MaplePrimes Questions

how can i get an 'implicit=false' form (no RootOf) of my eigenvalues from the Eigenvectors() command? Should one expect the behavior be the same in Eigenvectors() and Eigenvalues()?

thanks

 

restart:

 

 

M:=Matrix(3, 3, [[-2*lambda-kappa__c, -2*sqrt(2)*g, 0], [(1/2)*g*N*sqrt(2), -lambda-(1/2)*kappa__c-gamma__phi, -sqrt(2)*g], [0, g*N*sqrt(2), -2*gamma__phi]])

Matrix(3, 3, {(1, 1) = -2*lambda-`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, (1, 2) = -2*sqrt(2)*g, (1, 3) = 0, (2, 1) = (1/2)*g*N*sqrt(2), (2, 2) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2, 3) = -sqrt(2)*g, (3, 1) = 0, (3, 2) = g*N*sqrt(2), (3, 3) = -2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`})

(1)

LinearAlgebra:-Eigenvalues(M); #this is what i want but from Eigenvectors()

Vector(3, {(1) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+(1/2)*sqrt(-16*N*g^2+4*lambda^2+4*lambda*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-8*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`^2-4*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+4*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`^2), (3) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`-(1/2)*sqrt(-16*N*g^2+4*lambda^2+4*lambda*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-8*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`^2-4*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+4*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`^2)})

(2)

LinearAlgebra:-Eigenvalues(M, implicit=true); #RootOf notation; not what i want, but option works here

Vector(3, {(1) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2) = RootOf(_Z^2+(2*lambda+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`)*_Z+4*N*g^2+4*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, index = 1), (3) = RootOf(_Z^2+(2*lambda+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`)*_Z+4*N*g^2+4*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, index = 2)})

(3)

evals, evecs:=LinearAlgebra:-Eigenvectors(M); #RootOf everywhere;

evals, evecs := Vector(3, {(1) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1), (2) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2), (3) = -lambda-(1/2)*`κ__c`-`γ__φ`}), Matrix(3, 3, {(1, 1) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`)^2, (1, 2) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`)^2, (1, 3) = 2/N, (2, 1) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`), (2, 2) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`), (2, 3) = -(1/4)*sqrt(2)*(2*lambda+`κ__c`-2*`γ__φ`)/(g*N), (3, 1) = 1, (3, 2) = 1, (3, 3) = 1})

(4)

 

 

evals, evecs:=LinearAlgebra:-Eigenvectors(M, implicit=false); #still RootOf everywhere;

evals, evecs := Vector(3, {(1) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1), (2) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2), (3) = -lambda-(1/2)*`κ__c`-`γ__φ`}), Matrix(3, 3, {(1, 1) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`)^2, (1, 2) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`)^2, (1, 3) = 2/N, (2, 1) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`), (2, 2) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`), (2, 3) = -(1/4)*sqrt(2)*(2*lambda+`κ__c`-2*`γ__φ`)/(g*N), (3, 1) = 1, (3, 2) = 1, (3, 3) = 1})

(5)

 

 


 

Download evals.mw

 

 

 

 

The help for the package Differential Geometry suggests one way to create an anholonomic frame, but the method suggested assumes one knows the frame and can write it in the coordinates of the manifold, and use this representation to compute the structure equations. It is useful to turn this problem around: suppose I know the structure equations but I do not know the frame, how do I correctly enter this in Maple so that later computations are correct?

 

Here is an example:

with(DifferentialGeometry): with(LieAlgebras):
DGsetup([x, y], R2):          
Fr := [A, B]; StructureEquations := [[A, B] = a(x, y)*A];
LD := LieAlgebras:-LieAlgebraData(StructureEquations, Fr, M);
DGsetup(LD, verbose):

that creates the Lie algebra M. I thought it would produce the manifold M whose frame {e1,e2} (or {A,B})) obeys the structure equations. But it does not. Indeed, the simple example

LieBracket(e1, f(x, y)*e2);

returns

f(x,y) a(x,y) e1.

