It's ok isolate command? I need the solution sin(a)=+-1/(3^0.5)

attach photo, i need simple step after 2.78 like book, solution is sin(a)=+-1/(3)^0.5.

Dear all

I try to understand why maple does ot plot the behavior of x^1/3 for negative real number, 

inverse_function_xthree.mw

root(x,3) is function defined verywhere, but why maple plot only this function for x positive 

thank you

The Putnam 2020 Competition (the 81st) was postponed to February 20, 2021 due to the COVID-19 pandemic, and held in an unofficial mode with no prizes or official results.

Four of the problems have surprisingly short Maple solutions.
Here they are.

A1.  How many positive integers N satisfy all of the following three conditions?
(i) N is divisible by 2020.
(ii) N has at most 2020 decimal digits.
(iii) The decimal digits of N are a string of consecutive ones followed by a string of consecutive zeros.

add(add(`if`( (10&^m-1)*10&^(n-m) mod 2020 = 0, 1, 0), 
n=m+1..2020), m=1..2020);

       508536

A2.  Let k be a nonnegative integer.  Evaluate  

sum(2^(k-j)*binomial(k+j,j), j=0..k);

        4^k

A3.  Let a(0) = π/2, and let a(n) = sin(a(n-1)) for n ≥ 1. 
Determine whether the series   converges.

asympt('rsolve'({a(n) = sin(a(n-1)),a(0)=Pi/2}, a(n)), n, 4);

a(n) ^2 being equivalent to 3/n,  the series diverges.

B1.  For a positive integer n, define d(n) to be the sum of the digits of n when written in binary
 (for example, d(13) = 1+1+0+1 = 3). 

Let   S =  
Determine S modulo 2020.

d := n -> add(convert(n, base,2)):
add( (-1)^d(k) * k^3, k=1..2020 ) mod 2020; 

        1990

Hi again. I have been stuck on this for almost 3 hours by now, and i have ran out of ideas..

I am working on a proof called dandelin spheres, which proves you can get an ellipse by cutting a cone with a plane.

I have found the right equation for both semi circles, the line (cone) and the plane.

I have defined the spheres as semi circles, and the cone as a line, which i am plotting by using the surface of revolution command.

The problem lies within the fact, that i cannot use the intersectplot command with surface of revolution, and i need the plot to show the intersection between the plane and cone. 

The following shapes are defined:

cone line - f := x -> 0.5*x;
small sphere - g := x -> sqrt(0.8944271908^2 - (x - 2)^2)

bigger sphere - h := x -> sqrt(3.354101965^2 - (x - 7.5)^2)

plane - m(x, 0) := 1.216350358*x - 3.841106394

with the following command i recieve this output, which i nice, but i am missing the final part, the ellipse.

I hope someone can help a desperate student :)

- Oscar

Hello, everyone!

I have a problem. Colleague send me a figure in maple-file – .mw. How to export data from this plot? I usually use "plottools:-getdata" command, but what strategy should I apply in case of attached file?

Test-example.mw

Dear all,
I want to create a superscripted and subscripted variable in 1-D math. I know that I can establish a subscripted variable by using double “_”, for example, the execution of the following command causes assignment 2 to u__b, in which b is the subscript of u.
u__b:=2;
However, I don’t know any way to create either a superscripted variable or a variable having both the subscript and superscript in 1-D math.
Can anyone help me?
 Best wishes

Dear MaplePrimes community,

I'm trying to calculate the (Moore-Penrose) pseudoinverse of a matrix using the following code:

with(LinearAlgebra):
Identity := Matrix(2, 2, [[1, 0], [0, 1]]):
A := Matrix(2, 2, [[0.5661180126, 0.4338819876], [0.8316071431, 0.1683928571]]):
MatrixInverse(Identity - A, method = pseudo)

Unfortunately, the output appears to be meaningless (and it conincides with what I'm getting by calculating a simple matrix inverse using "MatrixInverse(Identity - A)"). Am I missing something? (And how do I calculate the (Moore-Penrose) pseudoinverse of the matrix (Identity-A)?)

