As tomleslie said, "*Maple now has two "modes" (Worksheet and Document) and two "input methods" (1D input and 2D input) - so overall you have four choices of "user interface""*

Unlike his and other's opinions, I think that worksheet mode + 2D-Math display of input is the best option, together with the (preferences) option: “How should Maple handle the creation of a new Math Engine?” definitely: “Ask each time a new document [or worksheet] is created”.

My rationale:

Unlike document, in worksheet mode, it is clear where the text is and the math. Visually, right away, because of the prompts. And you can still have math within the text (press Shift+F5 within text to write math, or write it as text using Maple syntax, then mark with the mouse and convert to 2D Math). The fonts are also times new roman italics, which resembles LaTeX standard math concretely more than courier new and fonts like that one.

Then let me say that there is the Maple syntax. Not 1D Maple syntax and 2D Maple syntax. But then, unlike in "1D Math input", when you use "2D Math input" the single Maple syntax is displayed in a way that resembles the way we write formulas with paper and pencil. E.g. exponents are displayed as superscripts, fractions as fractions and, automatically, there is a space surrounding the +, *, =, :=, ->, etc. symbols. Altogether, my brain reads formulas faster and clearer.

Note this my opinion has *nothing* to do with whether I write programs. As most people here know, I do write programs, since 1996 till today. In fact, I have this opinion after writing a significant amount of Maple programs when there was no 2D-math, and after realizing (in 2008) that on average I understood significantly faster (therefore code ideas also faster) when deriving knowledge using 2D-Math display of input. About the bugs mentioned by others in 2D-Math: post them, they are being fixed, nowadays faster than in the past.

About “Ask [whether to share an existing computational engine or start a new one] each time a new document is created”, with the (non-default) choice of “Ask each time a new document is created”, you have an implementation of the paper and pencil concept of draft computation. You can have a clean worksheet-computation, and in the middle, you may want to try something regarding the next step, using all the assignments and intermediate results you already have: just open a new worksheet sharing the kernel (computational engine) where you can (draft) experiment all you want. Then switch back to the main clean worksheet to continue. Other times the experiment needs to be done with a completely clean, new engine, so choose 'new engine' and again you can do experiments without messing your clean worksheet-computation.

Another good choice (doesn't work right in current Mac OS, the system I use) is to open new worksheets in new windows, which allows you to compare two computations side by side.

Edgardo S. Cheb-Terrab

Physics, Differential Equations and Mathematical Functions, Maplesoft