On Sat, Feb 29, 2020 at 5:29 PM Fernando Gouvea <fqgou...@colby.edu> wrote:

> Some years ago in a book review, David Roberts had the idea of plotting an
> algebraic curve using the transformation  (u,v) = (x,y)/(r2 + x2 + y2)1/2,
> which transforms the plane into a circle and makes it easy to visualize the
> projective completion of the curve.
>


> You can see some of his plots at
> https://www.maa.org/press/maa-reviews/rational-algebraic-curves-a-computer-algebra-approach
>
>
These look like 2d parametric plots.
https://doc.sagemath.org/html/en/reference/plotting/sage/plot/plot.html#sage.plot.plot.parametric_plot
To combine two (or more) par. plots on the same axis, just add the
corresponding graphics objects.
There are examples on the pages linked to above.



> I’d love to do this kind of plot for my students. Can anyone offer help on
> how to do it with Sage? (Of course the dream scenario would be to add this
> option to the plot method for curves...)
>
> I’ve been using implicit_plot for most of my examples, which seems to be
> equivalent of using C.plot() when C is a curve.
>
> Thanks,
>
> Fernando
>
>
>
>
>
> --
> ==================================================================
> Fernando Q. Gouvea                                          Editor, MAA
> Reviews
> Dept of Mathematics and Statistics
> http://www.colby.edu/~fqgouvea
> Colby College
> http://www.maa.org/press/maa-reviews
> Mayflower Hill 5836
> Waterville, ME 04901
>
> A training in mathematics is a prerequisite today for work in almost
> any scientific field, but even for those who are not going to become
> scientists, it is essential because, if it is only through speech that
> we can understand what freedom means, only through mathematics
> can we understand what necessity means.
>   -- W. H. Auden
>
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