On Wednesday, July 18, 2012 2:00:58 AM UTC-4, jason wrote:
>
> On 7/18/12 12:50 AM, Dan Drake wrote: 
> > On Tue, 17 Jul 2012 at 10:27PM -0700, R. Andrew Ohana wrote: 
> >> This is kind of fixed by #11475 (in that prime_pi becomes part of the 
> >> symbolic ring). 
> > 
> > Cool. 
> > 
> >> The bigger issue is that the symbolic ring does sampling for plotting, 
> >> which is horribly inefficient for prime_pi -- something that is solved 
> >> with the custom plotting method for prime_pi. 
> > 
> > Sampling is definitely a poor idea here. How does one access the custom 
> > plotting method? It seems like plot(prime_pi, 5, 100) does so -- but why 
> > then does plot(prime_pi, (5,100)) *not* use it? 
> > 
> > Is there a way to get the plot command to be smart enough to 
> > automatically use the custom method? 
>
> IIRC, if A.plot exists, then plot(A, ...) will call A.plot(...).  I 
> think plot(prime_pi, ...) *is* using the custom plotting method always. 
> The problem is that the prime_pi.plot method is very limited, and 
> doesn't recognize prime_pi.plot((5,100)). 
>

Correct.  Dan, you should have asked me yesterday while I was doing the 
related thing in the workshop - that the only way to plot 
prime_pi(x)-x/ln(x)

is 

plot(lambda x: prime_pi(x)-x/ln(x), (x,3,100))

which as Andrew points out isn't really good, though I suspect the 
recursive algorithm would do decently over small things.  Any ideas on that 
one?

This also causes problems in helping a different participant.  

E = EllipticCurve(...)

plot(E,-3,3)

works but 

plot(E,(x,-3,3))

doesn't. 

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