## EDIT: within "if": f(1,1)<3.0 condition cannot be ...

Hello,

I want to create a plot of a gradient field of a function with singularities I want to draw arrows only where the function has values below 3,   or written: where f(x,y) < 3.

MY CODE:

potfeld := f(x, y) -> 1/sqrt(y^2+x^2);
for i to 5 do
for j to 3 do
if sqrt(i^2+j^2) <> 0 and sqrt((i-2)^2+j^2) <> 0 and potfeld(i, j) < 3
then P[i, j] := arrow(`<,>`(i, j), `<,>`((D[1](potfeld))(i, j), (D[2](potfeld))(i, j)))
else P[i, j] := arrow(`<,>`(i, j), `<,>`(.1, .1))
end if
end do
end do;
Pseq := seq(seq([P[k, l]], k = 1 .. 5), l = 1 .. 3);
display(Pseq, view = [1 .. 5, 1 .. 3], scaling = constrained);

RESULTS IN:
Error, cannot determine if this expression is true or false:  (1/2)*2^(1/2) < 3.0

The "(1/2)*2^(1/2)" are the value of the function potfeld(x,y) evaluated at (1,1).

I ask for your help, as with many changes and variations I have not managed to solve this issue.
+Thx and regards+

## Principles of type definition for infinite sets in...

I wanted to define a set of all positive integer powers of 2, and I could determine whether a number is contained in the set.

When a set is a finite set and there are not many elements, it's not hard to do. We can form the set first and then determine whether the elements are included or not.

S:={seq(2^i,i=1..100)}:
is(64,S);
is(-3,S);

true

false

Because the set of all positive integer powers of 2 is an infinite set, or rather a countable set. I thought of using the positive type to define it.

map(type, [0, 4, -2], 'And'('positive', 'satisfies'(s -> type(log2(s), 'positive'))))

[false, true, false]

Interestingly, we find that the type of judgment condition is a function, whereas positive(or integer) are symbols.

whattype('And'('positive', 'satisfies'(s -> type(log2(s), 'positive'))));
whattype(positive);
whattype(integer);

function

symbol

symbol

So my question is how does Maple define integer types or positive integers or even real numbers? In other words if I don't use the positive integer type for the above question, can I define the set of all positive integer powers of 2.

## The Chaos Game and Generation of IFS...

Hi!

I have created a procedure for the so-called "Chaos Game" for the generation of Fractals. The file is the following:

Fractals_ChaosGame.mw

On the other hand, for a given day set D:={(x0,y0,(x1,y1),...., (xN,yN)}, for simplicity we assume D is contained in [0,1]x[0,1], one can to construct an "Iterated Functions System" such that its attractor set contains the set D. A detailed exposition of this topic can be found in the famous Barnsley's book "Fractals Everywhere". Also, in the following paper (sections 2.5 and 4-A):

https://arxiv.org/pdf/2102.09855.pdf

I have tried to implement in Maple 17 a procedure to create such Iterated Function System:

IFF_v2.mw

But, I feel that there is something wrong...After plot (with the Chaos Game procedure) a lot of points of the Iterated Functions System (i.e., an approximation of its attractor set), I have a "set of points", instead of a figure similar to a curve (which I feel that must be the correct).

Please, Somebody can have a look to the attached files?

## GNU compiler error ? Maple 2021...

Dear Sirs,
I was with my students today, and attempting to do a Math Maple exercise. The assignment contained the requirement to plot three graphs in one plot f,g,h. Those with windows pc and maple were able use the proper command.

plot({f(x),g(x),h(x)}) or plot([f(x),g(x),h(x)])  however some of those with MacOS would inside Maple 2021 get an error which said "GNU compiler not found", when using the same command. For those there was no other way (that I knew off) than to do a

p1:=plot(f(x)):

p2:=plot(g(x)):

p3:=plot(h(x)):

and then plots:-display([f(x),g(x),h(x)]):  which work.

But why the MacOS error ? Any idea?

## How can I get a copy of the solutions to the book ...

I have a printed book copy of Derek Richards' book, Advanced Mathematical Methods With Maple and would like to get the solutions to the problems in the book. Unfortunately the web download is no longer available. I have not been able to locate a copy or to contact Derek Richards directly.

