nm

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These are questions asked by nm

according to what is new in Maple 2025, it says

  • Maple 2025 introduces several important improvements to simplify regarding expressions containing exponential, trigonometric, hyperbolic, and/or inverse trigonometric functions, resulting in more compact results. Other commands in the math library also provide simpler results due to these improvements.

But I still see weakness in simplify. (see also recent question).

Here is an example, A and B below are equivalent mathematically. But A is almost twice as big. So one would expect simplify(A) to return B. right? But it does not. Also using size option has no effect.  

Does one need more tricks in Maple to make it simplify this? Is this not something that a powerful CAS software like Maple should have been able to do?

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`


A:=(-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4;
B:=(4*exp(x/2)-x-2)^2;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(4*exp((1/2)*x)-x-2)^2

#check leaf size
MmaTranslator:-Mma:-LeafCount(A);

22

MmaTranslator:-Mma:-LeafCount(B);

13

#check they are the same
simplify(A-B);

0

#then why Maple can not simplify A to B ??
simplify(A);
simplify(A,size);
simplify(A,size,exp);
simplify(A) assuming real;

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

Student:-Precalculus:-CompleteSquare(A)

(-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4

 

 

Download why_can_not_simplify_may_4_2025.mw

Using another software, all what is needed is call to Simpify to do it:

I also tried my most power full_simplify() function in Maple, and it had no effect

full_simplify:=proc(e::anything)
   local result::list;
   local f:=proc(a,b)
      RETURN(MmaTranslator:-Mma:-LeafCount(a)<MmaTranslator:-Mma:-LeafCount(b))
   end proc;

   #add more methods as needed

   result:=[simplify(e),
            simplify(e,size),
            simplify(combine(e)),
            simplify(combine(e),size),
            radnormal(evala( combine(e) )),
            simplify(evala( combine(e) )),
            evala(radnormal( combine(e) )),
            simplify(radnormal( combine(e) )),
            evala(factor(e)),
            simplify(e,ln),
            simplify(e,power),
            simplify(e,RootOf),
            simplify(e,sqrt),
            simplify(e,trig),
            simplify(convert(e,trig)),
            simplify(convert(e,exp)),
            combine(e)
   ];   
   RETURN( sort(result,f)[1]);   

end proc:

Calling full_simplify(A) did not simplify it.

I wanted to search for all files with some extention in directory tree. But when adding depth=infinity and also adding 'select'="*.log" (or whatever the extension I want is), then it returns an empty list even though there are files with this extension but deep in the tree.

If I remove select, then it does work, but it returns list of the files in the tree. Which I do not want. I want to filter these by select.

If I remove depth=infinity then select works but only finds such files at top level of the directory and does look down the tree where there are more such files.

It seems select and depth conflict with each others.  Adding 'all' option makes no difference.

I do not remember now if I reported this before or not.

Here is worksheet showing this problem

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

folder_name:="/home/me/maple2025"; #fails to find all such files
FileTools:-ListDirectory(folder_name,'select'="*.wav",depth=infinity);

"/home/me/maple2025"

[]

folder_name:="/home/me/maple2025"; #works but only top level
FileTools:-ListDirectory(folder_name,'select'="*.log");

"/home/me/maple2025"

["Maple_2025_Install_2025_04_03_12_34_10.log"]

folder_name:="/home/me/maple2025"; #works but this finds everything
FileTools:-ListDirectory(folder_name,depth=infinity);

"/home/me/maple2025"

`[Length of output exceeds limit of 10000]`

 


 

Download listdirectory_may_3_2025.mw

How can one get list of files with specific extension in the whole tree? And why is adding select makes it not work? Help does not say anything about select does not work when adding depth=infinity.

I suppose I can get list of all files in tree, then iterate over the list and remove all entries that do not end with the extension I wanted. But this is what select is supposed to do. For example

folder_name:="/home/me/maple2025/"; #works but this finds everything
L:=FileTools:-ListDirectory(folder_name,depth=infinity):
map(X->`if`(FileTools:-Extension(X)="wav",X,NULL),L);

Gives list of only files with extension "wav". So the above is workaround for now.

These are the same (i.e. mathematically equivalent for real x)

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

But can't see how to use Maple to show this, other than numerically and by plotting.

Any one knows of a trick? Below is worksheet. Using another software, it was able to show they are same:

Here are my attempts in Maple 2025
 

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

A:=-x*(x - 4*exp(x/2) + 2);
B:=x*sqrt((-8*x - 16)*exp(x/2) + x^2 + 4*x + 16*exp(x) + 4);

-x*(x-4*exp((1/2)*x)+2)

x*((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)

plots:-display(Array([plot(A,x=-3..3),plot(B,x=-3..3)]))

 

 

Digits:=16;
seq(MmaTranslator:-Mma:-Chop(A-B),x=-2..2,.1)

16

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

simplify(A-B);

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evala(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(normal(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(A-B,exp) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

simplify(evalc(A-B)) assuming real;

-x*(((-8*x-16)*exp((1/2)*x)+x^2+4*x+16*exp(x)+4)^(1/2)-4*exp((1/2)*x)+x+2)

 

 

Download show_same_may_3_2025.mw

For compution this is not important, for latex, I find  n>0 little more clear to read than 0<n 

Is there a way to tell Maple not to reverse terms on each side of the > just for latex purposes?

It seems Maple does this only for   > and not for  <

I know the latex output follows what is displayed on the screen in Maple. And that is what happens also for display. Maple rewrites n>0 as   0<n.   

I tried changing display->Typesetting level from extended to maple standard but this had no effect. 

Is there a trick to make Maple not all the > to  <  ?

Again, I wanted to do this just for the latex output because for computation and for screen display in worksheet, it is not an the issue for me, as I only use Latex output.

It seems Maple like to make everything  based on "<" internally and that is why it reverses it?

interface(version);

`Standard Worksheet Interface, Maple 2025.0, Linux, March 24 2025 Build ID 1909157`

restart;

latex(n>0,'output'='string'); #why this is reverse on output?

"0<n"

latex(n>m,'output'='string'); #why this is reverse on output?

"m <n"

latex(n<0,'output'='string'); #but this stays the same

"n <0"

latex(n<m,'output'='string'); #but this stays the same

"n <m"

n>0

0 < n

 

 

Download why_reverses_may_1_2025.mw

This happens in Maple 2025, but when I checked Maple 2024.2, same thing happen.

To reproduce, I typed ?coeff in the worksheet. Now the help page for coeff comes up OK. On the right, there are some links below "see also". 

Clicking on the one that says PolynomialTools[CoefficientVector] and now an EMPTY page opens up.

Also, typing ?PolynomialTools in worksheet, opens the help page for Overview of the PolynomialTools Package. Now clicking on CoefficientList link, opens an EMPTY page. Same when clicking on CoefficientVector, an EMPTY page !

Have not checked all the links in the help page, but why are some commands have empty help pages?

 

 

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