Maple 2020 Questions and Posts

These are Posts and Questions associated with the product, Maple 2020

Is there a Maple command to obtain a Taylor series and partial sums of exp(A) where A is a square matrix ?

Hello everyone!

I'm not experienced user since I am new to maple, right now I am struggling with partial derivatives.

I want to derivative formula L over diff(x(t), t). Im using dot notation.

 

Variable diff(x(t), t) is hidden under the name predkosc_x but using this variable name instead of x(t) with a dot also is not working.

 

What am I doing wrong that I cant derivative over few varaibles?

 

 

 

 

Also when im trying it this way

I also fail

Hello,

My name is Francisco Navarro. I have a problem when using diff and alias, together with seq or sum.

A very simplified worksheet of what I mean would be

restart

alias(a1 = a1(r), a2 = a2(r), a3 = a3(r))

array1 := [a1, a2, a3]

array2 := [seq(cat(a, i), i = 1 .. 3)]

array1 - array2

This gives [0,0,0] so they are the same thing but, under differentiation, they do not behave the same way (so they are NOT exactly the same object for Maple)

diff(array1, r)

diff(array2, r)

which are different. Any idea of what is wrong with this?

I need to create long arrays with funcions that depend on several values and then differentiate those arrays. But clearly this approach does not work. Thank you for your answer.

Francisco

Why is Maple 2020 in "abcapps.cloud.com" different from Maple 2020 in apps.abc.edu? I am connecting to maple 2020 in two different ways to the school where I work. The schools name is, say, "abc". The first version of Maple 2020 has two arrows at the top. The second arrow is the "upload" arrow and allows me to upload a file from my home computer the my folder at school.
The second version of Maple 2020 has no such arrows. Both versions allow me to get my Maple cloud working for local loading and saving Maple files. How can I upload a Maple file to my Maple cloud from my home computer in the second Maple 2020 version in apps.abc.edu? Or, how can I upload a file to my Maple cloud in any way from my home computer?
By the way, the second Maple 2020 version is coming from Microsoft's Remore Desktop Web Client. It look like it has its own navigation bar at the top.

Thank you!

mapleatha

Hello,

I'm using the command

Matlab(AA,resultname="A",optimize=tryhard)

to generate Matlab code for a quite big matrix. The first problem is, that I get a lot of the following warnings

Warning, cannot resolve types, reassigning t33's type

for a bunch of different t** variables. When I copy the generated code to Matlab I get the error: 'Dimensions of arrays being concatenated are not consistent.'

I found that some entries are obviously transposed like

t50 = [0 0 0 0 0 0 t34 0 0 0 0 -t33 t37 0 0 0 0 0 -t44 0 0 0 0 0 t49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0];

should be a column vector. Here is a snippet of how the resulting matrix A is constructed (I can't show the full code because it consists of some 100 lines):

A = [t50 t97 t143 t190 t237 t261 ... ]

I tried to manually transpose the entries. The matrix can be generated but the dimension is wrong, hence, it must be a wrong matrix then. Does anyone know what could be the reason for this? I generate the matrix via the Hessian-command

 

Look at the following Maple code and output, from Maple 2020. Can you explain the results? I know returning an uninitiated local variable is bad practice, but I cannot make sense of what happens when I do it anyway (just to understand the internals of the Maple language). Should I simply consider the results as undefined behavior?

> f:=proc()                                                                    
>     local x;                                                                 
>     return x;                                                                
> end proc:                                     

> a1 := f() + f();                                                             
                                   a1 := 2 x

> a2 := f() - f();                                                             
                                  a2 := x - x

> a1 + a2;                                                                       
                                  2 x + x - x

> a3 := f() + f() + f();                                                       
                                   a3 := 3 x

> a4 := f() + f() + f() - f();                                                 
                                 a4 := 3 x - x

EssayTools command SpellCorrectWord("trnu") will return "run" and not return "turn".

Is there a way for Maple to only find anagrams with the same length as the given string?

Can Maple do this referencing an external dictionary located on the internet e.g. a complete Websters?

