nm

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These are questions asked by nm

This is just an obervation. May be due to me missing some clarification.

My understanding is that in Maple 2021, one can now export a complete Maple worksheet/document to Latex successfuly.

According to https://www.maplesoft.com/products/maple/new_features/  it says under "Latex export"
  
  Export is available for individual expressions or the entire document, though the latex command

So I would have expected that now all the online PDF documents for the new features in Maple 2021 to be generated from Latex for better formatting.

But when going over number of documents, they do not appear to have converted to Latex before generating the PDF.

Even the PDF document about the new latex command does not appear to have been generated from Latex. I can quickly recognize a PDF that was generated from Latex, and these PDF files are clearly not.

Looking at sample PDF from Maple website, it says the generator is "iText" and not latex compiler.

It looks like these documents were just a direct export of the Maple worksheet to PDF, instead of being exporting to Latex first, and then compiled to PDF.

Am I missing something? Why not take advantage of the Maple Latex export, and convert all the documents to Latex first and then generate the PDF from Latex? This would make them look much better in terms of formatting and math rendering.

Here are some examples

  https://www.maplesoft.com/products/maple/new_features/Maple2021/PDFs/AdvancedMath.pdf  


  https://www.maplesoft.com/products/maple/new_features/Maple2021/PDFs/ODEsandPDEs.pdf


  https://www.maplesoft.com/products/maple/new_features/Maple2021/PDFs/GraphTheory.pdf


  https://www.maplesoft.com/products/maple/new_features/Maple2021/PDFs/Physics.pdf

  https://www.maplesoft.com/products/maple/new_features/Maple2021/PDFs/LaTeX.pdf

Why did not Maple documentation take advantage of the new export command of Maple's latex command? This would also have been a good way and an opportunity to show case the effectiveness of the new latex export command.

May be it was not done due to time constraint before the release date of maple 2021? Or are there other technical reasons?

 

 

In Maple 2021

restart;
B:=sqrt( (-4*u^(1/3)+1)*u^(4/3));
A:=1/(-12*u+3*u^(2/3)-3*B);
res:=int(A,u);
simplify(res)

This is one of the integrals, that in Maple 2020 did not handle. In Maple 2020, it gives this

restart;
B:=sqrt( (-4*u^(1/3)+1)*u^(4/3));
A:=1/( -12*u+ 3*u^(2/3)-3*B);
res:=int(A,u);

The difference is that in Maple 2021 int is able to solve this (but gives very long output which I will not post here). The problem is now simplify() gives an error on the result. I was trying to see if possible to obtain the same small result as Mathematica's after simplifying. Here is Mathematica's result

ClearAll[u];
B = Sqrt[(-4*u^(1/3) + 1)*u^(4/3)];
A = 1/(-12*u + 3*u^(2/3) - 3*B);
res = Integrate[A, u]

It is good that Maple can solve this integral, but why simplify gives error on the result? Is there a workaround?

 

I installed Maple 2021 on windows 10. And wanted to try it to see if the hangs I used to have are fixed now.

First I noticed that Physics package does not come pre-installed with Maple 2021, which is little strange. I would have expected Maple 2021 to come with latest Physics version.

Because when I did Physics:-Version() it says "`The "Physics Updates" package is not installed`"

Then I typed  Physics:-Version(latest) to install it, it gives error

Error, (in Physics:-Version) unable to determine the Physics Updates version, could you please report the problem to support@maplesoft.com
 

 

I remember something similar in earlier version of Maple but can't find or remember where that post now.

May be Physics needs to be updated at Maple site to work with Maple 2021? I am asking, because Latex() does not work without Physics installed.

Edit:

I think in Maple 2021, latex() now is the same as the earlier Latex() command from Physics? I remember a post saying this now. Since I see now latex() have different help page from old latex() help page.

So may be that is why Latex() did not work. I can easily change this in my code to change it to use latex() instead of Latex() in this case. 

Windows 10

 

 

 

I needed to normalize the eigenvectors of a matrix. (I did not see an option to do this so far in LinearAlgebra). So I figured I just need to map LinearAlgebra:-VectorNorm(x,'Euclidean')  of each vector of the generated eigenvectors matrix,. Where here means the vector in the matrix. But do not see a way to do it. 

I ended up just using seq, which works fine. But was wondering if there is a way to do it? map function on each column (or each row) and have the result be matrix ofcourse. 

Will show my attempt using map, and then using seq

Sx:=1/sqrt(2)*Matrix([[0,1,0],[1,0,1],[0,1,0]]);
lam,v:=LinearAlgebra:-Eigenvectors(Sx);

Just doing the following does not work ofcourse

map( x->x/LinearAlgebra:-VectorNorm(x,'Euclidean'), v) 

So I used seq

Sx:=1/sqrt(2)*Matrix([[0,1,0],[1,0,1],[0,1,0]]);
lam,v:=LinearAlgebra:-Eigenvectors(Sx);
normalized:=[seq( v(..,i)/LinearAlgebra:-VectorNorm(v(..,i),'Euclidean'),i=1..LinearAlgebra:-RowDimension(v) )];

Will be nice if one can use map or variation of it, which works on either columns or rows at a time.

Maple 2021.2

 

Why is a row of a matrix has type Matrix, but a column of a Matrix has type Vector (column vector)

I expected a row of a matrix to also be a Vector (row vector).

restart;
A:=Matrix([[1,2],[3,4]]);
A(1,..);
whattype(%);

A(..,1);
whattype(%);

This might be by design or documented somewhere. But I find it not consistent.  Either both results should be Matrices, or both should be Vectors (the more logical way).

 

Maple 2020.2 on windows 10.

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