Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

If a type is not known, an error is thrown

type([],foo)
Error, type `foo` does not exist

Since no error is thrown, these types are known

type({},'{}');# why that output?
                             false

type([],'[]')
                              true

I would have expceted {} and [] to be listed as subtypes of set and list since their counterparts (nonemptylist and nonemptyset) exist. Technically the types {} and [] are not needed since negating

not(type([],nonemptylist));
not(type({},nonemptyset));
                              true

                              true

works.  However, the types exist, hence my question

How can I make a legend for this plot?

 

plot([17.85*(2.65*t^2 + 1 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 47 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 97 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 147 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 197 + 3*t)^2/t^2], t = 0 .. 25, labels = ['t', 'x'], labelfont = [Times, 12])

 I got the following figure.

 plot([17.85*(2.65*t^2 + 1 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 47 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 97 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 147 + 3*t)^2/t^2, 17.85*(2.65*t^2 - 197 + 3*t)^2/t^2], t = 0 .. 25, labels = ['t', 'x'], labelfont = [Times, 12])


Now I want to put a legend box in this plot for each color line. How can I do it?
 

I need help trying to remove some null elements from a listlist, that i converted from an Array. 

Example: I have a list of coordinates r:=[[1,2],[1,3]], which i converted to an array, and nulled the first element.

r:=convert(r,Array): 
r[1]:=NULL:
r:=convert(r,listlist):

I now have r=[[],[1,3]] after converting it back to a listlist. How do i remove the first element, which is an empty entry, such that i end up with r=[[1,3]]

Thanks 

Hi guys!

I'm looking for a way to type in the same "calculation" in Maple instead of the Word-package WordMat.
This is a screenshot from Word of the calculation I wanna do in Maple. But I can't figure out how to type it correct. Maybe you guys could post a screenshot of the same entered in Maple. 
Note: (I'm a Maple-rookie, it might be a simple "trick")
I know how to assign/define fx IP, U and ZP. It's about calculating with the angle symbol in line, and getting a "readable" result.



Looking forward to hear from all of you...

I have a surface defined by C(x, y, x) = 0 that I visualize with implicitplot3d.
Using shading=shue does not suits me and I would like to define my own coloring function F(x, y, z).

The first error I got made me think that a coloring function cannot depend on 3 parameters.
But a simpler (and not visually satysfying function) F(x, y) already leads to an error, which makes me wonder if it is possible to use a colorig function with  implicitplot3d?

implicitplot3d_coloring.mw

Thanks in advance

I have a problem with the order  of the Eigenvalues and Vectors flipping. It is a bit random. I only found it trying to understand why a procedure sometimes rotated a conic one way and  then the other. This a really causing a quite a problem, I have only tried this in Maple 2024 so far. I have included screen shots to prove the effect.

restart

 

with(LinearAlgebra):

 

M:=Matrix([[0,1],[1,0]]);

a,b:=Eigenvectors(M)  ;#click here and press enter again possible a 4 times, output can filp

 

Matrix(2, 2, {(1, 1) = 0, (1, 2) = 1, (2, 1) = 1, (2, 2) = 0})

 

Vector[column](%id = 36893491125752073860), Matrix(%id = 36893491125752073980)

(1)

a

Vector(2, {(1) = 1, (2) = -1})

(2)

b

Matrix(2, 2, {(1, 1) = 1, (1, 2) = -1, (2, 1) = 1, (2, 2) = 1})

(3)

 

 

Download 2024-03-21_Q_Eigenvector_output_flipping.mw

Could anyone please help me to find the root means of the value of x for different values of k in the range 0.1..0.9  by putting the expression P=0 by using the Newton method? 

Help_Newton_Method.mw

Hi I have an n×4 matrix of answer data to a questionnaire I would like to convert into a pivot table. So I can do a Chi2test. 

 

How do I construct said table? 

I have a complicated tensor expression that is defined wtih all indices down. However if i consider a one-up-one-down configuration it appears to introduce new terms that no longer produce the same result as the all down configuration. Not sure what to make of this. 

IndexQuestion.mw

Hi, I am looking to color the area between the square and the circle (similar to the shadebetween command) and, in general, to color the area between two geometric shapes. Any suggestions? Thank you.

Couronne.mw

Just wonder if someone has any hints about correct code debugging.

Especially I'd like to know how often certain subroutines are called, and where from.

Dear Maple community,

I am facing a little problem verifying a power series solution obtained with Maple since the direct substitution back into the PDEs does not seem to be conclusive because the residual contains the powers of independent variables to almost any order.

