I have to take my equations for velocity, acceleration, and height and evaluate them in 4 second intervals and combine them into one table or columns.

Deal all

I would like to approximate the largest eigenvalue of a given maxtrix and its corresponding eigenvector. 
I have a problem in step 7, how obtain the index where the maximum is located, then How I return at the end of while loop 
a table contains eigenvalues, eigenvectors and err 

PWM.mw

Thank you 

The procedures "getCP" which uses "cpsub" (not exported) acts differently inside the package as opposed to them outside it.
In the package it returns a column matrix which is incorrect. Should return a 2 row matrix. They dismantle a polynomial into it's powers and coefficients. I know one cant run the package here. Included are the two procedures and the text of the notepad file to make the package.

Dismantlimg a polynomial  uses the following 2 procedures Notepad file to Create AlgCalc.   AlgCalc := module () export SignedArea,            `⊕`,              getCP,              diag,              diftab,              faulD,              faulS,              FundThrm;           option package; $include "SignedArea.mm" $include "`⊕`.mm" $include "cpsub.mm" $include "getCP.mm" $include "diag.mm" $include "diftab.mm" $include "faulD.mm" $include "faulS.mm" $include "FundThrm.mm" end module;

Download 6-11-22_Procedures_acting_differently_in_Package.mw

There is a document on the Maple website entitled "Writing Packages". It contains the following snippet when talking about libname

Note: Maple automatically adds lib subdirectories of directories in HOMEDIR/maple/toolbox as well as your current directory to the predefined variable libname. Therefore, modifying the .mapleinit or maple.ini file is only necessary if you want to designate a directory as the default location in which the savelib command will save your library files.

Is this snippet accurate?

If we create a directory called test and create a directory inside called lib and in it a repository called myRepo.mla, and in Maple the current working directory is test, will test/lib/myRepo.mla be found by libname?

It doesn't seem to be the case.

in the context of solving an ode, sometimes the constant of integration that will satisfy an initial condition is +infinity or -infinity.

But Maple's solve does not find such solutions to the constant of integration. It only can solve for finite value if it can.

When this happens, I manually try taking the limit as the constant of integration goes to +- infinity, until I get an equation where both sides are the same or fail, and then give up.

I was wondering if there is a way or different command/package which will find solution such as infinity (which is valid solution to constant of integration).

Here are two examples

ode:=diff(y(x),x)=1/(LambertW(-exp(-1+_C1+x))+1);
ic:=[diff(y(x),x)=1,x=0];
eq2:=eval(ode,ic);
solution_for_constant := solve(eq2,_C1,'allsolutions'=true,'tryhard'=true);

Maple can not solve for _C1. It gives

But when trying manually few values, I find that _C1=-infinity satisfies the equation

limit(rhs(eq2),_C1=0);
limit(rhs(eq2),_C1=1);
limit(rhs(eq2),_C1=-1);
limit(rhs(eq2),_C1=infinity);
limit(rhs(eq2),_C1=-infinity);

The above shows that _C1 = -infinity is the constant of integration. Another simpler example

eq:=exp(-1 + _C1) = 0;
solution_for_constant:=solve(eq,_C1) assuming real;
limit(lhs(eq),_C1=-infinity)

The above shows that _C1=-infinity is solution for exp(-1+C_1)=0.  which one can see by just looking at it as exp(-infinity)=0.  Adding assumptions did not help.I also tried symbolic option.

I am not familar with SolveTools package, may there is something there.

So for now, my code just try the limit until it finds solution or gives up.

Any suggestions if Maple itself can find such solutions?

Maple 2022.2

Does the below infinite sum involving primes converge?sum(1/(Prime(n)Prime(n+1)Prime(n+2)*Prime(n+3)),n=1... infinity) Free WolframAlpha app runs out of time while evaluating this sum... The term values which free WolframAlpha app shows for this sum (starting from the term 41 and on) is 0.0059292... If 0.0059292 is indeed the value for this sum, could then more significant digits be produced? Thanks, Best Regards, Alexander R. Povolotsky

Why is a more direct approach of defining a table now working and giving an indexed type, while the indirect approach is giving a table?

(1) (2) (3) (4) (5) (6)

Download tabledefinition.mw

Hello,

I am trying to create a Homogeneous transformation matrix, where I am given the point 'p' through which a unit rotation axis 'x' passes and the point/vector on which this Homogenous transformation acts is rotated by 'theta'.

