You have to change more. Consider which variables you want to be a list, a table or a Matrix.
If you wish to append x to the list r you must do:

r := [ op(r), x ]

There is no need to use a Vector for B and C.
You can simply do

C :=abs~( ar[y]-~ec );  # mind the tilde

You haven't initialized ar, so an assignment ar[y] := ... makes ar a table; in your case: a table of lists.
If ar[y] is a list, then C is also a list.

You have to change more. Consider which variables you want to be a list, a table or a Matrix.
If you wish to append x to the list r you must do:

r := [ op(r), x ]

There is no need to use a Vector for B and C.
You can simply do

C :=abs~( ar[y]-~ec );  # mind the tilde

You haven't initialized ar, so an assignment ar[y] := ... makes ar a table; in your case: a table of lists.
If ar[y] is a list, then C is also a list.

What do you mean by (only) "manipulating symbols"? If a and b are supposed to be products of symbols, then "proportial" means: "a and b have at least one symbol in common" You can do, for example:

evalb( {op(a)} intersect {op(b)} <> {} );

What do you mean by (only) "manipulating symbols"? If a and b are supposed to be products of symbols, then "proportial" means: "a and b have at least one symbol in common" You can do, for example:

evalb( {op(a)} intersect {op(b)} <> {} );

What error message do you get?

I don't get an error message, but only a very ugly document. Is that your problem? The worksheet that you have exported to LaTeX seems not meant for publication.
I see for example a latex(...)-command. That outputs a LateX code of an expression. If export the worksheet to LaTeX, this LateX-code will be simulated in LaTeX.

So choose clearly for one of the options:

• make a nicelooking worksheet, that you want to print as it is, and export to LaTeX;
• translate some expressions to latex, copy the output and paste in a LaTeX document.

What error message do you get?

I don't get an error message, but only a very ugly document. Is that your problem? The worksheet that you have exported to LaTeX seems not meant for publication.
I see for example a latex(...)-command. That outputs a LateX code of an expression. If export the worksheet to LaTeX, this LateX-code will be simulated in LaTeX.

So choose clearly for one of the options:

• make a nicelooking worksheet, that you want to print as it is, and export to LaTeX;
• translate some expressions to latex, copy the output and paste in a LaTeX document.

plot( [cos(t)^3, sin(t)^3, t=0..2*Pi], 
       tickmarks=[[-1="-a",-0.5="-a/2", 0.5="a/2", 1="a"]$2] );

plot( [cos(t)^3, sin(t)^3, t=0..2*Pi], 
       tickmarks=[[-1="-a",-0.5="-a/2", 0.5="a/2", 1="a"]$2] );

@amrramadaneg

> dθ:=2*Pi/M: M:=100:
> θ[1] := 0: for q to M+1 do θ[q+1] := θ[q]+dθ; end do: 

This makes θ a table:

> whattype(eval(θ));
                             table

Better is to make θ a list (or vector):

> θ := [ seq( n*θ, n=0..M+1 ) ]:
> x := cos~(θ):

Now you can approximate the values of the derivative:

> xdot := [`undefined`,seq( evalf((x[i+1]-x[i-1])/(2*dθ)), i=2..M ),`undefined`]:
> plot( [seq( [θ[i],xdot[i]], i=2..M )] );

Second derivative:

> x2dot := [`undefined`,seq( evalf((x[i+1]-2*x[i]+x[i-1])/(dθ^2)), i=2..M ),`undefined`]:

@amrramadaneg

> dθ:=2*Pi/M: M:=100:
> θ[1] := 0: for q to M+1 do θ[q+1] := θ[q]+dθ; end do: 

This makes θ a table:

> whattype(eval(θ));
                             table

Better is to make θ a list (or vector):

> θ := [ seq( n*θ, n=0..M+1 ) ]:
> x := cos~(θ):

Now you can approximate the values of the derivative:

> xdot := [`undefined`,seq( evalf((x[i+1]-x[i-1])/(2*dθ)), i=2..M ),`undefined`]:
> plot( [seq( [θ[i],xdot[i]], i=2..M )] );

Second derivative:

> x2dot := [`undefined`,seq( evalf((x[i+1]-2*x[i]+x[i-1])/(dθ^2)), i=2..M ),`undefined`]: