Hello everyone, my computer installed Maple 2016, 2020 and set Maple 2016 as default opening files .mw, .mws. How to change default to Maple 2020 . I tried searching on Google but not found.

Thank you very much.

Hello!

How to calculate the residual sum of squares of a Nonlinear Fitting?

I tried but was unsuccessful.

How I can prove the following equation in red box.

Also, Pn(v) and qn(v) are the real combinations of half-integer Legendre functions.

For more details please see 

https://math.stackexchange.com/questions/2746660/potential-flow-around-a-torus-laplace-equation-in-toroidal-coordinates/3809487#3809487

I did already some programmingexercises , but this sort of programming example i did not encounter in the programmingbook
How it is programmed in general lines ?
I do have a lot of small procedures to learn from

But it is too much asked here on the forum to explain all ins and outs for this procedure, because it is not that simple. 
 

Download Basisgrid_procedure.mw

When I'm doing math more complicated, than in the first line, Maple gives the incorrect type of unit.
I want the unit as displayed in the first line, but by using the math/syntax shown in the last line.

Maple does not have "Joule per kilogram times kelvin", as a choosable option when I do the syntax in the last line. 

Is there any way I can end up with the correct unit, even tho I am using syntaxes?
In theory, I should end up with the same answer as a result?.

Is it possible to make executed math aka 2D Outputs, automatically align left?
I'm doing it manually for every execution I make. But is there any setting, that does orient the text to the left by standard?

I have intervals A=(-infinity,7), B=(-10,25), and C=(15,infinity). How do I use Maple to perform the union and intersection of such intervals?

I spend all day on this, since some tests I have were failing when I changed to using Physics:-Latex() vs. latex(). I made no change at all in my own code other than to replace latex() by Physics:-Latex().

I am still not sure why that is, but it seems due to symbol clash somewhere.  First time I run my test, it passes, next time if fails. When I change back to latex(), the test passes each time.  

This seems to be due to when calling Physics:-Latex() the very first time, it automatically changing diff(y(x),x) to y'(x). May be it is storing its own x in there. (this happens on special input and not for each input, that is why only some tests fail and not all of them).

So next time I call the test it failes. May be due to different x being used. I do not know. 

All what I know now is that using latex() makes my dsolve test passes each time.  

But here I will show the issue which I think if fixed, should fix the main problem.

Calling Physics:-Latex() causes it to automatically change diff(y(x),x) to y'(x)  even though I am not using Typeseeting at all. 

restart;
s:= y = u*x:  #special case input which causes the typesetting to kick in
ode:=diff(y(x),x)=1:
print(ode);
Physics:-Latex(s,output = string):
print(ode);

Notice how the derivative changes on its own to using y'(x).  Now compare with latex()

restart;
s:= y = u*x:
ode:=diff(y(x),x)=1:
print(ode);
latex(s,output = string):
print(ode);

So something happens inside Physics:-:Latex which causes this.  

For now, I will change back to latex() until I figure more what is going on so that my test do not fail. I like to use Physics:-:Latex as it made the latex look much better.

Maple 2020.1, Physics 778
 

Additional observation

This change of typesetting does not happen all the time. For example if s:= y = x: then it works OK. i.e. it does not change typesetting. But if s:= y = u*x: then it changes typesetting. which is very strange why that is.

I stepped into Physics:-Latex using the debugger., The typesetting changes after the call to Physics:-Latex:-Print.

Download latex_issue_2.mw

Determine how many transitive relations there are on a set with n elements for all positive integers n with n<=7.

Custom Palettes and Palette Entries on windows Pro 7 
Read a tutorial from a user @les 185

https://www.mapleprimes.com/posts/207781-Custom-Palettes-And-Palette-Entries

Is this still valid this tutorial from 2015  in the current version of Maple ?
This seems to be userunfriendly.

I follow below question to generate binary sequence
but number of sequence is 6 not 5, why 011001 is wrong?

number of sequence should be catalan number.

how to generate this kind of sequence correctly?

