I just wanted to get into attention this thread once more. There were problems of rather different results using different optimization and different solvers. Those problems still remained unexplained.

Just look at the picture and try the attached file. Changing the symbolic/numeric/none optimization and using/not using eval() for the yellow regions, there will be different results. This time, we will get different results - sometimes scalars, sometimes vectors.

Regards,
Radovan

Edited by user 23 May 2013 11:46:21(UTC)  | Reason: Not specified

Or this one

EDIT: This is not good by all means. Something has to be done about it.

Edited by user 24 May 2013 18:00:33(UTC)  | Reason: Not specified

The reason for the problem is the type-unawareness of the symbolic optimization, as was already discussed in the Transpose function bug topic.

Thus, what can be done? When SMath does symbolic optimizations, certain assumptions are made (just like operators being scalar). Strictly taken, you would need to add a type checking instruction to any definition that is optimized under such assumptions. Alternatively you could block invalid optimizations by providing type information. Function arguments that are to assume matrix values would require to be marked as such. Otherwise matrix arguments are to be refused by the function.

I'd propose to use the ~ character including the boldface markup for matrix valued variables.

The drawback for me would be that the ~ character is inaccessible in SMath with german keyboard layout (acts as hotkey for boolean =)

Boldface marking matrices and vectors is quite common in engineering textbooks, thus this would be easy to comprehend for most users.

Currently, the ~ character is used for absolute variables. I never used this concept and have never seen any example from other users. If I remember correctly, Andrey announced this feature as essential for animations to work. However, this does not seem to require any user access to such variables. Thus I think that dedicating the math region capability to show boldface symbols to matrix and vector variables would be welcomed by most users.

Look at the attached image: Wouldn't that be nice? Boldfacing the function name would indicate that matrix values are expected to be returned. The boldface 1 would preferrable be interpreted as unit matrix of appropriate size. Alternatively, this could mean a matrix of all ones just like boldface zero would be a zero matrix. Unit matrix could be a boldface I.

Edited by user 25 May 2013 00:31:13(UTC)  | Reason: Not specified

That is how it is done in maple. It would be important to provide operator forms for the special functions.
The operators could be equipped with different (e.g. significantly larger) placeholders. If you type variables into them, then they are automatically boldfaced.

would it possible to use macron for vectors ? Custom special characters in SMath for vectors, just adding a bar (overline) over a letter.
You would type onto the canvas: vecg and automagically it'd be converted to ḡ
or converted to some calligraphical font.

Edit :

It would be faster, typing three times 'v' like vvvg to obtain ḡ
or just a toggle key working like CapsLock.

Edited by user 17 June 2013 15:16:01(UTC)  | Reason: Not specified

As you said I didn't put much thought and left my suggestions as loose ideas.
I rather had in mind this three "vvv" for any matrix like a fast to type shortcut unlikely to be a user defined function.
vvvg plus enter would become ḡ and this variable would be recognized by SMath as a matrix with undefined dimensions, the program would warn you about dimensions when needed and there'd be a dimensions indication in the dynamic assistance. Later on you would define ḡ as usual with ctr+m
I don't know if this makes sense, surely other fellows can give far better suggestions, maybe RisingEagle or even Andrey

Edit:

Again i'd prefer a toggle buton/key to enter matrix notation.
Who knows if it'd be easier for the current symbolic engine to detect which are the proper operations for the expression that the user is entering. SMath could map the vectorial operators required in that very same moment.
All in all my proposal would be: press key toggle and type one or more letters; press again the toggle and you'd get a matrix variable (I don't know if it'd be possible to put an overline ); hopefully SMath may have fewer problems to detect the correct operators if vectors are declared while the user enters the expression.

Edited by user 17 June 2013 15:16:55(UTC)  | Reason: Not specified

I have some follow-up thoughts.

There has been an issue discussed that smath can have misleading presentation where the internal encoding of formulas defined by the user may not match the user's intended meaning of the formula and the user may very well be unaware of the mismatch. This arises, for example, when one defines a formula under the numerical flag when one meant to define it under the symbolic flag. While the rules that smath follows are consistent (except, of course for bugs), the user interface is not friendly enough to keep the user fully cognizant of the internal encodings of a formula that smath may assign to a user's formula definition. The dynamic assistance helps, but doesn't go far enough. Ideally, the user interface should invoke intuitive impressions in the user's mind that are perfectly aligned with smath's internal encodings and representations. The following thoughts are intended to address this issue, though it certainly is not a full correction of the problem by any means. It will be clear how these thoughts relate to the scalar/vector discussion in this thread.

(1) using a tabbed presentation of worksheets would allow smath to provide its own non-worksheet tabs to provide users with extra information. The information I have in mind and would like to see is a tab containing a formatted presentation of the variables and formulas declared with their type properties (e.g., real, integer, vector, mxn matrix, etc.), their symbolic vs numerical flag in force at the time of declaration, and any other properties that might be relevant. This display is similar to a textbook showing the notation used throughout the book. The formatting would be logically collated in a way that makes sense, e.g., having all reals collected together, having all vectors collected together, etc. Or it could be better formatted in chronological order - user's choice. This declarations tab would be an information display that shows how smath encodes all formulas or variables, e.g., f = x + a would be shown as f = x + 2 if a is set equal to 2 before the declaration (whatever is shown in dynamic assistance is what would be seen). Any reuse or overloading of a variable or function would be seen clearly (sometimes one inadvertently reassigned a variable name, forgets that one has already used it, or is not fully cognizant of the smath environmental conditions surrounding the declaration).

(2) a more direct display of such things would be to have a mode invoked by the press of a button that shows the worksheet where all declarations are followed on the right by a grey highlighted region showing an equals sign and the smath encoding, e.g., f = x + a <grey area> = x + 2 <end grey area>.

(3) a left pane margin area that shows a warning when declarations in the worksheet to the right are making use of a previously defined variable name, are overriding an smath default, or are denied the override (as in the case with i).

Edited by user 15 June 2013 16:13:21(UTC)  | Reason: Not specified

A few more suggestions about user interfaces:

- There could be more views like the output from the view menu, a sort of a few inspectors of the worksheet properties (variables, operators, highlighting of elements according to code colors, search..), it could be something look a simplified version of the addon for Firefox "Firebug".

- I've just seen a gui control that may be of inspiration, the minimap from the text editor "Sublime Text". This kind of view could be useful for large worksheets, bookmarking, search.. see it in action in this video.

- About boldfacing for matrices, it'd be a really good looking notation. The problem is just that SMath could not use this formatting style for text in general, that's why I suggested a couple of alternatives.

Edited by user 17 June 2013 16:47:30(UTC)  | Reason: Not specified

Precisely I wonder how you got to apply the boldface style, I guess by adding some tag to the xml file.

Wouldn't be sort of a mess to mix boldface both in text and math regions ? I mean if SMath were to follow this matrix notation, shouldn't boldface be restricted to this sole purpose ?