I have the equation x^4=4(4x^2-y^2), and I keyed in maple

>with (plots):
>eq:=x^4=4*(4*x^2-y^2);

and recieve in response x^4=4. 

I want to get eq:=x^4=4(4x^2-y^2), in order to find and graph all possible tangents in the event that y=3 and to find the point of intersection for the tangents that lie in the first quadrant. 

Thanks 

how this integro-differential equation can be solved?
any assumption or suggestion is appreciated. tnx in advance

EDITED: parameters are added.

Download integro.mw

Is it possible to draw a graph without names for the vertices? I would get something like this.

The worksheet below is a failed attempt to produce the display of a pencil of conics tangent to four lines. The worksheet contains an image of the display.

Comments within the worksheet describe the details of the attempt and the solve command which fails.

dhaar provided an answer to a similar question which I posed on November 12 (its web address is in the worksheet) and I hope s(he) will reply to this one as well.

ConicsTangent.mw

Hello there, 

Would you allow me to ask this question?

What would be a way to make the 'expression' as 'expression_desired' below?

In other words, what would be a way to cancel I (or j) and exp(-pi/2) each other?

Thank you, 

Download Q20201118.mw

I  installed Maple 2020 a week ago.   When I try to update the Maple Physics Package, the installation stalls.

Output to the command  Physics:-Version(latest):

`The "Physics Updates" version "872" is installed but is not active. The active version of Physics is within the library C:\\Program Files\\Maple 2020\\lib\\maple.mla, created 2020, March 4, 19:36 hours`

I note that there was similar complaint in June.  I am surprised that this has not yet been fixed. The reply in June seemed to be do a manual update, but I am unclear how to do that.   I can download the latest package, but I do not know how to  (or where) to install this package.  Do I just delete the version in C:\\Program Files\\Maple 2020\\lib\\maple.mla and paste the new version?

I would greatly appreciate any help since the main reason I purchased the new Maple 2020 was to use the most recent versions of the Physics package.

There is an error in the series expansion for the JacobiTheta3 and JacobiTheta4 function

> q := exp(I*((2*I)*Pi*1.20388508772313))

>series(JacobiTheta3(z, q)-JacobiTheta3(0, q), z, 2);

gives -1+O(z^2)

>series(JacobiTheta3(z, q)-JacobiTheta3(0, q), z, 2);

gives -1+O(z^2)

The issue is that 

>series(JacobiTheta3(z, q),z,2);

gives

series(Sum(2*Q^(_k1^2),_k1 = 1 .. infinity)+O(z^2),z,2)

where the term n=0 is missing.  

The same for JacobiTheta4

series(JacobiTheta4(z, Q), z, 2);

series(Sum(2*(-1)^_k1*Q^(_k1^2),_k1 = 1 .. infinity)+O(z^2),z,2)

The same issue arises when taking the limit 

limit(JacobiTheta3(z, sqrt(q))-JacobiTheta3(0, sqrt(q)), z=0); 

gives -1

same for  limit(JacobiTheta4(z, sqrt(q))-JacobiTheta4(0, sqrt(q)), z=0); gives -1

This error occurs in maple 2018 and maple 2020. 

On the other side when taking numering values approching 0 there is no problems. 

So it seems that series and limit uses some codes wrong formulae.

How can one patch this? 

thanks in advance

Hi

I have created an model of a UR5e robot complete with mass and inertia however I have a problem with implementing the viscus friction. I have the viscus friction values for each of the joints calculated from another program, I just need to implement them.

Mvh

Eric Ragnarsson

Dear all

Can we compute the following integral using maple 

   int(cos(3+sin(x)), x = 0 .. 5)

Many thanks 

Both exp(x)^2 and exp(2*x) are correct and the same. 

simplify(exp(x)^2 - exp(2*x))

                     0

But I can't figure how to make Maple always use exp(2*x) instead. This is for exponent  in integers. This covers 90% of all cases in the Latex I generate.

This is only for Latex purposes and for typesetting only as it looks much better and more standard to use exp(2*x) than exp(x)^2.

Here is an example

restart;
expr:=-(2*x+1)*exp(-x)/(exp(-2*x))+(2*x+1)/exp(-2*x);
expand(expr)

The latex for the above looks like 

The Latex take much larger vertical space on the line. Compare the above to the same expression, but written with exponent inside

expr:=-2*exp(x)*x - exp(x) + 2*exp(2*x)*x + exp(2*x)

Which generates Latex

Which is much more pleasent to read and has less height as well.

Is there a way to automatically make Maple do that? Could I add my own `Latex\function` ? As described in 

https://www.maplesoft.com/support/help/Maple/view.aspx?path=latex%2ffunctions

How? Also, I am using Physics:-Latex and not :-latex, so I do not know if the above page would even apply here.

it will be hard to write code to manually fix this, by may be string searching and fix it as the program is running.

Any suggestions? Note that Mathematica automatically does this when the exponent is integer

Update

Thanks to the hint by Axel Voget below, I tried to use combine, but only target it to exp(x)^n part of the whole expression, as I do not want to apply combine to each expression. This is what I came up with

restart;
expr := -2*exp(x)*x - exp(x) + 2*exp(x)^2*x + exp(x)^2 + sin(x)^3 + cos(x)^2;
subsindets(expr,'exp(anything)^(anything)',f->combine(f));

Which seems to do what I want. It only applies to exp(x)^n and no other part. Compare this to applying combine to the whole expression

combine(expr)

Which might not be what I wanted.

I still need to test the above more, as may be I did not check for other cases. But if this works, then this will solve my problem. I can add this in one place, where it does this just before emitting the Latex. All my Latex generation is done inside one function which is called from everywhere. So I could easily add this there without changing anything else in the program.

A person asked me why the following code does not give the integral of (x^2+y^2)*z over the top of the unit sphere.

VectorCalculus:-SurfaceInt((x^2 + y^2)*z, [x, y, z] = Surface(<1, s, t>, s = 0 .. Pi/2, t = 0 .. 2*Pi, coords = spherical))

The correct answer is Pi/2, but Maple gives 2*(-1 + Pi)*Pi^2.

Will someonoe please explain this behavior?

I am trying to use Maple to provide numerical solutions to the energy levels of muonic lead by using the Shooting method to work out boundaries for the 1s, 2p, and 3d orbitals. However, I am unable to get Maple to graph or fsolve the roots of the function, since it is "unable to evaluate the function to numeric values in this region" despite the zero being within the bounds.

Here is the code:

Download Exercise_3.mw

I have to compare the probabilty density of a data set of the normalised gaps between eigenfunction energy levels of random matrices to the Wigner surmise Pi/2*n*exp((-Pi)/4*n^2). I have collected the data set, but cannot find a function to give a numerical value for the probability density function to compare. I have tried using KernelDensity but it doesn't seem to work.

Here is the code:

Download matrices.mw
 

Download matrices.mw

Let X be a random such that P[X=x]=x/10, x =1,2,3,4

And let S be the sum 

I want to calculate probabilities like P[S=2] where S is the sum of 2 independent random variable that are distributed like X. The solution should be P[S=2]=P[X=1]*P[X=1]=1/10*1/10=1/100. Or P[S=3]=P[X=1]*P[X=2]+P[X=2]*P[X=1]=4/100

I need this not only for 2 summands but also for 3 and 4 summands. 

How can I code this? I struggle to write a code so that X the random variable has the desired probabilities. Thanks in advance!

Thanks in advance

I have an assignment for Q that after subsequent other assignments and substitutions  results in 

-XC1*R1^2/((R1^2 + XC1^2)*(R1*XC1^2/(R1^2 + XC1^2) + 12960.54302))

when I type Q.

I would like to solve this for XC1, for values of Q that make  XC1 is real. 

How do I do this?  Can I rearrange this assignment?   

I guess I could do something like this:

eq1:= -XC1*R1^2/((R1^2 + XC1^2)*(R1*XC1^2/(R1^2 + XC1^2) + 12960.54302))

solve(eq1=Q,XC1)

but Q as a function of XC1 is a derived from other relationships.

The worksheet probably makes what I'm asking more clear.    I was able to get the result, but I'm sure there is a better, more elegant  way to do what I needed to do...

Thanks
 

Download pi-filter_anal_copy.mw