Why aren't all the variables in fin 1 equation?

And the answers are different from the solutions?

Download 0123.mw

Since C2=D1.D1inv should be equal to I. But return is just an expression (see attached). Further, how to obtain residue for a function C2?

residue.mw

MmaTranslator:-Mma:-Chop  does not seem to work as advertised.. It is supposed to work like Mathematica's Chop, but it does not. Is this by design or is it a bug?

restart;

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I)*t) ;

returns the same input (1.378834799*10^(-15))*I*t but

MmaTranslator:-Mma:-Chop(((1.378834798932344*10^(-15))*I));

now returns 0.

But compare to Mathematica:

This makes it not very useful to use if one has to remove all symbols from an expression first, Any workaround? Here is an actual example where I wanted to use it

ode:=[diff(x(t), t) = -3*x(t) + 4*y(t), diff(y(t), t) = 5*x(t) + 9*z(t), diff(z(t), t) = y(t) + 6*z(t)];
sol:=dsolve(ode):
evalf[16](sol);

gives

Gives

{x(t) = (0.8172764110864494 - (7.853170607134887*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) - (1.150854759654687 + (3.398186702482929*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.3780227930126823 + (9.268277369231981*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), y(t) = c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t), z(t) = (-0.2435641206911610 + (1.431838044809606*10^(-16))*I)*c__1*exp((1.894304969211800 - (1.378834798932344*10^(-15))*I)*t) + (-0.08015596744746927 + (4.286632781083632*10^(-16))*I)*c__2*exp((-6.475677505300665 + (3.730232887526917*10^(-17))*I)*t) + (0.6323620634472722 - (5.261170533293161*10^(-16))*I)*c__3*exp((7.581372536088866 + (1.198480681985453*10^(-15))*I)*t)}

But Chop does not work on this. 

Maple 2023.2

There seems to be a consensus about using ListTools:-SearchAll to locate an item in a list. However, this subroutine does not work on other expressions; A simple instance is that “ListTools:-SearchAll(1, [[1], 1]);” only outputs  while what I need is  (because both “op([1, 1], [[1], 1])” and “op([2], [[1], 1])” are ). And actually, I hope that there is a more general version in Maple.
For example, I intend to do something like 

restart;
expr, elem := ToInert(eval(`print/Diff`)), '_Inert_NAME'("_syslib"):
SearchAll(elem, expr);

and 

List:=[[[[cS,[[[cS,cS],cS],[[[cS,cS],[[cK,cK],cS]],cS]]],cS],cS],[[[cS,[[cK,cS],cK]],cK],cS]]: 
items:=Or([[[identical(cS),anything],anything],anything],[[identical(cK),anything],anything]): 
SearchAll(items,List); 

In other words, I need all positions of an operand of an expression (cf. op).

It may be manually checked that the "indices" of  in  include [5,1,1,2,1,1,1,2,1,2,1,2], [5,1,2,2,1,1,1,1,2,1,2], and [5,2,2,1,1,3,1,2], since 

patmatch(op([5, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2], expr), elem);
 = 
                              true

patmatch(op([5, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2], expr), elem);
 = 
                              true

patmatch(op([5, 2, 2, 1, 1, 3, 1, 2], expr), elem);
 = 
                              true

Similarly, after some manual searchs, 

[[1], [1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 1, 1, 2, 2, 1, 2], [2], [2, 1, 1, 2]]:
convert(typematch~(map2(`?[]`, List, `%`), items), `and`);
 = 
                              true

It turns out that all "indices" in  of  are [1], [1,1,1,2], [1,1,1,2,2], [1,1,1,2,2,1,2], [2], and [2,1,1,2].
But isn't there such a  command that can eliminate the need to manually retrieve them?

When the original poster receives or finds the answer to the question he/she posed, should he/she

1. Reply to it
2. Answer to it?

I have seen "true answers" that were converted to a reply, despite addressing the initial answer correctly. In case there are no other answers, the question will still be listed under unanswered question which is incorrect.

What practice should be applied in MaplePrimes for "true answers"?

I'm stucked in trying to prove that rel(n)  is true for each integer n > 1.

Download Prove_It_True.mw

Do you have any idea to do this?

TIA

Would Any one be able to give some explanation as to why calling a proc, which does not change anything globally but only acts on the input given, returns different answer the second time it is called with the same exact input? I am not able to understand this result at all. 

Maple 2023.2 on windows 10.

Download why_different_answer.mw

Hi there

I am using the Determinant() function in maple to calculate the determinant of 32 by 32 matrix consisting of variables like x1,x2, x3... as well as the products of these variables. This determinant calculation works very well less for 16x16 matrices. However in the 32 by 32 case it takes days and still no result (attached and below you can see the matrix) My first question is that problem actually solvable in reasonable time like within 2 days and do you have any advice how I can achieve this goal.

Thx

Rgds

Birol

1,x5,x4,x4*x5,x1,x1*x5,x1*x4,x1*x4*x5,x2*x5,x2,x2*x4*x5,x2*x4,x1*x2*x5,x1*x2,x1*x2*x4*x5,x1*x2*x4,x1*x3,x1*x3*x5,x1*x3*x4,x1*x3*x4*x5,x3,x3*x5,x3*x4,x3*x4*x5,x1*x2*x3*x5,x1*x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x2*x3*x5,x2*x3,x2*x3*x4*x5,x2*x3*x4
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x4,x4*x5,1,x5,x1*x4,x1*x4*x5,x1,x1*x5,x2*x4*x5,x2*x4,x2*x5,x2,x1*x2*x4*x5,x1*x2*x4,x1*x2*x5,x1*x2,x1*x3*x4,x1*x3*x4*x5,x1*x3,x1*x3*x5,x3*x4,x3*x4*x5,x3,x3*x5,x1*x2*x3*x4*x5,x1*x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x2*x3*x4*x5,x2*x3*x4,x2*x3*x5,x2*x3
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x1,x1*x5,x1*x4,x1*x4*x5,1,x5,x4,x4*x5,x1*x2*x5,x1*x2,x1*x2*x4*x5,x1*x2*x4,x2*x5,x2,x2*x4*x5,x2*x4,x3,x3*x5,x3*x4,x3*x4*x5,x1*x3,x1*x3*x5,x1*x3*x4,x1*x3*x4*x5,x2*x3*x5,x2*x3,x2*x3*x4*x5,x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4
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x1*x4*x5,x1*x4,x1*x5,x1,x4*x5,x4,x5,1,x1*x2*x4,x1*x2*x4*x5,x1*x2,x1*x2*x5,x2*x4,x2*x4*x5,x2,x2*x5,x3*x4*x5,x3*x4,x3*x5,x3,x1*x3*x4*x5,x1*x3*x4,x1*x3*x5,x1*x3,x2*x3*x4,x2*x3*x4*x5,x2*x3,x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5
x2*x5,x2,x2*x4*x5,x2*x4,x1*x2*x5,x1*x2,x1*x2*x4*x5,x1*x2*x4,1,x5,x4,x4*x5,x1,x1*x5,x1*x4,x1*x4*x5,x1*x2*x3*x5,x1*x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x2*x3*x5,x2*x3,x2*x3*x4*x5,x2*x3*x4,x1*x3,x1*x3*x5,x1*x3*x4,x1*x3*x4*x5,x3,x3*x5,x3*x4,x3*x4*x5
x2,x2*x5,x2*x4,x2*x4*x5,x1*x2,x1*x2*x5,x1*x2*x4,x1*x2*x4*x5,x5,1,x4*x5,x4,x1*x5,x1,x1*x4*x5,x1*x4,x1*x2*x3,x1*x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x2*x3,x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x1*x3*x5,x1*x3,x1*x3*x4*x5,x1*x3*x4,x3*x5,x3,x3*x4*x5,x3*x4
x2*x4*x5,x2*x4,x2*x5,x2,x1*x2*x4*x5,x1*x2*x4,x1*x2*x5,x1*x2,x4,x4*x5,1,x5,x1*x4,x1*x4*x5,x1,x1*x5,x1*x2*x3*x4*x5,x1*x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x2*x3*x4*x5,x2*x3*x4,x2*x3*x5,x2*x3,x1*x3*x4,x1*x3*x4*x5,x1*x3,x1*x3*x5,x3*x4,x3*x4*x5,x3,x3*x5
