MaplePrimes Questions

After doing 

A:=tan(3*x);
B:=expand(A)

How to get A back from B? I tried

combine(B);
simplify(B,size);
simplify(B,trig);
simplify(B);

They do not give A back. tried few conversions to exp() and back and forth. Can't get original expression back.  trigsubs() does not help here.

This is all need to be done in code, assuming one can not look at the expression and decide what to do on any A/B pair. But I am mainly now looking at trig expressions.

Any suggestions?

Maple 2020.2

Hi there!

I am trying to tell Maple to print something one time once a condition has been met for a variable that ranges from a to b, let's say from 1 to 9 in this case. Testbestanden is to be printed, if (F[i]+F[i+1]<20) is true for every i, and Durchgefallen is to be printed as soon as one counterexample is found. The following code illustrates what I need, it doesn't work, however. What is the correct syntax? Switching the lines "if (F[i]+F[i+1]<20)" and "for i from 1 to 9" leads to Maple printing "Testbestanden" for every i that fulfils the statement which is not what I need either.

for i from 1 to 10 do
  F[i]:=i
end do;

if (F[i]+F[i+1]<20)
for i from 1 to 9
then print(Testbestanden)

else print(Durchgefallen)
end if
end do

Thank you in advance! :)

Here's a possible bug in ExcelTools.

When importing from an Excel file, Maple drops text which is referenced from a different sheet. That does not apply to numbers.

Workbook_Excel_indirect.zip

I have a table T with 10 numbers .How can I plot this table ?

Thanks for any explanation !

I am trying  to solve a first order differential equation.  But the maple is not able to solve. Please help me in finding the solutions...

Exact solution is not necessary. Solution in the series expansion is also be very helpful.

Here is the attached maple code..Please do check. Please scroll down to download the given maple file.


 

``

``

restart

with(Student[NumericalAnalysis])

with(PDEtools)

with(DEtools)

with(MmaTranslator)

[FromMma, FromMmaNotebook, Mma, MmaToMaple]

(1)

``

``

``

C1 := 2*M/(4*M*R^2*a-3*R^3*a)

``

D1 := -M*(8*M-9*R)*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(3*R^2*(-16*M^2+26*M*R-9*R^2+(16*M^2-30*M*R+11*R^2)*ln(1+2*M/(4*M-3*R))+R^2*ln(-3*R/(4*M-3*R))))

``

A1 := R^2*(3*ln(1+2*M/(4*M-3*R))+2*ln(1-2*M/R))/(-32*M^2+52*M*R-18*R^2+(2*(16*M^2-30*M*R+11*R^2))*ln(1+2*M/(4*M-3*R))+2*R^2*ln(-3*R/(4*M-3*R)))

``

explambda := simplify((-2*C1*a*r^2+1)/(C1*a*r^2+1))

``

density := simplify(a*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pr := simplify(-D1+3*a*A1*C1*(2*C1*a*r^2-3)/(-2*C1*a*r^2+1)^2)

``

pt := simplify((D1*(-D1*r^2+4)-4*a^4*C1^4*r^6*(9*(1+A1)^2-(4*(1+3*A1))*D1*r^2+4*D1^2*r^4)+2*a*C1*(18*A1-(16+9*A1)*D1*r^2+4*D1^2*r^4)-3*a^2*C1^2*r^2*(9+16*A1+27*A1^2-(28*(1+A1))*D1*r^2+8*D1^2*r^4)+4*a^3*C1^3*r^4*(18+3*A1*(17+9*A1)-(10*(2+3*A1))*D1*r^2+8*D1^2*r^4))/((4*(C1*a*r^2+1))*(2*C1*a*r^2-1)^3))

``

drhodp := simplify(1/A1)

``

dptdp := (diff(pt, r))/(diff(pr, r))

``

A := simplify(-(-1-explambda)/r+4*explambda*Pi*r*(pr-density))

``

B := -(explambda^2+4*explambda+1)/r^2-64*explambda^2*Pi^2*r^2*pr^2-16*explambda*Pi*((-2+explambda)*pr-pt-density)-(-4*explambda*Pi*(pr+density)-4*explambda*Pi*drhodp*(pr+density))/dptdp

``

sys := {r*(diff(y(r), r))+y(r)^2+(A*r-1)*y(r)+r^2*B = 0}

 

[moderator edited to remove pages of output]
 

Download CALCULATION_OF_Y_v1.mw
 

I would like to use a template in Maple to create a sampled data custom component to mimic a digital controller in order to study the effects of the non-linear features of the controller.  Is it possible to do this in Maple using a template?

