## Sums of certain series and a bug...

This question is related to the recent post
http://www.mapleprimes.com/questions/211460-Series-Of-Bessel-Functions

1. Consider the following fast convergent series:

f:=n->(-1)^(n+1)*1/(n+exp(n));
S1:=Sum(f(n),n=1..infinity);
evalf(S1);
S2:=Sum(f(2*n-1)+f(2*n),n=1..infinity);
evalf(S2);

As expected, the sum of the series is obtained very fast (with any precision), same results for S1 and S2.

2. Now change the series to a very slowly convergent one:

f:=n->(-1)^(n+1)/sqrt(n+sqrt(n));

evalf(S1) is computed also extremely fast, because the acceleration algorithm works here perfectly.
But evalf(S2) demonstrates a bug:

Error, (in evalf/Sum1) invalid input: `evalf/Sum/infinite` expects its 2nd argument, ix, to be of type name, but received ...

3. Let us take another series:

f:=n->(-1)^(n+1)/sqrt(n+sqrt(n)*sin(n));

Now evalf(S1) does not evaluate numerically and evalf(S2) ==> same error.
Note that I do not know whether this series is convergent or not, but the same thing happens for the obviously convergent series

f:=n->(-1)^(n+1)/sqrt(n^(11/5)+n^2*sin(n));

(because it converges slowly (but absolutely) and the acceleration fails).
I would be interested to know a method to approximate (in Maple) the sum of such series.

Edit. Now I know that the mentioned series

converges (but note that Leibniz' test cannot be used).

## Error and nonsense in eulermac outputs

by: Maple

eulermac(1/(n*ln(n)^2),n=2..N,1);  #Error
Error, (in SumTools:-DefiniteSum:-ClosedForm) summand is singular in the interval of summation

eulermac(1/(n*ln(n)^2+1),n=2..N,1);  #nonsense

## Series with equation number bug?...

Hi,

When I execute the command

series(exp(x),x)

and then refer to the equation in a new execution group using a equation label (CTRL-L on Windows), the equation is shown in Maple 18, but in Maple 2015 I get an error message: 'Error, missing operator or ';'. Using the % instead does work for both versions.

Is this intended behaviour or a bug in Maple 2015?

Thanks,

Bart

## Serious Maple2015 bug ...

in LinearAlgebra Eigenvectors calculation.

So the above output startled me.  I have used the Maple Linear Algebra Eigenvalues, Eigenvectors commands many times with no problem.  Can any one explain to me what is going on.  The program correctly calculates the eigenvalues for the matrix which are all distinct for a real symmetric matrix, and thus should have three distinct non-zero eigenvectors, yet the eigenvectore command returns only zeros for the eigenvectors.  I calculated an eigenvector by hand corresponding to the eigenvalue of 1 and obtained (1, -sqrt(2)/sqrt(3), -1/sqrt(3).

So this is either a serious bug or I am going completely insane.

## Computation of radical ideal ...

In the running of an example I faced to computation of radical ideal of the following ideal:

<-c*m*u+d*c*n+m*b*v+m*c*t>

I used from Radical command in PolynomialIdeals package. But I dno't now why it's computation is very hard and Time-consuming?

What I have to do? I think there is a bug, since this ideal is simple, apparently.

## Possible Bug in Maple ?

by: Maple

Has anyone tried to run the following in Maple command-line mode (i.e. in terminal window, type "maple" to start it without the graphic interface),

"

expr1:=t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15+t16+t17+t18+t19+t20+t21+t22+t0-t0+t23;
expr2:=t1+t2+t3+t4+t5+t6+t7+t8+t9+t10+t11+t12+t13+t14+t15+t16+t17+t18+t19+t20+t21+t22+t0-t0+t23;
print(expr1-expr2);

"

Surprisingly, I didn't get "0" with my Maple 17 (under Linux platform) or 18 (under Mac OSX platform). Can anyone help me confirm this?

## Need to verify a PDE solution...

Hi,

I'm trying to solve this PDE, and Maple 2015 gives me a solution quickly. I can test the solution with pdetest() and this verifies that it works. However, when I try to verify this myself I don't get zero. Is there some trick pdetest() is using to that I am missing? Or is pdetest() wrong in this case?

