimes team,

If I assume a plot-based function or procedure C(s,t) and P1(t) are hidden in a package somewhere I don’t care about the type of geometry (spacecurve or plot3d). Now, I just want to animate P1(t) following the variable t. How do I do?

Example 1: Curve Animation in variable t

1. Equation

C := (s,t)-> Vector([cos(s), sin(s), t*s/2]):     #Helix shape as example

2. Plot

P1 := t-> display(spacecurve(C(s,t), s = 0..3*2*Pi, linestyle = solid)):

Example 2: Surface Animation in variable t

1. Equation

S := (x,y,t)-> Vector([x, y, t/(1 + x^2 + y^2)]):

2. Plot

P2 := t-> display(plot3d(S(x,y,t), x = -2..2, y = -2..2)):

If I assume the function or procedure S(x,y,t) and P2(t) are hidden in a package somewhere I don’t care. Now, I just want to animate P2(t) following the variable t. How do I do?

Example 3: Mixing Curve and Surface Animation in variable t

The ideal/”dream” basic syntax would be:

animate(display, [P1(t), P2(t)], t = t1..t2)

But it does not work.

Best.

Guy.

## What is the problem in the following code to solve...

What is the problem in the following code to solve given PDE?

pde_question.mw

Thanks.

## error in maple file...

hi everybody:

I have two Maple files that file 1.mw file is a package and 2.mw file is based on the 1.mw file when running the 2.mw file I see the error and don't know how to solve it, I attach these files, thank you for helping me.

1.mw

2.mw

## No doubt that someone will provide a smarter solut...

No doubt that someone will provide a smarter solution:

 > # the main idea f := exp(a-b); subs(B=-b, expand(subs(b=-B, f)));
 (1)
 > # ad hoc application restart: f := 2*gamma(t, r)-2*alpha(t, r)-2*beta(t, r); c := op~(1, [op(f)]); C := [seq(u[i], i=1..numelems(c))]; subs(C=~c, expand(subs(c=~C, exp(f))))
 (2)
 >

## Error in one of the sample applications shipped by...

Could someone confirm if this is a problem in this sample application?

In 2019, in the folder

C:\Program Files\Maple 2019\samples\ProgrammingGuide\RandomnessTests

There is sample application. Opening the main module file RandomnessTests.mpl  and scrolling down a little bit to the include statements show

```\$include "WaldWolfowitz.mm"
\$include "BitFrequency.mm"
\$include "SequenceFrequency.mm"
\$include "Compressibility.mm"
\$include "BinaryRank.mm"
\$include "Entropy.mm"

\$include "Data.mm"
\$include "Visualization.mm"```

However, in the same folder, there is no Data.mm file. There is only Data.mpl file.

So how could this sample application work?

This sample app have more problems. The file Visualization.mm  say

```Data := module()
option package;
...```

And the file Data.mpl has

```Data := module()
....```

This is all so confusing. Seems someone made some typos and not tested this app? Why put a sample application which makes learning packages in Maple more confusing?

ps. I did not yet try to figure how to locad it and run it myself, I was just browsing it.

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