student_md

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restart:
N:=3:
for i from 1 to N do
x[i]:=evalf((2*i-1)/(N)) :
end do:
for i from 1 to N do
t[i]:=evalf((2*i-1)/(N)) :
end do:
f:=unapply(x*t,x,t);
g:=unapply(x^2*t,x,t);

Question 1: We have two functions f and g as above. How can we create a table which contains merged cells as follows by Maple? 

Question 2:  How to convert or export the table to LATEX?

I wrote a code for the following sequence. But I have a problem. What are the good methods for defining recursive sequence?

THE CODE

restart;
#FIRST STEP: Lets find the recursive formula for 
d:=proc(m)
option remember;
d(1):=1;
if m>1 then return -sum(xi(i)*d(i-k+1),i=2..m) else 1 fi;
end proc:
#lets check
for i from 1 to 4 do
d(i);
end do; 

 

 

Secondly, I want to create a matrix as follows. I wrote the code. I think it is right.

restart:
m:=4:
DD:=Matrix(m,m):
#SECOND STEP: Lets find the matrix 
for i from 1 to m do 
p:=0:
for j from 1 to m do 
 
if i<=j then p:=p+1:
DD[i,j]:=d(p);
 fi: 
end do;
p:=1: 
end do:
DD;

 

 

 

 

We can see the context of  Matlab code in the Windows preview pane as follows, but we can' t see the context of Maple codes.

I wonder whether it is possible for Maple, too or not. Is there any method to achieve this? Because it really offers a great advantage for the fast browsing context of code in a folder that includes a lot of maple files.

 

(I use Maple 2019 and Windows 10)

 

 
 
 
 
 

 

I try to write a Maple Code. But I can' t finish it. 

This is very important for me. Could you help me? download_Maple Code.mw

 

I think we will write nested for loops or nested sequences. But I can' t achieve.

Could you help me?

EDITED AND EXTENDED:

In fact, the original question is as follows:

and

where it is a standard inner product on L^2 and u(x,t) is a function. For example; u(x,t) =x*t etc.

(The screenshots is taken from a book)

I want to write a code for finding Matrix U whose elements are u_ij.

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