x2*x4,x2*x4*x5,x2,x2*x5,x1*x2*x4,x1*x2*x4*x5,x1*x2,x1*x2*x5,x4*x5,x4,x5,1,x1*x4*x5,x1*x4,x1*x5,x1,x1*x2*x3*x4,x1*x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x2*x3,x2*x3*x5,x1*x3*x4*x5,x1*x3*x4,x1*x3*x5,x1*x3,x3*x4*x5,x3*x4,x3*x5,x3
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x1*x2,x1*x2*x5,x1*x2*x4,x1*x2*x4*x5,x2,x2*x5,x2*x4,x2*x4*x5,x1*x5,x1,x1*x4*x5,x1*x4,x5,1,x4*x5,x4,x2*x3,x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x3*x5,x3,x3*x4*x5,x3*x4,x1*x3*x5,x1*x3,x1*x3*x4*x5,x1*x3*x4
x1*x2*x4*x5,x1*x2*x4,x1*x2*x5,x1*x2,x2*x4*x5,x2*x4,x2*x5,x2,x1*x4,x1*x4*x5,x1,x1*x5,x4,x4*x5,1,x5,x2*x3*x4*x5,x2*x3*x4,x2*x3*x5,x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x3*x4,x3*x4*x5,x3,x3*x5,x1*x3*x4,x1*x3*x4*x5,x1*x3,x1*x3*x5
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x3*x4*x5,x3*x4,x3*x5,x3,x1*x3*x4*x5,x1*x3*x4,x1*x3*x5,x1*x3,x2*x3*x4,x2*x3*x4*x5,x2*x3,x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x1*x4*x5,x1*x4,x1*x5,x1,x4*x5,x4,x5,1,x1*x2*x4,x1*x2*x4*x5,x1*x2,x1*x2*x5,x2*x4,x2*x4*x5,x2,x2*x5
x1*x2*x3*x5,x1*x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x2*x3*x5,x2*x3,x2*x3*x4*x5,x2*x3*x4,x1*x3,x1*x3*x5,x1*x3*x4,x1*x3*x4*x5,x3,x3*x5,x3*x4,x3*x4*x5,x2*x5,x2,x2*x4*x5,x2*x4,x1*x2*x5,x1*x2,x1*x2*x4*x5,x1*x2*x4,1,x5,x4,x4*x5,x1,x1*x5,x1*x4,x1*x4*x5
x1*x2*x3,x1*x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x2*x3,x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x1*x3*x5,x1*x3,x1*x3*x4*x5,x1*x3*x4,x3*x5,x3,x3*x4*x5,x3*x4,x2,x2*x5,x2*x4,x2*x4*x5,x1*x2,x1*x2*x5,x1*x2*x4,x1*x2*x4*x5,x5,1,x4*x5,x4,x1*x5,x1,x1*x4*x5,x1*x4
x1*x2*x3*x4*x5,x1*x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x2*x3*x4*x5,x2*x3*x4,x2*x3*x5,x2*x3,x1*x3*x4,x1*x3*x4*x5,x1*x3,x1*x3*x5,x3*x4,x3*x4*x5,x3,x3*x5,x2*x4*x5,x2*x4,x2*x5,x2,x1*x2*x4*x5,x1*x2*x4,x1*x2*x5,x1*x2,x4,x4*x5,1,x5,x1*x4,x1*x4*x5,x1,x1*x5
x1*x2*x3*x4,x1*x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x2*x3,x2*x3*x5,x1*x3*x4*x5,x1*x3*x4,x1*x3*x5,x1*x3,x3*x4*x5,x3*x4,x3*x5,x3,x2*x4,x2*x4*x5,x2,x2*x5,x1*x2*x4,x1*x2*x4*x5,x1*x2,x1*x2*x5,x4*x5,x4,x5,1,x1*x4*x5,x1*x4,x1*x5,x1
x2*x3*x5,x2*x3,x2*x3*x4*x5,x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x3,x3*x5,x3*x4,x3*x4*x5,x1*x3,x1*x3*x5,x1*x3*x4,x1*x3*x4*x5,x1*x2*x5,x1*x2,x1*x2*x4*x5,x1*x2*x4,x2*x5,x2,x2*x4*x5,x2*x4,x1,x1*x5,x1*x4,x1*x4*x5,1,x5,x4,x4*x5
x2*x3,x2*x3*x5,x2*x3*x4,x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x3*x5,x3,x3*x4*x5,x3*x4,x1*x3*x5,x1*x3,x1*x3*x4*x5,x1*x3*x4,x1*x2,x1*x2*x5,x1*x2*x4,x1*x2*x4*x5,x2,x2*x5,x2*x4,x2*x4*x5,x1*x5,x1,x1*x4*x5,x1*x4,x5,1,x4*x5,x4
x2*x3*x4*x5,x2*x3*x4,x2*x3*x5,x2*x3,x1*x2*x3*x4*x5,x1*x2*x3*x4,x1*x2*x3*x5,x1*x2*x3,x3*x4,x3*x4*x5,x3,x3*x5,x1*x3*x4,x1*x3*x4*x5,x1*x3,x1*x3*x5,x1*x2*x4*x5,x1*x2*x4,x1*x2*x5,x1*x2,x2*x4*x5,x2*x4,x2*x5,x2,x1*x4,x1*x4*x5,x1,x1*x5,x4,x4*x5,1,x5
x2*x3*x4,x2*x3*x4*x5,x2*x3,x2*x3*x5,x1*x2*x3*x4,x1*x2*x3*x4*x5,x1*x2*x3,x1*x2*x3*x5,x3*x4*x5,x3*x4,x3*x5,x3,x1*x3*x4*x5,x1*x3*x4,x1*x3*x5,x1*x3,x1*x2*x4,x1*x2*x4*x5,x1*x2,x1*x2*x5,x2*x4,x2*x4*x5,x2,x2*x5,x1*x4*x5,x1*x4,x1*x5,x1,x4*x5,x4,x5,1

