Add another cube root plotting example to plot doc

[kcrisman]

Gregory Bard of the University of Wisconsin, Stout has the following solution for the always-vexing cube-root plotting issue.

def cuberoot(x):
    return sign(x)*((x*sign(x))^(1/3)) 

plot( cuberoot(x), -4, 4) 

Probably just adding plot(sign(x)*(x*sign(x))^(1/3)) or something to ​the plot doc (search for 'cube') as another example would be sufficient for now. I don't know whether we would want to add a whole new function, since we'd then need one for every odd integer root function... or? Maybe that would be ok, real_nth_root()...

Putting under documentation component, feel free to change if graphics is more appropriate.

[jason]

Can I suggest plot(sign(x)*(x*sign(x))^(1/3), (x,-4,4)) as the code to add?

[jason]

I guess I've always used: plot(lambda x: RDF(x).nth_root(3), (x, -4, 4))

[kcrisman]

Can I suggest plot(sign(x)*(x*sign(x))^(1/3), (x,-4,4)) as the code to add?

That's what I attempted to suggest above.

The point of adding this example was that a number of users (including the originator of this example) thought that students wouldn't know what lambda functions were - not to mention the dot notation. I guess I view them as equally complicated, though the sign solution has the advantage that most of use probably implicitly use this when discussing the absolute value function as a piecewise linear function and not just "make it positive" early in any course where cube roots would be plotted.

[jason]

Replying to kcrisman:

Can I suggest plot(sign(x)*(x*sign(x))^(1/3), (x,-4,4)) as the code to add?

That's what I attempted to suggest above.

Right---I just added the (x,-4,4) notation for the range, since we need to specify the variable because it is a symbolic expression instead of a callable function :).

The point of adding this example was that a number of users (including the originator of this example) thought that students wouldn't know what lambda functions were - not to mention the dot notation. I guess I view them as equally complicated, though the sign solution has the advantage that most of use probably implicitly use this when discussing the absolute value function as a piecewise linear function and not just "make it positive" early in any course where cube roots would be plotted.

Yeah, adding both examples wouldn't be a bad idea. I thought the nth_root example was already there...

[kcrisman]

Can I suggest plot(sign(x)*(x*sign(x))^(1/3), (x,-4,4)) as the code to add?

That's what I attempted to suggest above.

Right---I just added the (x,-4,4) notation for the range, since we need to specify the variable because it is a symbolic expression instead of a callable function :).

Naturally, I was just being terse.

The point of adding this example was that a number of users (including the originator of this example) thought that students wouldn't know what lambda functions were - not to mention the dot notation. I guess I view them as equally complicated, though the sign solution has the advantage that most of use probably implicitly use this when discussing the absolute value function as a piecewise linear function and not just "make it positive" early in any course where cube roots would be plotted.

Yeah, adding both examples wouldn't be a bad idea. I thought the nth_root example was already there...

I meant adding this example; you are right that the other one is already there. Ideally, they'd be together.

Ideally, we'd also have time to create some nice document that answers all such questions, perhaps cribbed from our PREP documents... which we should really finally make ready for the Sage documentation this summer. Not that you don't have other things to do.

Anyway, any thoughts on adding some such function (with a name making it clear it's really just for this purpose) globally for plotting/pedagogical purposes only? This has been discussed before without resolution, just raising the question again.

[jason]

We need more than you and me to address the question of adding a top-level function :). Maybe a post to sage-devel (which will probably just have a few answers, but then at least people can't say they weren't warned).

[benjaminfjones]

Greg Bard and I are colleagues. I definitely support adding this example to the plot documentation next to the lambda function example. I don't think there's any need for a top-level function, though. I think it's better to acknowledge the subtlety rather than sweep it under the rug.

[jason]

After thinking about it, +1 to benjaminfjones' comment.

[kcrisman]

Huh, this seems to have gotten lost. There was recently yet another discussion about this somewhere, but I forget where.

[kcrisman]

Okay, adding an example and a slight reorganization of that section (there are already two examples! but starts with lambda, yuck) and also adding to FAQ, since this is a very FAQ.

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New commits:

​3fe2da9

Added even more plot cube root info, incl. to FAQ

[ncohen]

Good to go !

Nathann