 > restart;
 > eq := I*exp(-(2*I)*k*t)*k*sin(theta)*r^2*cos(theta)^3+4*exp(-(2*I)*k*t)*r*cos(theta)^3+2*(diff(Vr(t, r, theta), theta, theta))*cos(theta)*exp(-I*k*(sin(theta)*r+t))-6*(diff(Vr(t, r, theta), theta))*sin(theta)*exp(-I*k*(sin(theta)*r+t))-4*Vr(t, r, theta)*cos(theta)*exp(-I*k*(sin(theta)*r+t))-4*exp(-(2*I)*k*t)*r*cos(theta);
 (1)
 > sol := pdsolve(eq);
 (2)
 > pdetest(sol, eq);
 (3)
 > eq2 := eval(eq, Vr(t,r,theta) = rhs(sol)): eq2 := simplify(%);
 (4)
 > evalb(eq2 = 0);
 (5)
 >
 >

## I found a bug in Maple...

I think that I found a bug in Maple! Please run the following command:

I need the Generators of above Ideal. What is your idea?!

## Defining tensors as arrays VS as expressions in Ph...

Hi,

I was just curious about the difference between defining tensors as arrays/matricies/TensorArrays vs defining them as algebraic symbols. I found that defining them as an expression lead to the wrong answer, and I was forced to define a tensor (LKh) as an array. I've attached a worksheet demonstrating my problem.

I apologize for the amount of tensors needed to find this problem, but it is the only one I have reproduced the issue. I basically define the metric
Metric = g_
auxillary tensor = h
Killing vector = K
LieDerivative of h, wrt K = LKh (not a tensor array)
LieDerivative of h, wrt K = LKh2 (tensor array)
Then I compare two expressions, rho1 and rho2 computed from LKh and LKh2 and they disagree.

Thanks!

## Bug in LPSolve in Maple 2015.1...

When solving a simple assignment problem in Maple 2015.1 the bug occurs:

In Maple 2012 there are no problems:

A := Matrix([[1, 7, 1, 3], [1, 6, 4, 6], [17, 1, 5, 1], [1, 6, 10, 4]]):

n:=4:

sol:=Optimization[LPSolve](z, restr, assume=binary);

## Important Bug in Series...

In Maple 2015, on windows 8.1 64-bit the command
series(2*x*(x-y)/y, y = 0, 3);
gives

which is incorrect. The answer is

You can notice the minus sign in front the the -2x is incorrectly typeset, which makes me wonder if it's a bug in the typsetting program and not series itself.

## Issue using matrix sparse storage...

Consider the following code, which just generates two "identical" matrices, differing only in their requested storage type, and then does some simple manipulations.

restart;
#
# Define matrix using sparse storage
#
testM:= Matrix( 40,40,
(i,j)->`if`(j>=i,1,0),fill=0,
storage=sparse
):
#
# Define identical(?) matrix with rectangular storage
#
nm:= Matrix( 40,40,
testM,
storage=rectangular
):
#
# Define procedure to return some matrix properties
#
matData:= proc( myMat::Matrix)
return op(3, myMat)[2], # check storage type
myMat[5, 1..-1], # get 5-th row
end proc:
#
# Get properies of the two matrices - should be identical
# but check result of adding elements in the 5-th row
#
matData(testM);
matData(nm);

The matData procedure ought to produce the same results for the two matrices, with the exception of the storrage type. But the 'add()' command does not. The 'myMat[5, 1..-1]' command produces the same vector, the 5-th row - but stick an add() wrapper around it and all hell breaks loose.

Is this a bug or am I missing something?

Suggestions such as avoiding sparse data storage are not really acceptable: the above is a much simplified version of my original problem where I was using graph theory to play with a "cost function" and (with G a graph) the command,

WeightMatrix(MinimalSpanningTree(G))

returned a sparse-storage matrix - and I didn't notice. There appears to be no option on the WeightMatrix() command to control the storage tyoe of the returned matrix. Result was that all subsequent code based on slicing/dicing/and particularly 'add()ing' sub-blocks of this weight matrix fell apart

Don't get me wrong: I can sort of accept that the weight matrix of minimal spanning tree would (hopefully) be mainly zeros so sparse-storage might be a good default option but I don't see why the results of a command such as

should vary depending on the internal storage used for the matrix, particularly when I have no control over the storage type being adopted

## Can Maple 2015 properly handle a Print to PDF on a...

Starting with Maple 18, the Print to PDF feature caused the document page to be hard-aligned at the left margin of the page. Maple 2015 still seems to have this problem / bug.

Does anyone else have the same problem? Has a work-around been posted? Is a fix in the works after nearly 9 months?

--
JJW

## Bug in Maple 2015...

Why does Maple 2015 solve this very simple system incorrectly?

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});

With Maple 12 no problem:

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});

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