## 1400 Reputation

18 years, 290 days
University of Twente (retired)
Enschede, Netherlands

My "website" consists of a Maple Manual in Dutch

## Continued...

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.

## Continued...

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.

## Proportional?...

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)} <> {} );`

## Proportional?...

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?...

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?...

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.

## Interpret a as the unit on the axes...

`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] );`

## Interpret a as the unit on the axes...

`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] );`

## Central differention formula...

`> 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`]:`

## Central differention formula...

`> 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`]:`
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