Hello,

HazardRate seems not to work for a convolution - it always returns zero.

restart;
with(plots);
with(Statistics);
X1 := RandomVariable(Uniform(0, 1));
X2 := RandomVariable(Uniform(0, 1));
HazardRate(1/2*X1 + 1/2*X2, 0.4); #returns zero
plot(HazardRate(1/2*X1 + 1/2*X2, t), t = 0 .. 0.9, legend = "Hazard Rate"); #plots zero
#writing hazard rate explicitly works fine
plot(PDF(1/2*X1 + 1/2*X2, t)/(1 - CDF(1/2*X1 + 1/2*X2, t)), t = 0 .. 0.9, legend = "Hazard Rate explicitly");

Thank you!

 

Hello,

I plot a pdf of the average of two iid random variables, and get that it is negative. What am I doing wrong?

Here is an example:

restart;
with(plots);
with(Statistics);
X1 := RandomVariable(BetaDistribution(4, 4));
X2 := RandomVariable(BetaDistribution(4, 4));
plot([PDF(X1, t), PDF(0.5*X1 + 0.5*X2, t)], t = 0 .. 1, color = [red, blue], legend = ["PDF X1", "PDF average"]);

I want to plot3d this function :
(2*Int(3*piecewise(x < 1, x, 1 < x, 2 - x)*piecewise(y < 3/2, y, 3/2 < y, 3 - y)*sin(Pi*x/2)*sin((2*Pi*y)/3), [y = 0 .. 3, x = 0 .. 2]))/3
 

So, I wrote : 

plot3d((2*Int(3*piecewise(x < 1, x, 1 < x, 2 - x)*piecewise(y < 3/2, y, 3/2 < y, 3 - y)*sin(Pi*x/2)*sin((2*Pi*y)/3), [y = 0 .. 3, x = 0 .. 2]))/3, x = 0 .. 2, y = 0 .. 3)

and I get :

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

I am totally new with integrals and I think there is a pb related to a bad writing of them.
Thank you for your answers.

Hello, 

is there any possibility how to write just a part of axis label e.g. in Italic? For example if I want want a label to be "ln(h)" and i want just the "h" to be written in Italic font.

Thanks a lot.

Hi all, 

I am trying to plot the amplitude spectrum of a square wave. I plotted the wave by using its fourier series but I want to find the 5th harmonic which should be around 0.5 however, maplesoft retruns it as 0.7 for some reason. When the stem plot is plotted even that look likes 0.5 at the 5th harmonic but the F(5) is giving wrong value. 

Please have a look at the screenshot and file attached. 

Pulse_width_8us.mw

 

(Note: Maple was not giving wrong answer, I accidently uploaded the wrong file and have edited/updated the question)

I easily found the roots of the following equations,

s:=solve(x^3+x^2-2*x-1,x)

I accidentally discovered that  2*cos((2*Pi)/7) is also the root of this equation. 

simplify(eval(x^3+x^2-2*x-1,x=2*cos((2*Pi)/7)))

0

It’s easy to know that 2*cos((2*Pi)/7) is equivalent to the third root found above

s1:=fsolve(x^3+x^2-2*x-1,x);
2*cos((2*Pi)/7.)

         s := -1.801937736, -0.4450418679, 1.246979604

                          1.246979604

 

Maybe I don’t like the use of imaginary units, and I prefer  2*cos((2*Pi)/7) .

In the case that I don’t know that  2*cos((2*Pi)/7) is the solution of the equation, can I make a certain transformation without using the imaginary unit to represent the real number. For example, trigonometric functions, exponential functions, etc.

I tried to use the following functions, all failed.

s:=solve(x^3+x^2-2*x-1,x);
convert(s[3],cos);
identify(s[3])

 

What is interesting is the following phenomenon. Even if Zeta function does not look great:

s1:=fsolve(x^3+x^2-2*x-1,x):
identify(s1[3])

 

 

For this example, can all roots be transformed into trigonometric expressions by maple.

 

 

I would like to use the command "TensorArray"  to create the contravariant tensor.  As seen in the following simple routine, the command output seems to assign values to the contravariant tensor, but, on the last line, the contravariant value is still unassigned. 




 

 

 

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