Nice idea. Thanks.
Fernando
On Tue, Mar 3, 2020 at 6:27 PM Dima Pasechnik <dimp...@gmail.com> 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
> > >
> > > --
> > > You received this message because you are subscribed to the Google
> Groups "sage-support" group.
> > > To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-support+unsubscr...@googlegroups.com.
> > > To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/b1b0c01c-7dfd-0e17-a3d4-61012ab66d8b%40colby.edu
> .
> > >
> > > --
> > > =============================================================
> > > 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
> > >
> > > --
> > > You received this message because you are subscribed to the Google
> Groups "sage-support" group.
> > > To unsubscribe from this group and stop receiving emails from it, send
> an email to sage-support+unsubscr...@googlegroups.com.
> > > To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/6117cc36-6771-179c-2887-38c05305fd58%40colby.edu
> .
>
> --
> You received this message because you are subscribed to the Google Groups
> "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an
> email to sage-support+unsubscr...@googlegroups.com.
> To view this discussion on the web visit
> https://groups.google.com/d/msgid/sage-support/CAAWYfq1gnU%2BH55XmFEueQvPe8JTaiRSJ7G9k0cc8hSbdY2S9Zw%40mail.gmail.com
> .
>
--
==================================================================
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
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-support+unsubscr...@googlegroups.com.
To view this discussion on the web visit
https://groups.google.com/d/msgid/sage-support/CAPON7s9Z3f%2Bmg1XigzT6Vp6J%3D_4dUUOG%2BEWU8CSXNoTVoy7zaA%40mail.gmail.com.