Hi!

Are there any plans to release a native Maple version for the Apple silicone (ARM architecture) Macs? I suppose that the current versions will work fine through Rosetta 2 emulation layer, but the Rosetta 2 will be removed from Mac OS in 2-3 years. Moreover, the native app would be much faster.

Thank you  

Good morning,

I'm new to Maple and have an informal learning relationship with calculus.

I'm exploring an expression but want the max value of a variable to be based on another equation. 

I'd be curious how to do this and then how to also graph and table the exploration. 

I'd like to evaluate, graph, and table this:

s = u*t + 1/2*a*t^2

Where the maximum value of t = (v - u)/a

s = distace

u = starting velocity

v = final velocity

a = acceleration

t = time for acceleration to reach final velocity

Thank you.

How to write the differential equation only according to the graph? Is the temperature related to newton's cooling law? 

Quite confused about this graph. 

Anyone can help me? Thank you so much! 

I cannot install the latest physics update 877 even after installing 2020.2 update. Geting an error message will try to attach screen shot. Update worked fine on physics update yesterday. Maple 2020.2 on MacBookPro OS 10.15.7

Don't know how to attach screen shot so here is text from install window;

Fetching package "Physics Updates" from MapleCloud...
ID: 5137472255164416
Version: 877
URL: https://maple.cloud

An error occurred, the package was not installed: 
Could not open workbook: /private/var/folders/bb/1n47nzcx18v_l2wy573v7z0c0000gn/T/cloudDownload5932106080613470167/Physics+Updates.maple

Tried at least 3 times before 2020.2 update and 2 times after. Similar results (diiferent download numbers each time).

Is there any useful preprocessing -- or a better data structure -- for efficient set membership testing?

I have a list X of 1.5 million hashes (30-digit compressions of arrays) and want to find an element which belongs to both this set and another set. The other set Y has 270 billion elements so I will generate just a fraction of these (a sample size of a few hundred million should be enough to give a collision). Will membership testing be faster if I first sort X? Or is the sort operation too expensive to see any visible benefit?

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.


 

restart

w[c]:=0.01:delta:=5:Omega:=5:w[0]:=1:gamma_0:=1:k[b]:=1:T:=100:nu[n]:=2*Pi*n*k[b]*T;

200*Pi*n

(1)

F:=2*gamma_0*w[c]^2*exp(-w[c]*tau)*sin(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau):

k1:=2*k[b]*T*w[c]^2*sum((w[c]*exp(-w[c]*tau)-abs(nu[n])*exp(-abs(nu[n])*tau))/(w[c]^2-nu[n]^2),n=-infinity..infinity):

G:=cos(delta/Omega*(sin(Omega*t)-sin(Omega*(t-tau)))+w[0]*tau)*k1:

eq:=diff(rho(t),t)+Int(G*rho(tau),tau=0..t)=1/2*Int(G-F,tau=0..t);

diff(rho(t), t)+Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))*rho(tau), tau = 0 .. t) = (1/2)*(Int(0.200e-1*cos(sin(5*t)-sin(5*t-5*tau)+tau)*(sum((0.1000000000e-1*exp(-0.1000000000e-1*tau)-628.3185308*abs(n)*exp(-628.3185308*abs(n)*tau))/(-394784.1762*n^2+0.1000000000e-3), n = -infinity .. infinity))-0.2e-3*exp(-0.1e-1*tau)*sin(sin(5*t)-sin(5*t-5*tau)+tau), tau = 0 .. t))

(2)

 


 

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

 

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