Download VarchenkoMatrix.txt

In an old question, @nm asked how to . While the answer in that question was almost up to the mark, there remains a regret. 

As the instance listed below shows, Maple, by default, draws arrows on a rectangular grid (rather than on a hexagonal mesh): 

  # Example of a three-dimensional vector field: 
vf__2d := VectorCalculus:-VectorField([sin(x)*(cos(x) + cos(y)), 
                                       sin(y)*(cos(x) - cos(y))], 'cartesian'[x, y]):
  # Example of a two-dimensional vector field: 
vf__3d := VectorCalculus:-VectorField([1 - (sin(u - v) + sin(u - w)), 
                                       1 - (sin(v - w) + sin(v - u)), 
                                       1 - (sin(w - u) + sin(w - v))], 'cartesian'[u, v, w]):
  # Phase portrait. 
Student:-VectorCalculus:-PlotVector(vf__2d, (x, y) =~ -Pi .. Pi, 
                                            'grid' = [`$`](25, 2), 
                                          'arrows' = 'THICK', 
                                   'fieldstrength' = log[63], 
                                           'color' = ColorTools:-Color("#0072BD"), 
                                            'axes' = "box"(*, …omitted…*));
= 

Note that I have changed some of the options in order to make the layout of arrows more prominent.
However, according to the help page of Mma's VectorPoints, among the following methods of location generation, Mma by default uses Hexagonal for 2D field vectors and FaceCenteredCubic for 3D field vector: 

, 

Here is a collection of different settings available in Mma:

So if the requirement is to get the Maple's output looking like Mathematica's (see the beginning), the number and placement of vectors to plot should be thought of as well. In Maple, “the number of vectors” can be controlled by the plot (or plot3d) opinion , but how do I specify “the placement of vectors” (e.g., Mma's "Hexagonal" and "Mesh")?

Although there exists an  chapter in the documentation, randomly positioned arrows do not fit the bill. Is there any workaround?

This is linear ode, third order, Euler type and inhomogeneous ode.

If I solve the homogeneous ode only, then ask Maple to give me a particular solution, then add these, I get much much smaller solution which Maple verifies is correct.

Now when asking Maple to solve the original inhomogeneous ode as is, the solution is much more complicated and much longer with unresolved integrals.

Why does not Maple give the simpler solution? Both are verified to be correct.

