@janhardo 

proof_with_integer_existence_.mw

@dharr 

 "In Maple, this cannot generally be proven using the characteristic polynomial" :

What I mean is that you cannot prove this second-order general recurrence relation using an algorithmic proof in Maple.
The solution involves the roots of the characteristic polynomial.
Maple can never compute all the induction steps.
At most, you can outline the theoretical proof scheme for this in Maple.
Indeed, you can distinguish between an algorithmic proof and a mathematical-theoretical proof for full induction
An algorithmic proof involves a finite number of steps executed in Maple, whereas a true mathematical proof does not have a finite number of steps

@dharr 
In Maple, this cannot generally be proven using the characteristic polynomial.
At most, Maple can outline the theoretical proof or perform a few calculations to provide an indication that the proof is correct. 

"As I don't know MMA enough to use such a script I can't go further on" .
Is there such script , then probably ai can translate it to maple ?

@sand15 
The question is whether Maple users will all start using AI as well?
That’s what I mean when I say you can’t stop AI anymore, and development in this area will continue.
Maplesoft itself is also embracing AI, so yes, there’s a risk that users won’t develop a truly solid foundation in Maple.
Using AI makes it easy to gain a deeper understanding of a topic.
You’d have to ban the use of AI on the forum and expect all code to be written manually.

Hi, its ai what is be used more and it cannot be stopped.
The human contributions made here on the forum to learn Maple probably won't be recognized by the AI as knowledge.

animation twincircles

@Ronan 
Look again to my example ..

@Ronan 
Do you understand this ? : savelibname := "C:/Users/jando/Maple/toolbox/Cliffordlib":
 .ini file is located in Maple folder  in this path ( sorry.  i was not clear enough) 

The nest step is the package "mapel.ini" file needs to be placed in "C:\Program Files\Maple 2026\Users". : 
It seems that the ini file is outside Maple program itself. 

I am on Windows 11 pro and use now Maple 2026.1, this seems to work for me 

Users this map 

@Ronan 
Yoy can do it with this ?

savelibname := "C:/Users/jando/Maple/toolbox/Cliffordlib":
libname := savelibname, libname:

read cat(savelibname, "/define.m"):
read cat(savelibname, "/definemore.m"):
read cat(savelibname, "/Walshpackage.m"):

 .ini file is located in Maple folder
Cliffordlib is name of package 

Maple 2026.1

@Ronan 
Its working on Windows 11 pro 

Pattern  from triangle (not a euclidian)  and twincircles?

UHG_module_2D_-_6-9-2026.mw

a non-periodic function

@Kitonum 
Note that the planes are positioned perpendicular to each other, so this requires additional code.and other  things in a earlier example, so  i don't see your point  ? 
No textplots are possible with draw and display.commands.
 

restart:
with(geom3d):
plane(P1,x+y=1,[x,y,z]):
plane(P2,x-y=2,[x,y,z]):
point(A,1,0,0):
point(B,2,0,0):
intersection(L,P1,P2):
draw([P1(color=blue,transparency=0.55,style=surface),P2(color=yellow,transparency=0.55,style=surface),L(color=black,thickness=4),A(color=red,symbol=solidsphere,symbolsize=16),B(color=red,symbol=solidsphere,symbolsize=16)],axes=boxed,labels=[x,y,z],scaling=constrained,view=[-3..5,-4..4,-3..4],orientation=[55,65],title="Two Planes using geom3d");