Please see the enclosed Maple file with a minimal working example:

restart:

with(DETools):

PDE1 := diff(eta(t,x),t) + 1/2*diff(u(t,x),x) + 1/2*eta(t,x)*diff(u(t,x),x) - 1/48*diff(u(t,x),x$3) + diff(eta(t,x),x)*u(t,x);

diff(eta(t, x), t)+(1/2)*(diff(u(t, x), x))+(1/2)*eta(t, x)*(diff(u(t, x), x))-(1/48)*(diff(diff(diff(u(t, x), x), x), x))+(diff(eta(t, x), x))*u(t, x)

(1)

PDE2 := diff(u(t,x),t) + u(t,x)*diff(u(t,x),x) + diff(eta(t,x),x,t,t) + diff(eta(t,x),x) - 1/6*diff(u(t,x),x,x,t);

diff(u(t, x), t)+u(t, x)*(diff(u(t, x), x))+diff(diff(diff(eta(t, x), t), t), x)+diff(eta(t, x), x)-(1/6)*(diff(diff(diff(u(t, x), t), x), x))

(2)

sys := rifsimp([PDE1, PDE2]);

table( [( Solved ) = [diff(diff(diff(eta(t, x), t), t), x) = -u(t, x)*(diff(u(t, x), x))-(diff(u(t, x), t))+(1/6)*(diff(diff(diff(u(t, x), t), x), x))-(diff(eta(t, x), x)), diff(diff(diff(u(t, x), x), x), x) = 24*eta(t, x)*(diff(u(t, x), x))+48*(diff(eta(t, x), x))*u(t, x)+48*(diff(eta(t, x), t))+24*(diff(u(t, x), x))] ] )

(3)

id := initialdata(sys[Solved]);

table( [( Finite ) = [], ( Infinite ) = [eta(t, x[0]) = _F1(t), (D[2](eta))(t[0], x) = _F2(x), (D[1, 2](eta))(t[0], x) = _F3(x), u(t, x[0]) = _F4(t), (D[2](u))(t, x[0]) = _F5(t), (D[2, 2](u))(t, x[0]) = _F6(t)] ] )

(4)

sols := rtaylor(sys[Solved], id, point=[t = 0, x = 0], order = 3);

[eta(t, x) = _F1(0)+(D(_F1))(0)*t+_F2(0)*x+(1/2)*((D@@2)(_F1))(0)*t^2+_F3(0)*t*x+(1/2)*(D(_F2))(0)*x^2+(1/6)*((D@@3)(_F1))(0)*t^3+(1/2)*(-_F4(0)*_F5(0)-(D(_F4))(0)+(1/6)*(D(_F6))(0)-_F2(0))*t^2*x+(1/2)*(D(_F3))(0)*t*x^2+(1/6)*((D@@2)(_F2))(0)*x^3, u(t, x) = _F4(0)+(D(_F4))(0)*t+_F5(0)*x+(1/2)*((D@@2)(_F4))(0)*t^2+(D(_F5))(0)*t*x+(1/2)*_F6(0)*x^2+(1/6)*((D@@3)(_F4))(0)*t^3+(1/2)*((D@@2)(_F5))(0)*t^2*x+(1/2)*(D(_F6))(0)*t*x^2+(1/6)*(24*_F1(0)*_F5(0)+48*_F2(0)*_F4(0)+48*(D(_F1))(0)+24*_F5(0))*x^3]

(5)

assign(sols);

simplify(PDE1);

((D@@2)(_F1))(0)*t+_F3(0)*x+(1/2)*((D@@3)(_F1))(0)*t^2-t*(_F4(0)*_F5(0)+_F2(0)+(D(_F4))(0)-(1/6)*(D(_F6))(0))*x+(1/2)*(D(_F3))(0)*x^2+(1/2)*(D(_F5))(0)*t+(1/2)*_F6(0)*x+(1/4)*((D@@2)(_F5))(0)*t^2+(1/2)*(D(_F6))(0)*t*x+6*((_F1(0)+1)*_F5(0)+2*_F2(0)*_F4(0)+2*(D(_F1))(0))*x^2+(1/2)*(_F1(0)+(D(_F1))(0)*t+_F2(0)*x+(1/2)*((D@@2)(_F1))(0)*t^2+_F3(0)*t*x+(1/2)*(D(_F2))(0)*x^2+(1/6)*((D@@3)(_F1))(0)*t^3+(1/2)*(-_F4(0)*_F5(0)-(D(_F4))(0)+(1/6)*(D(_F6))(0)-_F2(0))*t^2*x+(1/2)*(D(_F3))(0)*t*x^2+(1/6)*((D@@2)(_F2))(0)*x^3)*(_F5(0)+(D(_F5))(0)*t+_F6(0)*x+(1/2)*((D@@2)(_F5))(0)*t^2+(D(_F6))(0)*t*x+(1/2)*(24*_F1(0)*_F5(0)+48*_F2(0)*_F4(0)+48*(D(_F1))(0)+24*_F5(0))*x^2)-(1/2)*_F1(0)*_F5(0)-_F2(0)*_F4(0)+(_F2(0)+_F3(0)*t+(D(_F2))(0)*x+(1/2)*(-_F4(0)*_F5(0)-(D(_F4))(0)+(1/6)*(D(_F6))(0)-_F2(0))*t^2+(D(_F3))(0)*t*x+(1/2)*((D@@2)(_F2))(0)*x^2)*(_F4(0)+(D(_F4))(0)*t+_F5(0)*x+(1/2)*((D@@2)(_F4))(0)*t^2+(D(_F5))(0)*t*x+(1/2)*_F6(0)*x^2+(1/6)*((D@@3)(_F4))(0)*t^3+(1/2)*((D@@2)(_F5))(0)*t^2*x+(1/2)*(D(_F6))(0)*t*x^2+(1/6)*(24*_F1(0)*_F5(0)+48*_F2(0)*_F4(0)+48*(D(_F1))(0)+24*_F5(0))*x^3)

