## Reconciling roots of a series...

I have resolved the roots of a series both numerically & analytically.  Let me qualify numerical  versus analytical.  Analytically I evaluate the series without substituting values for the various parameters of the series.  I then differentiate the series, then substitute in the appropriate parametric values, & then solve.  By this method I obtained 5 complex roots.

The numerical approach has values already assigned to the parameters of the series.  I then differentiate & solve.  I obtain only REAL roots in this instance.  I then restricted these results to obtain the solution I believe to be correct given by result (7).

I cannot seem to steer the solver in the analytic case to obtain the correct REAL result that I am expecting.  Can anyone help on this?

Before any website moderator thinks this is the same question as Error-in-Isinternal-Too-Many-Levels, it is not.  I have resolved that question.  This is a different question, but on the same problem!

reconcile_solns.mw

## how to convert this matlab code and use it?...

i have two functions , first naive function has error after used.

if run FromMatlab, does it mean that do not need to copy the result and run again because it had already run?
as i do not understand the output code after translated.

there is syntax error when translate second function

with(Matlab):
FromMatlab("function X = sylv_naive(A,B,Q)
% X=SYLV_NAIVE(A,B,Q) solves the Sylvester equation AX + XB = Q
%    A, B, Q: matrix coefficients
%    X : solution of AX + XB = Q
[m,n] = size(Q);
H = kron(eye(n), A) + kron(B.', eye(m));
Qvec = reshape(Q,m*n,1);
Xvec = H\Qvec;
X = reshape(Xvec,m,n);
");
sylv_naive(Jesus7,Jesus7,Matrix([[0,0],[0,0]]));
sylv_naive(Jesus7,Jesus7,Matrix([[0],[0]]));
Error, (in ArrayTools:-Reshape) the desired output contains a different number of elements than the input

with(Matlab):
FromMatlab("function X = sylvester(A,B,Q)
% X=SYLVESTER(A,B,Q) solves the Sylvester equation AX + XB = Q
% by using the Bartels and Stewart algorithm based on the complex
% Schur decomposition
%    A, B, Q: matrix coefficients
%    X : solution of AX + XB = Q
[m,n] = size(Q);
[U,A1] = schur(A,'complex');
[V,B1] = schur(B.','complex');
Q1 = U'*Q*conj(V);
X = zeros(m,n);
X(:,n) = (A1 + B1(n,n)*eye(m))\Q1(:,n);
for i = n-1:-1:1
v = Q1(:,i) - X(:,i+1:n)*B1(i,i+1:n).';
X(:,i) = (A1 + B1(i,i)*eye(m))\v;
end
X = U*X*V.';");

Error, (in Matlab:-FromMatlab) on line 15, syntax error
X(:,i) = (A1 + B1(i,i)*eye(m))

## how to find the necessary and sufficient condition...

if known solution [a,b,c,d]

solve([eq2, eq3, eq4, ....], [a,b,c,d])

but not equal to known solution a,b,c,d even if number of equations more than number of variables.

then guess that there are some necessary and sufficient conditions unknown.

how to find the necessary and sufficient conditions from solutions?

is there options to set for this?

or can eliminate function help to find necessary and sufficient conditions and how to do?

## Error, (in is/internal) too many levels of recursi...

Error, (in is/internal) too many levels of recursion

I get the error above when attempting to solve for the roots of partial derivative.  My results are below:

Despite the the simplifications MAPLE generated above MAPLE does not recognize the expressions as being equivalent.  So set the following for the Fourier coeffs:

 (1)

The Fourier series can now be expressed as a 1 sided series employing both the Sum vs sum vs add commands for comparison:

 (2)

 (3)

 Error, (in is/internal) too many levels of recursion

 Error, (in is/internal) too many levels of recursion

## Inconsistent results...

I have been attempting to resolve a particular problem to which I have posted a number of questions in the past.  In my attempts I have stumbled onto a number of command syntax issues & inconsistent result outputs.  Each time I try to post questions that appear to me to be separate questions even though it pertains to the same problem.  On numerous occasions a website moderator has deleted my questions unilaterally because the moderator has the opinion the question is identical to a previous question.

Deleting my questions instead of placing them into a previous thread without a response impedes my progress.  I am going to repost this inconsistent output, ONCE again!  If it is directly related to another thread then notify me of the response somehow instead of simply deleting the question.

The following inconsistency as far as I can tell is not explained in any of my previous questions.  I have a series that represents a particular waveform.  The series representation gives a definitive output.  However, when attempting generate the series of the derivative of this waveform (Q3 & Q4), which does exist (Q1 & Q2), MAPLE chokes on that representation & simply continues to evaluate for days & weeks without generating an output.  Why is this?  If anyone gets a definitive result please post it so that I might be able to reproduce the results.

inconsistent_results.mw

## How to enumerate a complete set of patterns?...

Is it possible to use Regex to generate a complete list of patterns?

for search pattern in a list of characters

## how to sort hashtable?...

A[k]:= x;
A:= table().

how to sort hashtable by key which is a list of matrix

after sort, is possible to group by key? and how?

## How to display more decimal numbers in maple...

Why input fraction to eigenvector and then evalf output are all the same when input different ?

i would like to see more decimal numbers

digits := 36

why can not see the difference?

if start from fraction

After set round screen display to 36 digits in options

If start from floating value

the result different from start from fraction

start from which is the most accurate and correct?

if fraction is correct, why all result are the same even if input are different?

## How display complex number?...

Real part + complex part

but

sometimes it display

complex part + real part

how to consistent display real part + complex part?

## Warning, solutions may have been lost...

I posted this earlier on a question I asked more than a month ago due to the similarity of the problem.  However, I got no response.  So I will post this as a new question in an effort to get a response.

I get the following error when working with the "INERT" Sum?

Warning, solutions may have been lost

I do not get the message when working with the "ACTIVE" sum.  I tried the AllSolutions option, but still get the same message.  How can I get the proper output working with the "INERT" form?

lost_solutions.mw

## Decimal places correct or not?...

I got decimal places problem,

not known correct or not

the value are different but difference is constant

i do not know how many places needed to get exact result

i do not believe the difference is constant

because the matrix are different

but even if using 36 decimal places still constant,

i notice increasing decimal places , the constant difference is changed

is it possible  to output fraction when calculate eigenvector?

## is there a method to group by pattern or recognize...

if there a series of matrix,

current matrix and previous matrix has same value , then defined as pattern

and

then define x and y are the position of pattern , if Matrix([[777,x,x],[77,7,7],[2,y,y]]

then code auto exchange x and y become Matrix([[777,y,y],[77,7,7],[2,x,x]]

but this recognization need to observe manually,

can this be automated for any kind of pattern , such as exchange or other operations of pattern?

can neural network or deep learning in maple code recognize the operations such as exchange part of row or flip or symmetric about axis or other need imaginable operations ?

## Convert symbolic expression to text commands...

I would like to convert a symbolic expression to text commands.  I recently used the expression palette to create a series summation; however, I was confused whether the sigma represented Sum vs sum.  I attempted to convert to string, but MAPLE attempts to evaluate the symbolic series prior to outputting the text commands.  Unfortunately, the evaluation of the series is computationally expensive & MAPLE will run out of memory.  I do not need MAPLE to evaluate the series.  How can it simply spell out the text commands that represent the symbolic form without resorting to evaluating the expression?

 (1)

## MAPLE crashing due to memory?...

I believe I am having memory issues which is causing the MAPLE kernal to terminate.  If I assign m a value then it seems to work, but I would like to leave m unassigned so that S1 can later be evaluated for any arbitrary m.  Is there a way around this?