so it's going to be painful for implicit_plot to work.
That being said, the following tweak runs ok but it's not exactly what you describe.
var('x y u v')
x=u*sqrt(9/abs(1-u^2-v^2))
y=v*sqrt(9/abs(1-u^2-v^2))
pl=implicit_plot(y^2-x^3+x==0,(u,-1,1),(v,-1,1))
pl+=implicit_plot(u^2+v^2==1,(u,-1,1),(v,-1,1))
pl.show()
This other tweak raises an error, I don't see why :
var('x y u v')
x=u*sqrt(9/max(1-u^2-v^2,0))
y=v*sqrt(9/max(1-u^2-v^2,0))
pl=implicit_plot(y^2-x^3+x==0,(u,-1,1),(v,-1,1))
pl+=implicit_plot(u^2+v^2==1,(u,-1,1),(v,-1,1))
pl.show()
>> ValueError: negative number to a fractional power not real
On 03/03/2020 22:15, 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.
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