Thanks

## Better Lissajous curves animation...

Hi! Do you know how can we make more transparent code for this animation plot? I want something similar to this but only for one spot:

my code:

restart;
with(plots);
with(plottools);
display(plot([cos(x), sin(2*x), x = 0 .. 2*Pi]), animate(pointplot, [[[cos(a), 0], [0, sin(2*a)], [cos(a), sin(2*a)]], color = [red, green, green], symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), 0], [cos(a), sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[0, sin(2*a)], [cos(a), sin(2*a)]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), implicitplot(x = cos(t), x = -1 .. 1, t = 0 .. 2*Pi), animate(plot, [[[0, a], [cos(a), a]], color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[0, a], [cos(a), a]], color = green, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), implicitplot(y = sin(2*t), t = 0 .. 2*Pi, y = -1 .. 1), animate(plot, [[[a, 0], [a, sin(2*a)]], color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(pointplot, [[[a, 0], [a, sin(2*a)]], color = red, symbolsize = 23, symbol = solidcircle], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [a, sin(2*a)]], linestyle = dash, color = red, thickness = 3], a = 0 .. 2*Pi, frames = 100), animate(plot, [[[cos(a), sin(2*a)], [cos(a), a]], linestyle = dash, color = green, thickness = 3], a = 0 .. 2*Pi, frames = 100));

## prime 2 tuple with difference of 36...

Maybe some expert can help me with this.

I am trying to improve oeis.org/A156104. It is pairs of prime numbers p and p+36.
According to the k-tuple conjecture, this should be potentially an infinite list. I want to make the database .b file larger - from 1,000 to 10,000.

The virtual clipboard was too large to copy to notepad.  I could not figure out how to write this to a file.  I tried fopen() and fclose().

See my efforts

pairs_p_and_p+36_2.mw

pairs_p_and_p+36_2.pdf

Let me know.

Matt

## &x cross product with LinearAlgebra and Physics[Ve...

restart;
with(Physics);
with(Physics[Vectors]);
with(geom3d);
with(LinearAlgebra);
with(ColorTools);
with(plots);

When I define a vector with Physics[Vectors] as:

a1 := a/2*(0*_i + _j + _k)

Maple returns:

a1:= a/2*(_j + _k)

Which is fine but if you try to take the cross product it won't work because the command expects a vector in R3 but interprets a1 as a vector in R2.

How do I ensure Physics[Vectors] understands a1 is a vector in R3

zero_component_problem.mw

## How can Maple produce this kind of display?...

The worksheet below contains an example of the tiling of the hyperbolic plane.

I would like to produce this and other hyperbolic plane tilings from Maple worksheets, but I don't know the math technique for doing so.

Please direct me to a source of the requisite knowledge or an example worksheet which I can study and imitate.

Hyperbolic_Plane_Tiling.mw

## Webscrapping: Importing text in HTML file / webpag...

On virtually any webpage is a mixture of images and text. I can go to the page, select all contents, copy the contents into an Excel spreadsheet, save the spreadsheet file and then use the ExcelTools:-Import function to read the file into a DataFrame. At that point, I can work with the data.   All the text on the webpage, even if it is embedded in some HTML command, is copied as text into the spreadsheet which eventually can be read as text by Maple.

My quesiton is, what is the method for me to bypass Excel and import the webpage directly into Maple, striped of the HTML code? Can someone point me to an example? (The only examples I have seen use the Sockets package, but I thought this mode has been superceded with Import.)

## Why does Maple tend to display expressions with un...

Here is an example. Why not apply the minus sign to the numerator?
Is there a simple way to change this behavior.

t__FET_TurnOff := solve(-C__iss2*V__gs_th2 + Q__total = i__GateDriveN*t__off, t__off);

Preferred result

## Programatically assigning colors to points in geom...

Programatically assigning colors to points in geom3d not working.  I just want all the points drawn by the draw command, to be the same color.  The output does not respond to programatic specification of the object color.

Maple 2021 Help says: "

geom3d: draw command

calling sequence:
draw(obj,...)
draw([obj_1,...,obj_n],...)

A typical call to the draw function is draw([ obj_1(localopts_1),...,obj_n(localopts_n) ], globalopts) where obj_1, ..., obj_n are geometric objects, localopts_1, ..., localopts_n are local options for a particular object, and globalopts are  options which apply to all of the objects.

localopts_i is a sequence of type equation. The set of options allowed for localopts_i is color = red."

I tried: color = "Red", color = "red", color = Red, color=red.  The command goes through but the colors remain distinct per point.  You can use the context menu to change the color after the command goes through but it is inefficient for my purposes.

Here is an image of it not working:

## Wrong integral result...

Hello, There seems to be a bug in the int() routine when CPV is being used i.e.

restart;
f1 := (int(t^(2*a - 1)/(-t^2 + 1), t = 0 .. infinity, CPV = true) assuming (0 < a, a < 1));

the result given is

f1 := Pi/(2*sin(Pi*a)*(-1)^(1 - a))

but the correct result is

f1 := Pi/2*cot(Pi*a).

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