This is my theory: When asking maple to find only the particular solution, it seems to have used a different and advanced method to find yp. Which is new to me and trying to learn it. It is based on paper "D'Alembertian Solutions of Inhomogeneous Equations (differential, difference, and some other).

Undetermined coefficients method can't really be used on ode's such as this because its coefficients are not constant.

Now, when asking Maple to solve the inhomogeneous ode, it seems to have used variation of parameters method, which results in integrals, which can be hard to solve.

My question is: Why does not Maple give the same much shorter answer when asked to solve the ode as is? Should it not have done so? Any thoughts on why such large difference in answer? Why it did not use the same method to find yp when asked to solve the whole ode as that leads to much smaller and more elegant solution.

ps. debugging this, it uses LinearOperators:-dAsolver:-dAlembertianSolver which is called from ODEtools/particularsol/linear to find yp when calling DETools:-particularsol(ode); but for some reason, it does not do this when asking it to solve the whole ode directly (if it did, then one will expect same answer to result, right?)

Maple 2023.2 on windows 10.
 

Download why_such_difference_in_dsolve_answer.mw

Hi i study as an marine engenieer and use phasors alot.

I came across Acers startup code to use. 

At the moment i have been been using the gym package for my calculations. Is there a way to setup this startup code to function every time when i load maple? Also how does it go about using units in general? 

I currently have an issue where it outputs some strange format i can not understand 

I do not know why there is added so many decimals. I work on a macOS computer and have thought about using mathCAD for the ease of use instead of all of this. I am hoping for a helping hand to stay with maple because this is what i know and have used the last 3 years. 

I'm confused.  How come the two "is" aren't "true"?

assume(x <= y);
is(-5*x <= -5*y);
                             false

is(-5*(x <= y));
                              true

THis came up in another maple forum.  Any one knows why

restart;
expr := -(r0+Delta_r)^2*(46*r0-41*Delta_r)*r0^5;
subsop(1=a,2=b,3=c,4=d, expr);

gives error Error, improper op or subscript selector

but changing the order works ok

subsop(4=d,3=c,2=b,1=a, expr);

               # a*b*c*d

Looked at help and nothing there I could see that would explain this. 

Maple 2023.2. 

I am solving 3 nonlinear equations for 3 variables: lambda_1, lambda_2, and lambda_3. I would expect these lambdas to be real and positive.

Instead of solving my original equations, which are convoluted and not in polynomial form, I try to solve for their numerators first (since their numerators are polynomials). Broadly speaking, such solutions should also solve the original non-polynomial system. More specifically, the solutions thus obtained may be a nontrivial superset of the solutions of the original system. They need to be verified, which should be a much much easier process than obtaining that superset. In the case at hand, my original system is rational functions, and thus the only thing that really needs to be verified is that the solutions do not make any of the original denominators zero.

1st question: How to actually implement such verification? In other words, how to verify that the polynomial solution that I obtain also solves the original non-polynomial system?

2nd question: As you can see from my attached script, I obtain one polynomial solution. How to analyze it? What can I say about its roots? In case there are an infinite number of roots, how can I pin down a closed-form, real, and positive expression of lambda_1, lambda_2, lambda_3 in terms of the four parameters gamma, p, sigma_e and sigma_v?*

*Please note that in SolveTools:-PolynomialSystem I set backsubstitute=false to favour compactness and computational efficiency (which means that I need to do the backsubstitution myself now - how to do it?).

**Perhaps is useful to know that gamma, sigma_e and sigma_v are all real and positive and that p is a real, positive number between 0 and 1 (it represents a probability).

SCRIPT: 141123_Problem_NoCorrelation.mw

Thanks a lot!

Hi,

I would like to calculate Laplacian(1/r) in spherical coordinates

Considering that 1/r in spherical coordinates defines a distribution function (understood in Laurent Schwartz meaning) , the result has to be -4πDirac(r)

I tried to establish this result on Maple but that doesn't work. The result given is -Dirac(r)/r²  (see below)

What is the mistake I made?

Thanks

with(Physics[Vectors]);

SetCoordinates(spherical[r, phi, theta]);

F := Laplacian(1/r);
                               Dirac(r)
                        F := - --------
                                    r²