Dear Prof Crisman, Prof Coleman, and perhaps Prof Dündar, On the specific issue of symbolic manipulation inside of physics formulas, there's a little bit of risk because I haven't taught a course that uses that. The last time I took such a course would have been the Summer of 1996 or 1997. (I'm not certain.) So, it has been a while! :) With that in mind, would you both please examine these two examples?
The first is pretty pedestrian, just converting Newton's Inverse-Square Law of Gravity to polar coordinates. https://sagecell.sagemath.org/?z=eJxNzUsKgzAUheG54B4OdpJYsDRxVHCqu1BsURR8tF5tDaV7bx6CDjK48H8n73JiQYoMfVHpR1ihMDUj5qaay4D7nu9Vr-GKBCmSBFmow9CEF7A1FzhD5UJnJ-hM6kyZTC-E1A7MrtgRasYPM0vcDgpdmiui5U7su-JmzWOkzfz4boQz0hmxGbWZ_Z-jkc7EzsiI2v7ZtbUq6qXr2CGM-R8sr02-&lang=sage&interacts=eJyLjgUAARUAuQ== The second considers two electric charges of q_1 Coloumbs, located at (0, L) and (0, -L). Another charge of q_2 Coulombs is located at (x,y). The example computes the Coulomb's Law force, again in polar coordinates. Of course, if rho is fairly large, then this physical arrangement can be considered equivalent to an electric charge located at the origin, but with a charge of 2q_1 Coulumbs. I used a Taylor expansion of b=1/rho at b=0 (i.e. rho=infinity), of the sixth degree, and converted back from b's to rho's. Accordingly, we get some rho^4 and rho^6 terms, with and without even powers of either sin(theta) or cos(theta), depending on which simplify command is chosen. <goog_873518195> https://sagecell.sagemath.org/?z=eJx1kMlugzAURfeR8g9X2cQmlIQxg8Q2q3xDIkiZVAoJhhZU9d9r-6GWVs0Cybx3zvWV36KGLY54uSS4X2z5OegxoMlrtHnSRjghXvD5LAvTrrq2RV2xZbaUg3wyyNVgPkvulY0QR4ShCjRkoKEC12D92cEKbHg68bPD5fHBfqX3Kkzk9TtTiVwHOzJY_VmiiwX76HFQHY1rLZjuyT_5j-OQ45LjjM4wOqKo_nFccjxy3NFR73CAvY6nqEeoT6hnieL1VhbpcEm7smQT0CcwkGDGYq7epY2Gsm6YEn2ryQXjJmITGxMBJmZA5pauCP5egZGEZojdEbsdm8e6t-z_3RwaInhP8O5Bd2iEUHtD7N5K-ltUPf-C5JJ_AcUQqXY=&lang=sage&interacts=eJyLjgUAARUAuQ== It might be cool to make a plot of the coordinate plane, and see for which points this approximation is accurate to within +/-1%. Is this the sort of thing that is desirable? Is it too easy? too hard? Is the physics correct? Perhaps you had something completely different in mind? Would degree 8 be better? I can easily add this as a new section, late in Chapter 4. ---Greg On Friday, May 29, 2020 at 10:51:02 AM UTC-5, kcrisman wrote: > > >> >> Symbolic manipulation, substitutions, simplification for basic physics >> formulas. I have done some limited symbolics with Mathematica, but I just >> had to retire for medical reasons and can't personally justify the cost. I >> have heard good things about Sage symbolic manipulation capabilities, but >> so far I have not seen any really good discussion on it, particularly for >> the newest version. I apparently tried to join the Sage bandwagon right >> when so many changes took place, and many older code examples just don't >> seem to work right. If you had a discussion on symbolics it would be a >> no-brainer to buy your latest edition. >> >>> >>> > That is true, as a more "advanced" section. See e.g. > https://math.stackexchange.com/questions/2383818/sagemath-replace-an-expression-in-a-formula-by-a-function-define-previously > > for one of the many widely scattered examples of where to find info on > doing this well :-( > -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-edu/23c5ae55-7939-4ff3-8aa1-64d7b1d9b06co%40googlegroups.com.
