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Labels: Type-Enhancement Priority-Medium Documentation

New issue 3915 by [email protected]: Ideas for improving the tutorial
http://code.google.com/p/sympy/issues/detail?id=3915

Adapted from a comment on https://github.com/sympy/sympy/pull/2106:

Some things I would like to see done in the tutorial.

- [ ] Write something about pattern matching and `replace`
- [ ] Expand the advanced expression manipulation section. The main issue here is that I got stuck on what the actual way we should recommend doing things should be. I originally thought it was `atoms/xreplace`, but it seems this is wrong, because it doesn't handle nested replacements correctly. There are also questions of the invariant. - [ ] Move the IPython notebook exercises from http://certik.github.io/scipy-2013-tutorial/ to SymPy itself. There are some issues with this, such as where the best place to put these would be, and what to do with the IPython doctester. - [ ] Write more interesting examples for the end of the sections. Right now, we just have the continued fractions example. I'd like to have more things like that, to lighten up the discussion, and to show that SymPy really is useful to solve mathematical problems.

Furthering this last point, at SciPy, Ondrej showed some notebooks of some things he has used SymPy for in his actual research. It resonated with many people there, partly because they too were physicists, and partly just because it showed that this mathematical manipulation tool can actually be used to compute something useful at the end of the day. It would be nice to have more of this sort of things, and have it prominently linked to from the docs. Our examples tend to focus on the physics (because that is what Ondrej does), but we should focus on a wide range of applications: physics, education, numerical calculation, and pure mathematics, among others.

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