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Unfortunately, i is not really similar to a physical unit but rather to a base vector in two dimensions. Therefore, the ordinary unit display mechanism fails, as it is based on division by a unit and separate display of that unit in the result. SMath can do that with the imaginary unit as well but that is probably not really sensible. I agree that the use of 'i as imaginary unit enables simultaneous usage of i (e.g. as loop counters). The drawback is that there is no way to enforce a consistent notation, as SMath still formats complex results using the original i. I am not inclined to sacrifice consistency just for getting rid of the rule "Never use i as variable name". Typographical alternatives for the imaginary unit cannot consistently been introduced without support by Andrey (or can plugin writers access results formatting?). One could think of an options menu entry "imaginary unit" with alternatives i, I, j, or i without dot etc. The internal representation would need to be different from any allowed variable name (e.g. #i) File Attachment(s):  i.sm (5kb) downloaded 22 time(s).mkraska attached the following image(s): |
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Originally Posted by: mkraska  Typographical alternatives for the imaginary unit cannot consistently been introduced without support by Andrey (or can plugin writers access results formatting?). One could think of an options menu entry "imaginary unit" with alternatives i, I, j, or i without dot etc. The internal representation would need to be different from any allowed variable name (e.g. #i)
I checked it out and must agree with you. Unfortunately, the handling of i in smath is flawed. What it should do is give the option to clear and release the default symbol i for general use when assigning the imaginary unit to some other symbol. The option to release the reservation of i should be true by default with the ability to override the release placed in the user's control. Until this or some other workable strategy for i and the imaginary is implemented in smath, the use of i as anything other than the imaginary is likely to lead to problems. The rule of the road is to forgo use of i for any reassignment and use it and only it as the imaginary unit. Originally Posted by: mkraska Unfortunately, i is not really similar to a physical unit but rather to a base vector in two dimensions. Therefore, the ordinary unit display mechanism fails, as it is based on division by a unit and separate display of that unit in the result. SMath can do that with the imaginary unit as well but that is probably not really sensible.
True the imaginary is not physical in the same sense as mass or a displacement vector, however, I would include it as a unit of measure as I would any unit in a mathematical model. Many units have their own peculiarities (e.g., temperature units) and must be dealt with on case by case basis. The peculiarity of i is that it can be converted to a real (or rotated 90 degrees as it were) by multiplying it by itself. But the one uniform thing among them all is that they are indivisible, intuitively understood reference points for quantitative evaluation. They have no discernible meaning without a quantitative coefficient (even a base unit has 1 understood as its quantitative coefficient). The standard kg and meter are in a vault somewhere in Sevres, France and are examples of 1 unit of standard measures which are specifically defined by the physical prototypes. If we remove the quantity 1 from the prototype, it loses its meaning, showing that the unit itself is abstract when not associated with a quantitative coefficient. As with all units, the imaginary has this same property. I think smath would be served well if physical units and basis vectors of all types were treated using the blue tagging. I will have much more to say about vectors and, as well, the hyperbolic unit (where u^2 = 1, but u =/= 1) in the coming weeks, as I would like to see improvements in smath in the handling of vector math related formatting and automation.
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Originally Posted by: Rising Eagle I think smath would be served well if physical units and basis vectors of all types were treated using the blue tagging. I agree with that, given the handling is consistent. Originally Posted by: Rising Eagle I will have much more to say about vectors and, as well, the hyperbolic unit (where u^2 = 1, but u =/= 1) in the coming weeks, as I would like to see improvements in smath in the handling of vector math related formatting and automation. Mechanics of continua has quite some applications for hypercomplex analysis, thus I am looking forward to your contributions, even if I probably never shall teach this at our university of applied sciences. The symbolic capabilities of our students are comparable to those of SMath. In the same way as teaching vector calculus in 7-term bachelor of engineering courses would be waste of time I wonder if smath has the potential of mastering such advanced topics. I use SMath not because of it's mathematical strength but because of the 2D doc interface, just good enough for homework assignments, simple engineering calculations or demonstration of numerical procedures. The more complex (if not even hypercomplex) the tasks become, the less important is the user interface compared to the core capabilities such as simplification, integration, symbolic solving. Currently in SMath we don't have symbolic integration, eigenvalue solvers, etc. What is the motivation for you to care about SMath if you perhaps are much better off with tools like maxima? I am just curious. This reminds me of the question if it would not be a nice open source project to give maxima a 2D Mathcad like interface. Given that Andrey is heavily distracted from improving the core by making an android version, we should perhaps not expect too much in terms of core functionality. |
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Thanks so much for posting this information.
I knew i wasn't going crazy when i was getting weird results in my sheets. I knew there was some kind of weird namespace collisions going on but couldn't figure it out completely. Even after reading the above explanation, the namespace issues are still going to be a problem.
I thoroughly support the idea of a 'best practice' thread until the kinks in smath can be worked out.
Thanks all,
-Pete
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