The extra term where e1 differentiates f(x,y) does not appear. Just to be clear, the correct answer is

f(x,y) a(x,y) e1 + e1[f] e2.

 

How should I correctly setup this manifold?

When I load the Physics package - with (Physics)- I get the following error message:

r level initialization for package `Physics' failed: Heaviside not defined for non-real values


Later on while executing some code there may pop a plethora of other errors with apparently no relation to the running code. No problem for p.e. PDETools. Ihave loaded the 348 physics upgrade but it happened also with 347. Any Idea what it is and what to do?

 

Our company is producing a kind of smart electronic drying rig Vinadry. We want to apply physical formulas to calculate the lift and tension of the drying rigs when operating. By this Vinadry drying rig we want to design it as a pulley system but can control it via electric buttons. Hence I want to consult people how I should calculate accordingly

Should Maple handle this error internally and may be give no solution if it can't solve it instead of this  error?

When setting boundary condition to zero, maple gives error below. Heat PDE in a sphere. No angle dependency. Only the radial part.

unassign('r,u,t');
pde:=diff(u(r,t),t)= 1/r*diff(r*u(r,t),r$2); #Laplacian in spherical
ic:=u(r,0)=1;
bc := u(1,t) =0;
pdsolve([pde,ic,bc],u(r,t),HINT =boundedseries(r=0)) assuming t>0

Error, (in assuming) when calling 'ln'. Received: 'when calling 'ln'. Received: 'numeric exception: division by zero''


Adding assumptions such as 0<r,r<1 did not help.

Physics version 348. Maple 2019 on windows 10. Is there something I am doing wrong? 

 

The following code yields "false" for the trace being non-negative.  This, however, is incorrect.

A look at the final expression for the trace shows it is a sum of products of positive values.

Does anyone know what the problem is?

restart;

with(LinearAlgebra);

n := 3;

p := 2;

Y := Matrix(n, p, symbol = y);

W := Matrix(n, n, symbol = w, shape = symmetric);

for i from 1 to n do

for j from 1 to n do

assume(w[i, j], RealRange(0, 1))

end do:

end do:

d := DiagonalMatrix(W . Matrix(n, 1, 1))

is(simplify(Trace(simplify(Transpose(Y) . (d-W) . Y))) >= 0)

 

Maple has powerful tools to manager styles of its documents. Similar to word processors, it is possible to set up font and paragraph options. Unfortunately, the styles of Help System, as I understand, are completely unchangeable. Meanwhile, it makes sense to improve the view of Help pages. Say, Help’s hyperlinks are pale and unpleasant  for eyes. Maybe, are there some hidden options for changing Help styles?

Hi!

Maple returns typographic the functions applied in a definition, which hardens the reading. Can anybody hint me on what to do to change this setting? Also symbolic variables are not being calculated:

 

All the best,

Why does Maple display eval(diff(f(r),r),r=C)=0;  differently when C is a number?

unassign('f,C,r');
eval(diff(f(r),r),r=C)=0;
eval(diff(f(r),r),r=5)=0;

I wanted the first one to display the same as the second one. First one looks confusing. it looks like taking derivative w.r.t to C. Is there a way to make the first one look like:

Hi,

I am having issues with switching from math mode to text mode, when it comes to adding a new line of text under a line of math mode, without evaluating the math. In a previous version of Maple (not sure witch one, probably Maple 2018), I would switch from math mode to text mode by using the shortcut "command + T", followed by hitting the "->" button on the keyboard and then hit enter to start a new line in text mode. But this does not work in the latest version of maple. Does anyone have a solution for this problem?

Also, is there a way to remove the "toolbox" (i.e. "solve for"/"expand"/"simplify"/"isolate"/etc.), so it only appears when right-clicking on the expression you want to edit?

It's no secret that I liked the older versions of Maple, but I'd very much appreciate some assistance with the 2019 version!

Kind regards,

Lisa

Hi Experts

The following code

with(plottools);
P := plot3d(cos(x)*cos(y), x = -Pi .. Pi, y = -Pi .. Pi);
exportplot("./test.eps", P, "eps");

results in a very different exported image, depending on if it is executed from a .mw file or a .mpl. How can I get the .mpl export to look like the .mw export?

