On Wed, Mar 4, 2020 at 12:20 AM Fernando Gouvea <fqgou...@colby.edu> wrote:
>
> But no, it doesn't work, since it gives a rectangular plot instead of one in
> polar coordinates. But maybe we are closer.
I looked at the labels on the axes, and they do match the ranges of r
and phi, so I don't udnerstand
how it's possible.
>
> I still think implicit_plot should be smarter about values that do not make
> sense.
>
> Fernando
>
> On 3/3/2020 6:26 PM, Dima Pasechnik wrote:
>
> even better:
>
> sage: var('x y u v r phi')
> ....: u=r*cos(phi)
> ....: v=r*sin(phi)
> ....: x=u*sqrt(9/(1-r^2))
> ....: y=v*sqrt(9/(1-r^2))
> ....: implicit_plot(y^2-x^3+x==0,(r,0,999/1000),(phi,-pi,pi))
>
> On Tue, Mar 3, 2020 at 10:28 PM Dima Pasechnik <dimp...@gmail.com> wrote:
>
> On Tue, Mar 3, 2020 at 10:10 PM Fernando Gouvea <fqgou...@colby.edu> wrote:
>
> The whole point of this is to show the behavior of the curve near infinity,
> so changing the limits is not an option.
>
> just paste together a number of rectangles where (u,v) stay inside the
> unit circle.
> (yes, this would need writing a loop, ideally)
>
> Fernando
>
> On 3/3/2020 4:15 PM, Dima Pasechnik wrote:
>
> On Tue, Mar 3, 2020 at 8:20 PM Fernando Gouvea <fqgou...@colby.edu> wrote:
>
> Here's what I ended up trying, with r=3:
>
> var('x y u v')
> x=u*sqrt(9/(1-u^2-v^2))
> y=v*sqrt(9/(1-u^2-v^2))
> implicit_plot(y^2-x^3+x==0,(u,-1,1),(v,-1,1))
>
> That gives an error:
>
> /opt/sagemath-8.9/local/lib/python2.7/site-packages/sage/ext/interpreters/wrapper_rdf.pyx
> in sage.ext.interpreters.wrapper_rdf.Wrapper_rdf.__call__
> (build/cythonized/sage/ext/interpreters/wrapper_rdf.c:2237)()
> 74 for i from 0 <= i < len(args):
> 75 self._args[i] = args[i]
> ---> 76 return self._domain(interp_rdf(c_args
> 77 , self._constants
> 78 , self._py_constants
>
> ValueError: negative number to a fractional power not real
>
> Is there some way to tell implicit_plot to stay inside u^2+v^2\leq 1? Or to
> ignore complex values?
>
> I'd just change the limits of u and v to make the rectangle of the
> values you plot in, anyway,
> to well stay inside the unit circle.
>
> The equivalent code seems to give the correct graph in Mathematica.
>
> Fernando
>
> On 2/29/2020 5:29 PM, Fernando Gouvea 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
>
> 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
>
>
> --
> =============================================================
> Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
> Carter Professor of Mathematics
> Dept. of Mathematics and Statistics
> Colby College
> 5836 Mayflower Hill
> Waterville, ME 04901
>
> If little else, the brain is an educational toy.
> -- Tom Robbins
>
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> --
> =============================================================
> Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
> Carter Professor of Mathematics
> Dept. of Mathematics and Statistics
> Colby College
> 5836 Mayflower Hill
> Waterville, ME 04901
>
> If little else, the brain is an educational toy.
> -- Tom Robbins
>
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>
> --
> =============================================================
> Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
> Carter Professor of Mathematics
> Dept. of Mathematics and Statistics
> Colby College
> 5836 Mayflower Hill
> Waterville, ME 04901
>
> If little else, the brain is an educational toy.
> -- Tom Robbins
>
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