The whole point of this is to show the behavior of the curve near
infinity, so changing the limits is not an option.
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
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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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=============================================================
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.
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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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