Details: I understand that .mpl might require adding axes=boxed, but especially the orientation is very odd. It doesn't even orient it like the ASCII plot.

Hi Maple Expert,

c*(r-1)*exp(x*beta)/((1+varphi*exp(x*beta))*(-varphi*exp(x*beta)*r+varphi*exp(x*beta)+1))

c = exp(exp(x*beta)*(r-1)/(1+varphi*exp(x*beta)))

with

ln(r) = varphi*exp(x*beta)*(r-1)/(1+varphi*exp(x*beta))-1

Please help me, and thank you in advance.

 

Regards,

Sarni

 

Good Morning,

 

Can anyone help on an Excel linking problem (and in general DB, non-SQL data sets)  for data lookup.   

 

I have several static data sets stored in flat files like Excel (xls) format. 

 

I understand Maples connectivity via the import function to an array.  I also understand the export and use of Maple from within Excel vi the add-in..

 

When doing data lookups it is not convienet to import the entire database and is memory intensive for large data sets.  As such it is much more convienenit to open/attach like the old ODBC connectivity schemes.   The goal is to open/attach to the data file (xls), search a column and return other column's data as a subset for further analysis in maple.  An example would be a steel properties xls file.

My Maple worksheet is calculating the dynamic loads and stresses of an object.  With that answer of say stress, I want to link to my excel data file and search the Yield strength and return the material name and props for those grades of steel that have yield strength greater than 1.5 times my caclulated answer.

 

This can then be returned into a smaller array for further analysis using Maple with different properties of my retrieved subset.  The link would be closed after getting the subset.

 

I have read all the Maple document Excel help info and the excel add-in info which is the wrong direction.   I can easily code this search into a vlookup within excel - but completely defeats the purpose for using Maple in the first place.   Again, importing is not a method as these data sets are static and come from various sources like "AMS" which need to live outside maple.

 

I have looked into FileTools pakcage and old C type fopen, scanf, etc. without much luck on Maple implementation.   The fopen seems to be for text or csv data sets?   according to the documentation.  But, I'll keep looking while waiting any replies.

 

Any assistance very appreciated.

 

Bill

 

 

 

 

 

 

 

 

I am trying to get this to work

{seq(isolve({a = k, irem(a*b, 10000) = 2391}), k = 1 .. 9999)}

but am not getting any answer. One solution is irem(297*9503, 10000).

Dear friends~

Recently I wanted to create some funny gif with Maple based on other interesting pictures but I met some problems:(1)I read many commands in ImageTools but few can aid me.(2)If I use “plot(,background=file_address)”,then the whole background will be filled with pictures but I just want it to be a part of my gif.I finally noticed that “plot3d(,image=file_address)”can realize my idea to some extents if I adjust orientation’s value  suitably.

However,I still think my operations can be improved(for example,my code consumes a fair amount of  memory) and there maybe one better approach to be good too. Hence I upload my code and sincerely look forward your suggestions and help~

#Janesefor do it in 2019/4/15 13:20 with Maple2018~
with(plots):
# smile.jpg's address
image_file:="C:/Users/ysl-pc/Desktop/":
str:="有","朋","自","远","方","来","不","亦","乐","乎","?":
location_func,dy,dz:=3*sin(2*3.14/10*y),.75,.75:

display(seq(display(textplot3d([0,1,4.5,cat(str[1..ha])],align='right'),textplot3d([0,3.5,-4.5,"By Janesefor ~"],align='right'),plot3d([0,s,t],subs(y=ha-1,[s=y-dy..y+dy,t=location_func-dz..location_func+dz])[],image=cat(image_file,"smile.jpg"),axes=none,scaling=constrained,orientation=[180,90,-180],view=[default,0..10,-5..5],glossiness=0,lightmodel=light4)),ha=[`$`(1..nops([str]))]),insequence=true);
Export(cat(image_file,"smile.gif"),%)


smile.mw

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