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These are replies submitted by lcz


Thank you very much. Something is better than nothing.

@Carl Love Thank you!Now I get it.

@Kitonum Thank you!  I do not understand what the mechanism  of index in sum is.

@Kitonum  Thank you !

But When I use your second codes

P := plot(sin(x)-x+(x^3)/3!, x=-2*Pi..2*Pi) :
L := plots[textplot]( [ 3 , 17 , sin(x)-x+(x^3)/`3`!],  axes = none) :
plots[display](P ,L, axes = normal)

 I found there is a difference between font of 3 in the denominator of x^3/3! and other symbol's



indeed,Table[] is like seq() in Maple, I mean the following code in mathematica

ls[[1 ;; -1 ;; 2]]
ls[[2 ;; -1 ;; 2]]


I thought there was something similar that could be done in Maple.



At the beginning I thought there would be a simple and fast function. Just like mathematica.

expr .. expr  is not flexible  for me . For example:

ls[ .. 2]


Maybe if it can be set like this, it will be better.


In fact

@mmcdara I'm very sorry, I didn't pay attention to the information before! 

Thank you for your great  work and explanation

This program is very good!

@Carl Love  

Thank you so much, I was negligent and didn't pay attention to observation that  each b_i  is  free unknown variable

@vv  Fortunately, I found an alternative.  Some people did a lot of work 

@vv Indeed. I might be asking more broadly. 

I once asked such a question about crossing number of graph :

This can be found in SageMath, but it is very slow. Of course, it was expected.

My goal is to test whether a given graph is 1-planar. Of course, it is difficult! We tend to consider the combination method. But we can try draw different drawing  before we prove it. This may involve different isomorphism drawing of graph.



@acer  Thanks, This is good enough.

@Carl Love Thanks for the advice. Your suggestion is valid for dealing with parallel edges. But I still can't handle it effectively.

I used FindEulerianCycle in mathematica  indirectly by G-e7+{13}.

  g = Graph[{1 <-> 2, 1 <-> 3, 1 <-> 4, 3 <-> 4, 3 <-> 4, 2 <-> 4, 
   1 <-> 3}, VertexLabels -> Automatic]

FindEulerianCycle[g, All]

We found 16 Eulerian trails. That's all we want. I don't know how to do in Maple. 

 There is no  function like  FindEulerianCycle[g, All]

@vv Thanks ,Good ideas!

@nm  Thanks But Why use A^+? A may be enough.




@Kitonum  Extremely grateful! One more question I care about.

how do I estimate errors  in maple if I use Optimization:-Maximize  .   does maple have any tools to analyze?

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