MaplePrimes Questions

Hi so ive been working on a few codes making Eulers method and RungeKutta and Taylor Series (second order) and I cant figure out why my code is giving me a weird output? I will attach my maple files here, I can post more information if you'd like. Also have no idea how to start for taylor series so any help with code on that would be appreciated!

 


 

euler1 := proc (f, a, b, alpha, h, N) local i, t, w; i := 1; t := a; w := alpha; while i <= N do w := w+h*f(t, w); t := a+i*h; i := i+1 end do; [w] end proc

proc (f, a, b, alpha, h, N) local i, t, w; i := 1; t := a; w := alpha; while i <= N do w := w+h*f(t, w); t := a+i*h; i := i+1 end do; [w] end proc

(1)

euler1(e^(5*3-y), 0, 3, .5, .2, 2)

[.5+.2*e(0, .5)^(15-y(0, .5))+.2*e(.2, .5+.2*e(0, .5)^(15-y(0, .5)))^(15-y(.2, .5+.2*e(0, .5)^(15-y(0, .5))))]

(2)

NULL

NULL

NULL


 

Download p5one.mw
 

RK4 := proc (f, a, b, alpha, h, N) local t, w, i, k1, k2, k3, k4; i := 1; t := a; w := alpha; while i <= N do k1 := h*f(t, w); k2 := h*f(t+(1/2)*h, w+(1/2)*k1); k3 := h*f(t+(1/2)*h, w+(1/2)*k2); k4 := h*f(t+h, w+k3); w := w+(1/6)*k1+(1/3)*k2+(1/3)*k3+(1/6)*k4; t := a+i*h; i := i+1 end do; [w] end proc

proc (f, a, b, alpha, h, N) local t, w, i, k1, k2, k3, k4; i := 1; t := a; w := alpha; while i <= N do k1 := h*f(t, w); k2 := h*f(t+(1/2)*h, w+(1/2)*k1); k3 := h*f(t+(1/2)*h, w+(1/2)*k2); k4 := h*f(t+h, w+k3); w := w+(1/6)*k1+(1/3)*k2+(1/3)*k3+(1/6)*k4; t := a+i*h; i := i+1 end do; [w] end proc

(1)

RK4(exp(5*3-y), 0, 3, .5, .2, 1)

[.5+0.3333333333e-1*(exp(15-y))(0, .5)+0.6666666667e-1*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5))+0.6666666667e-1*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5)))+0.3333333333e-1*(exp(15-y))(.2, .5+.2*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(.1000000000, .5+.1000000000*(exp(15-y))(0, .5))))]

(2)

``


 

Download rk4new.mw

 

How to write down the differential equation for this practical question? 

I can use dsolve to solve the system equation. 

Thank you! 

I am still checking output using latest Latex and Maple 2020.2. I noticed a small problem.

Current Latex uses \mathrm{ln} instead of as before, which is just \ln this casues the space before the operator now to be lost, cause hard to read math.

It is better not to use \mathrm on ln

Here is an example

restart;
Latex:-Settings(UseImaginaryUnit=i,
      UseColor = false,
      powersoftrigonometricfunctions= computernotation,
      leavespaceafterfunctionname = true
):
expr:= 4*exp(3*x)+3*ln(x);
Latex(expr)

                       4 {\mathrm e}^{3 x}+3 \mathrm{ln}\left(x \right)

It should be

4 {\mathrm e}^{3 x}+3 \ln\left(x \right)

Without even \, between the letter before \ln as old latex() did:

latex(expr)

           4\,{{\rm e}^{3\,x}}+3\,\ln  \left( x \right)

As the Latex engine itself takes care of the spacing around math operators best.

Here is the difference when the Latex is compiled. The use of mathrm with exponential is not an issue, since it is one letter operator, but not with ln.

\documentclass[12pt]{book}
\usepackage{amsmath}
\usepackage{mleftright} 
\mleftright

\begin{document}
This is how it is now
\[
4 {\mathrm e}^{3 x}+3 \mathrm{ln}\left(x \right)
\]
                      
This is what it is better to be
\[
4 {\mathrm e}^{3 x}+3 \ln\left(x \right)
\]                                         
\end{document}

Compiled with lualatex compiler gives

The above shows the space problem.

Using Maple 2020.2 and Physics   879

 

There might be a setting for this. I do not know.

I  noticed, once I call Latex() first time, if I then later issue Typesetting:-Settings(prime=x,typesetprime=true); and after that, call Latex() again, it has no effect.  The derivative does not change.

But calling Typesetting:-Settings(prime=x,typesetprime=true); before calling Latex() the first time, works.

Since I do not want to do restart() in a running program, and I would like to call Typesetting:-Settings(prime=x,typesetprime=true); may be different times to change the letter and after having called Latex earlier, is there a way to make this work without having to do restart? I do not rememebr now if this was the case in earlier version or not. I looked at Latex:-Settings() and see no setting for this inside Latex itself to use in place of the above global Settings.

Please see worksheet below.


 

interface(version);

`Standard Worksheet Interface, Maple 2020.2, Windows 10, November 11 2020 Build ID 1502365`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 879 and is the same as the version installed in this computer, created 2020, November 19, 20:10 hours Pacific Time.`

restart;
Latex:-Settings(UseImaginaryUnit=i,
      UseColor = false,
      powersoftrigonometricfunctions= computernotation,
      leavespaceafterfunctionname = true
):
ode:=2*diff(y(x),x)*x=(1+x-6*y(x)^2)*y(x):
#This works, since setting is called BEFORE calling Latex first time
Typesetting:-Settings(prime=x,typesetprime=true):
ode;
Latex(ode)

2*(diff(y(x), x))*x = (1+x-6*y(x)^2)*y(x)

2 y^{\prime}\left(x \right) x =
\left(1+x -6 y \left(x \right)^{2}\right) y \left(x \right)

restart;
Latex:-Settings(UseImaginaryUnit=i,
      UseColor = false,
      powersoftrigonometricfunctions= computernotation,
      leavespaceafterfunctionname = true
):
ode:=2*diff(y(x),x)*x=(1+x-6*y(x)^2)*y(x);
Latex(ode);

#This does not work, since setting is called AFTER calling Latex.
#The latex generated remains the same.
 
Typesetting:-Settings(prime=x,typesetprime=true);
ode;
Latex(ode)

2*(diff(y(x), x))*x = (1+x-6*y(x)^2)*y(x)

2 \left(\frac{d}{d x}y \left(x \right)\right) x =
\left(1+x -6 y \left(x \right)^{2}\right) y \left(x \right)

x, false

2*(diff(y(x), x))*x = (1+x-6*y(x)^2)*y(x)

2 \left(\frac{d}{d x}y \left(x \right)\right) x =
\left(1+x -6 y \left(x \right)^{2}\right) y \left(x \right)

 

 

Download how_to_change_setting.mw

 

 

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?

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