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 insage.ext.interpreters.wrapper_rdf.Wrapper_rdf.__call__
(build/cythonized/sage/ext/interpreters/wrapper_rdf.c:2237)()
74 for ifrom 0 <= i< len(args):
75 self._args[i] = args[i]
---> 76return 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?
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)/(r^2 + x^2 + y^2 )^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
--
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Fernando Q. Gouvea Editor, MAA Reviews
Dept of Mathematics and Statistics http://www.colby.edu/~fqgouvea
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can we understand what necessity means.
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=============================================================
Fernando Q. Gouvea http://www.colby.edu/~fqgouvea
Carter Professor of Mathematics
Dept. of Mathematics and Statistics
Colby College
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