Presenters:

Affiliated Research Professor Mohammad Khoshnevisan

Physics Department, Northeastern University

United States of America

&

Behzad Mohasel Afshari, Admitted Ph.D. student

School of Advanced Manufacturing & Mechanical Engineering

University of South Australia

Australia

Note: This webinar is free. For registration, please send an e-mail to m.khoshnevisan@ieee.org. The registration link will be sent to all the participants on April 26, 2021. Maximum number of participants =60

Vibrational Mechanics - Practical Applications- Animation 1

Vibrational Mechanics - Practical Applications- Animation 2

Vibrational Mechanics - Practical Applications- Animation 3

Special characters like æ,ø,å are causing some troubles when used in Maple Code attachments in workbooks.

I've managed to get around the problem by using HTML equivalents in the first run, but then this will cause problems when exporting the same strings to Excel.

Funnily this problem just arises in Workbooks, not when using the same code in a code edit region.

Special.zip

Rotating Disk(Click to Play the Movie)

Natural Frequency(Click to Play the Movie)

Hanging Mass(Click to Play the Movie)

Rotating Pendulum(Click to Play the Movie)

Cross Over a Bumper(Click to Play the Movie)

I have two functions u(x,y,t) and p(x,y,t).

I want to find the total derivative of D_x( p*u) (where * is the multiplication)

where D_x is as given in the attached file formula_of_D_x.pdf 

Also, it is given in the following link but it's not clear to me. I think it somehow resembles my query, but not clear about the syntax so that I should implement it on mine.

https://www.maplesoft.com/support/help/Maple/view.aspx?path=DifferentialGeometry/JetCalculus/TotalDiff

Dear all

Strange phenomena...Every thing is well coded.
Using numeric solution pdsolve and  and solution based on iterative solution, gives a slighty different curve.. 

All matrices are well coded, and everything is okay... But  what happen... to get two different curves at same time.

New_code.mw

Thank you for any help 

Dear all

if I have a vector defined as u[1..11,1]:=

How can display the coeffients of  this vectors 
can I plot the vector 

Thanks for any help

I have a complex PDE as follows:

where u(x, t) is a complex function.

The following function u_11(x, t) is a solution for the PDE above. 

where

I want to check whether the u_11(x,t) is a solution for the PDE or NOT. 

 How to correctly define the complex PDE in MAPLE?
 

PDE:=I*diff(u(x,t),t)+diff(u(x,t),x$2)+alpha*(abs(u(x,t))^2)*u(x,t)+ I*( gamma[1]*diff(u(x,t),x$3) + gamma[2]*(abs(u(x,t))^2)*u(x,t) + gamma[3]*diff((abs(u(x,t))^2),x)*u(x,t) )=0;

or

PDE:=I*diff(u(x,t),t)+diff(u(x,t),x$2)+alpha*(evalc(abs(u(x,t))^2))*u(x,t)+ I*( gamma[1]*diff(u(x,t),x$3) + gamma[2]*(evalc(abs(u(x,t))^2))*u(x,t) + gamma[3]*diff((evalc(abs(u(x,t))^2)),x)*u(x,t) )=0;

Let's check the solution is right or not:

k:=(gamma[2]+2*gamma[3]-3*gamma[1]*alpha)/(6*gamma[1]*gamma[3]);
omega:=(((1-3*gamma[1]*k)*(2*k-c-3*gamma[1]*(k^2))  )/(gamma[1]))+(k^2)-gamma[1]*(k^3);

uu[11]:=1/(gamma[2]+2*gamma[3])^(1/2)*(-3*(3*k^2*gamma[1]+c-2*k))^(1/2 )*sin(1/2/gamma[1]*2^(1/2)*(gamma[1]*(3*k^2*gamma[1]+c-2*k))^(1/2)*(-c*t+x))/ cos(1/2/gamma[1]*2^(1/2)*(gamma[1]*(3*k^2*gamma[1]+c-2*k))^(1/2)*(-c*t+x))*exp( I*(k*x-omega*t));

pdetest(u(x,t)=uu[11],PDE);

 download-code.mw