Maple how to prove Sin2x=2sinxcosx for every real number 

Thank you! 

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Hello everyone,

I have a problem when searching in a document. Namelly is there a way to search in the whole worksheet including all code editing regions?

In order to show a point, there is a worksheet. I determine a variable

x11:= 12;

This variable is used in the document and code edit regions. Then I want to change a variable name from x11 to x11data. In order to do that, I use Ctrl+F to find all the times when the variable is used. I have a problem while  searching 'x11'. Namelly, the cases outside a code edit region are displayed, and the ones that are situated in the code edit regions are not seen.

Best regards

The dsolve function is not working to solve a set of differential equations I have written. No error message is showing, but the code does not work.
 

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Hello 

I need a procedure P that given two lists of sets A and B returns a list of lists L such that L[i] is the list of j such that A[i] subset B[j]. Here is an example:

ans6 := [{alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 8], alpha[3, 6], alpha[3, 9]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 8], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 6], alpha[3, 8]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 8]}, {alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 2], alpha[2, 4], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 1], alpha[2, 2], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 8], alpha[2, 0], alpha[2, 2], alpha[2, 5], alpha[3, 3], alpha[3, 6]}, {alpha[1, 5], alpha[2, 8], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8]}]:

ans7 := [{alpha[1, 8], alpha[2, 2], alpha[2, 5], alpha[2, 7], alpha[3, 3], alpha[3, 6], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 3], alpha[3, 4], alpha[3, 5], alpha[3, 6], alpha[3, 7]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 6], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 5], alpha[3, 6], alpha[3, 7], alpha[3, 8]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 7], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 6], alpha[3, 8], alpha[3, 9]}, {alpha[1, 5], alpha[2, 8], alpha[3, 2], alpha[3, 4], alpha[3, 6], alpha[3, 7], alpha[3, 9]}]:

and my procedure

SubsetPairs:= (A::list(set), B::list(set))->
    map(z-> [ListTools:-SearchAll](true, map(w-> z subset w, B)), A)
:
SubsetPairs(ans6, ans7);

The result of applying SubsetPairs is:

[[], [], [1], [1], [1], [], [], [], [2, 3, 8, 23], [2, 4, 9, 24], [2, 5, 10, 25], [2, 6, 11, 26], [2, 7, 12, 27], [3, 4, 13, 28], [3, 5, 14, 29], [3, 6, 15, 30], [3, 7, 16], [4, 5, 17], [4, 6, 18], [4, 7, 19]]

When it is used for long lists, it takes a long time to return the results.  I wonder if a more time- and memory-efficient code can be implemented (perhaps Threads or Grid can be used).

In addition to that, how can a diagram (figure, plot, ...) be drawn to show which subset of the first list is linked to which subsets of the second list (including no link as well).  The length of the first list is always smaller than the length of the second list.  

Many thanks

I noticed that something changed with the output of translating abs() to latex. I am not sure when this happened.

Current version use \mid ...\mid  instead of the original \left| .... \right|

The problem with \mid is that the spacing no longer symmetric. It generate too much space on one side of | compared to the other side, and makes the output not pretty any more.

Is it possible to revert this back to the original way it was done? Please see example

restart;
Latex(ln(abs(1+x))=x)

                     \ln \! \left({\mid 1+x \mid}\right) = x

latex(ln(abs(1+x))=x)

                   \ln  \left(  \left| 1+x \right|  \right) =x

The second example gives better looking Latex where the space is symmetric. Here is the output

\documentclass{book}
\usepackage{amsmath}
\begin{document}          
\[
\ln \! \left({\mid 1+x \mid}\right) = x
\]

\[
\ln \! \left(  \left| 1+x \right|  \right) =x
\]
\end{document}

The second output is much better since \left|...\right| automatically sets the spacing the same between them and the math on each side.  (same if \lvert and \rvert were used)

I just noticed this first time looking at current output. I do not think this is how it used to be, else I would probably seen it before.

I am using Maple 2020.2 and Physics 890 (latest).

If not possible to change back to \left| ... right| . may be a new configuration parameter could be added to alow a user to choose which one?

Window 10.

Hi, 

Working with Legendre Polynomials (LegendreP) I observed that solve doesn't find the correct number of zeros.
More precisely, for N > 17, solve(LegendreP(N, x)) finds less zeros than N.

I wrote a procedure based on a theorem about the intertwined location of the zeros of orthogonal polynomial of successive degrees. So this problem is not blocking, but I would like to understand while solve(LegendreP(N, x)) doesn't always do the job.

Thanks in advance.
 

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This ode

ode:=diff(y(x),x)=sqrt(1-y(x)^2)

has general solution y(x) = sin(x + _C1) but it also has solution y=-1 and y=+1. Since these extra solutions can't be obtained from the general solution by specific value of the constant of integration, they are singular solution.

But I am not able to get Maple to show these:

restart;
ode:=diff(y(x),x)=sqrt(1-y(x)^2);    
dsolve(ode);
dsolve(ode,'singsol'='all',[separable]);
dsolve(ode,[separable]);

We can check that y=1.,y=-1 are solutions

odetest(y(x)=1,ode);
odetest(y(x)=-1,ode);

0
0

Only after I used this, was Maple able to gives these solutions

dsolve(ode,'Lie');
dsolve(ode,'Lie',singsol=all);

So only when using `Lie` symmetry methods and also using singsol=all it worked.

Most people will not think of using this specialized option.

Why Maple did not give these singular solutions using the standard dsolve(ode,singsol=all) command?

Should it not have done so? Now it makes it more confusing as to which option to use to obtain the singular solution, as one might have to keep trying different options.

What do others think? 

Maple 2020.2

I used dsolve to solve the Initial value problems numericaly.
When I set the parameter range=1..5*10^4 , it works and cost only about 200s cpu time.
But if I set range=1..2*10^5, it stop running ( cpu time stop) when the mserver memory reach about 1.5 G. (the memory record in the bottom-right of maple interface is about 700M .)

What is the reason please?  

Hello. I want to use the command verify but with two variables. For example:

verify(x^2 + y^2, 0, {'greater_equal'});

but I get FAIL as an answer. I tried adding before the verify command assume(x, 'real'); assume(y, 'real');

but notihng changed.

Thanks for any help.

I need help for designing a procedure for Schubert Kronecker polynomial program in maple.

I am trying to solve this type of problem:

I thought I could double check my answers by creating a RandomVariable and calculating the probablity using the Probability function.

But from the RandomVariables documentation,  it seems only univariate random variables are supported.

Is there really no way to define a RandomVariable given a joint distribution?

so i have a little school laptop and maple on it works just fine. Then i have my all powerful gaming desktop with an AM RTX 3700x ,RTX 2070S, SSD and 32GB ram.

I have never seen maple run so slow on any pc as i have on my desktop. It is completely impossible to use maple. Just writing normal input like 123 takes forever. One thing i have noticed is evertime i do some sort of action, then the icons to the left slowly go from being colored to grey and back to colored before i can do a new action.

The two images below show an example here you can see it is about to go from being colored to being grey, when i try to mark stuff. I have tried to install the x64 and x86 version, i have tried giving it 4096 ram in the ini file and i have tried removing splash. Nothing works....

This is the last step of my calculation. I get  following system of equations：

I want to solve this system of equations

But I  didn't get any more valuable information 

Actually I'd like to  know if there is no  real solution.

If there is a real number solution,   one is enough for me.

Any help would be greatly appreciated

contour.mw

I'm having trouble executing the following contour plot.

I'm attaching my file. Kindly Help!