For ecah positive integer n, how many 2n-digit binary sequence
 b1,b2,b2n with n "0" and n "1" are there such that
for each i=1,2,...2n, the number of "0" is larger than or equal 
to the number of "1" in the subsequence b1,b2,...bi?

with(combinat):
with(ListTools):
with(SumTools):
source := permute(Flatten([seq([0,0,0,1,1,1], k=1..1)]), 6);
aavxa := []:
for z in source do
if Summation(z[k], k = 1 .. nops(z)) = 3 then
if z[nops(z)] = 1 and z[1] = 0 then
if Reverse(z) in aavxa then
else
aavxa := [op(aavxa), z];
end if:
end if:
end if:
od:
nops(aavxa);
aavxa;
 

I am learning Typesetting so I can get better Latex.

I'd like to have all derivatives generated as y'(x) and not dy/dx regardless of what the derivative variable is. (It is more clear this way).

I found I can't even give Maple a list of the variables. But must do it each time one at a time.

I have thousands of ODE's I need to typeset, (they use different variables (depending on the textbook), and not always x or t, but the set of variables is not large).

so having to check and keep changing this setting each time is awkward (but I think is doable, as I know what the independent variable is for each ode so I can call Typesetting at start of each ode processing, once I know what the variable is).   

It wil be much easier if there is a way to tell Maple to do this for all variables. May be there is a good reason why Maple does not seem to allow such an option?

Here is an example

Typesetting:-Settings(usedot=false,prime=t,typesetprime=true):
ode:=diff(y(t),t$2)+diff(y(t),t)+y(t)= 0:
Physics:-Latex(ode);

Which gives the Latex I want

But if the variable was x instead of t, I have to do this

Typesetting:-Settings(usedot=false,prime=x,typesetprime=true):
ode:=diff(y(x),x$2)+diff(y(x),x)+y(x)= 0:
Physics:-Latex(ode);

I tried doing prime=[x,t] but Maple did not like this.

Is there a way or trick to tell Maple to use typesetprime=true for any letter?  I looked at https://fr.maplesoft.com/support/help/Maple/view.aspx?path=Typesetting%2fSettings but do not see a way so far.

Maple 2020.1 with Physics 776

I am trying the new Physics:-Latex command in version 774.

Couple of isssues I found:

1) One test I have failed with this error

Error, (in anonymous procedure called from anonymous procedure called from anonymous procedure called from anonymous procedure called from Physics:-*) invalid boolean expression: NULL
 

Using the normal latex() command works OK. I hope it is not too hard to fix since this new version seems to have fixed the fraction problem in latex(). Please see

restart;
sol:=dsolve(t*(t-2)^2*diff(diff(y(t),t),t)+t*diff(y(t),t)+y(t) = 0,y(t));
latex(sol);  #OK

Physics:-Latex(sol); #error

2) Maple now generates Latex using maple macro, which I do not know what it is.  Comparing

restart;
ode:=t*(t-2)^2*diff(diff(y(t),t),t)+t*diff(y(t),t)+y(t) = 0;
latex(ode)

which gives 

t \left( t-2 \right) ^{2}{\frac {{\rm d}^{2}}{{\rm d}{t}^{2}}}y
 \left( t \right) +t{\frac {\rm d}{{\rm d}t}}y \left( t \right) +y
 \left( t \right) =0

compare to

Physics:-Latex(ode)

which gives

t \left(t -2\right)^{2} \Mapleoverset{\ldots}{y}\left(t \right)
      +t \Mapleoverset{.}{y}\left(t \right)+y \left(t \right) = 0

What is \Mapleoverset ? googling around, these look like part of internal Maple style sheet for Latex?

Does this mean when using the new Physics Latex command, now one needs to use the package maplestd2e.sty?  With the normal latex() command, this was not needed. 

Just trying to understand the new setup.

What are the things you most like to see improved/add to next version of Maple? 

This is my list for a starter:

1.  Improve the debugger. Debugger is very useful but needs more work. At least be able to see code listing in larger view as one steps in for example. See Matlab debugger for inspiration.

2.  Improve Latex. It still does not do fractions well. Posted about this before.

3. Eliminate hangs when using timelimit(). On long runs, random hangs happen when timelimit() do not expire as requested. Posted about this before.