I used the Rodrigues formula (the one in the blue-green box) to define the rotation matrix;

unit_axis_cross_mat := unapply(<<0 | -x[3] | x[2]>, <x[3] | 0 | -x[1]>, <-x[2] | x[1] | 0>>, x::Vector);
rot_mat := unapply(LinearAlgebra[IdentityMatrix](3) + unit_axis_cross_mat(<x[1], x[2], x[3]>)*sin(theta) + MatrixPower(unit_axis_cross_mat(<x[1], x[2], x[3]>), 2)*(1 - cos(theta)), x::Vector, theta)

I then tried to concatenate them to generate the matrix function

, where the exponential term represents the rotation matrix (defined above) as such:

trans_mat_ang := unapply(ArrayTools[Concatenate](1, ArrayTools[Concatenate](2, rot_mat(<x[1], x[2], x[3]>, theta), (LinearAlgebra[IdentityMatrix](3) - rot_mat(<x[1], x[2], x[3]>, theta)) . <p[1], p[2], p[3]>), <0 | 0 | 0 | 1>), x::Vector, theta, p::Vector)

But I end up getting the error 

"Error, (in ArrayTools:-Concatenate) number of columns must match"

To diagnose it, I try to evaluate the 1st Concatenation:

trans_mat := unapply(<ArrayTools[Concatenate](2, rot_mat(<x[1], x[2], x[3]>, theta), (LinearAlgebra[IdentityMatrix](3) - rot_mat(<x[1], x[2], x[3]>, theta)) . <p[1], p[2], p[3]>)>, x::Vector, p::Vector, theta);

which runs successfully, but when I try to evaluate it:

trans_mat(<1, 0, 0>, <1, 0, 0>, 0)

, I get a symbolic expression .

Although the expression is correct algabrically, I expected a full evaluation for the numerical inputs.

I am attaching my Homogeneous_Transformation.mw for your ease of diagnosis.

Is this the cause of the error of "Number of Columns must match"?

Any help towards this would be appreciated.

Regards

 

Hello,

I'm attempting to scale the vertical axis of a histogram plot such that each bin reflects the percentage of the total bins (all bins sum to 1). Matlab has an option ('probability') for their histogram command which does this. I've attempted to solve this myself in the attached worksheet but I'm not satisfied with the results (just a hack to replace axis labels). Specifically, I would like for the underlying data in the plot to match the axis scaling. An example can be seen in the image below.

Thank you for your consideration,

Ron

Histogram_percentage.mw

 

 

 

I've worked as a programmer before, but now I dedicate a lot of time to learning math, and so I have been using Maple.

I was wondering if there is some standard way that people work when they have a relatively large codebase. For example, can we define procedures in one file (like a document) and then just import them in another document?

I am reading about the difference between document and worksheet mode on the Maple website.

There is a table called "Difference between Documents and Worksheets" and one row has the following information


My question is about the operation on the left side. The impression I get from reading that is that if I just enter the equation in 2D math mode and hit enter it will solve the equation without me having to type in the command "solve". But Maple simply echoes the equation back to me when I do this in Maple 2022. What am I missing?

Dear all

I have a coupled system of PDEs, 
I would like to return the exact solution of the system using error integral function or complementary error function is possible

compute_integral_using_erfc_fct.mw

thank you for your help 

How to display the coordinate set that was used to create the following plot:

with(plots):

de := plot3d(y*sin(x), x = 0 .. 2*Pi, y = -2 .. 2)

Regards

Oliveira

Does anyone have any idea why Maple can obtain a closed form of 

Int(f, t=1..3);

but doesn't for 

Int(g, t=1..3);

?

The Int forms are quite close and I don't understand what makes Maple's task that difficult in the second case (the issue seems to come from the conditions in the piecewise function).
Can we force Maple to perform the second integration ?

TIA

>  restart: >  interface(Version) (1) >  f := piecewise(z/t < 0, 0, z/t < 1, 630*z^8/t^8-2520*z^7/t^7+3780*z^6/t^6-2520*z^5/t^5+630*z^4/t^4, 0)/t: Int(f, t=1..3); value(%);  # returns a closed form of the integral >  g := piecewise(z/t < 1, 0, z/t < 2, 10080-60480*z/t+156240*z^2/t^2-226800*z^3/t^3+202230*z^4/t^4-113400*z^5/t^5+39060*z^6/t^6-7560*z^7/t^7+630*z^8/t^8, 0)/t: Int(g, t=1..3); value(%): # unable to return a closed form of the integral

Download MyIntegral.mw

Fig := proc(t) 
local xD, yD, D, C, Ii, Points, tex,sol; 
global A, B, b, Omega1, EL1, EL2; 
xD := Omega1[1] + aa*cos(t); 
yD := bb*sin(t); 
D := [xD, yD]; 
C := [xD + b, yD]; 
sol:=solve({EQ(A,D),EQ(C,B)},{x,y});
Ii:=[subs(sol,x),subs(sol,y)]:
Points := pointplot([A[], B[], C[], C[], D[], E[], Omega1[]], symbol = solidcircle, color = [red], symbolsize = 6); 
tex := textplot([[A[], "A"], [B[], "B"], [C[], "C"], [D[], "D"], [E[], "E"], [Omega1[], "Ω1"]], align = ["above", "right"]); 
display([polygonplot([A, B, C, D], color = blue, filled = true, transparency = 0.9), Points, tex, EL1, EL2,plot([D,Ii]),plot([Ii,C])], axes = normal, scaling = constrained); end proc:
Fig((3*Pi)/4):
display([seq(Fig((2*Pi*i)/40), i = 1 .. 80)], insequence = true);
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
Warning, data could not be converted to float Matrix
I am sorry; How to manage with such a message. Thank you very much.