(6)

simplify(PDE2);

((D@@2)(_F4))(0)*t+(D(_F5))(0)*x+(1/2)*((D@@3)(_F4))(0)*t^2+((D@@2)(_F5))(0)*t*x+(1/2)*(D(_F6))(0)*x^2+(_F4(0)+(D(_F4))(0)*t+_F5(0)*x+(1/2)*((D@@2)(_F4))(0)*t^2+(D(_F5))(0)*t*x+(1/2)*_F6(0)*x^2+(1/6)*((D@@3)(_F4))(0)*t^3+(1/2)*((D@@2)(_F5))(0)*t^2*x+(1/2)*(D(_F6))(0)*t*x^2+(1/6)*(24*_F1(0)*_F5(0)+48*_F2(0)*_F4(0)+48*(D(_F1))(0)+24*_F5(0))*x^3)*(_F5(0)+(D(_F5))(0)*t+_F6(0)*x+(1/2)*((D@@2)(_F5))(0)*t^2+(D(_F6))(0)*t*x+(1/2)*(24*_F1(0)*_F5(0)+48*_F2(0)*_F4(0)+48*(D(_F1))(0)+24*_F5(0))*x^2)-_F4(0)*_F5(0)+_F3(0)*t+(D(_F2))(0)*x-(1/2)*t^2*(_F4(0)*_F5(0)+_F2(0)+(D(_F4))(0)-(1/6)*(D(_F6))(0))+(D(_F3))(0)*t*x+(1/2)*((D@@2)(_F2))(0)*x^2

(7)

NULL

Download MinWorkingExa.mw

Thanks a lot in advance for any help or suggestions.

Kind regards,

DDe

Suppose I have an expression like the following:

h(t, x) :=  (m*t^2 + 6*t - 2*x)^2/(36*g*t^2)

I want to calculate multiple values of t in a single expression. Say, for t:= 1,5,10,15,20. I want to evaluate h(t,x) in vector form. so that I can extract for each t. How to write it?

 

Hello everyone, I am trying to generate a relation for x in terms of lambda by putting my expression (A=0) but do not get the explicit relation. Could anyone please help me generate data points between x=[0..1] and lambda by putting A=0 and then making a polynomial by using the fit curve for x in the term of lambda?

Help_Data_points.mw

I do not know if this caused by same crash in Reproducible--Server-Crash-Kernel-Connection-Has-Been-Lost  or not.

Could someone be able to find out? It happens each time the code is run on windows 10. 

 

26028

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715 and is the same as the version installed in this computer, created 2024, April 3, 20:27 hours Pacific Time.`

restart;

10168

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);


Download another_server_crash_on_int_maple_2024_april_4_2024.mw

ps. reported to Maplesoft.

The above is new crash in Maple 2024. Below shows no crash in Maple 2023:

26028

interface(version);

`Standard Worksheet Interface, Maple 2023.2, Windows 10, November 24 2023 Build ID 1762575`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1715. The version installed in this computer is 1672 created 2024, February 7, 18:34 hours Pacific Time, found in the directory C:\Users\Owner\maple\toolbox\2023\Physics Updates\lib\`

restart;

23104

u:=Int(2/3/alpha^(3/2)*sin(1/2*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2),alpha = 0 .. x)

Int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

value(u);

int((2/3)*sin((1/2)*3^(1/2)*ln(alpha))*sin(alpha)*3^(1/2)/alpha^(3/2), alpha = 0 .. x)

 

 

Download int_on_maple_2023.mw

Update:

Here is a movie showing the crash. It also happens from the command line. All on windows 10.

My ini file has  nothing in it, other than one command which prints the process ID which I had there for over a year now.  This is after restarting Maple fresh and nothing else running other than this one worksheet.

 

Here is movie showing the crash from command line also. On windows 10 pro.

 

 

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