Here's a first attempt at imitating your first link:
{{{
var('x,y')
ngamma = n(euler_gamma)
def dirich(r):
return r*log(r)+(2*ngamma-1)*r
def lattice_pts(r):
tab = [[i,j] for i in range(1,ceil(r)) for j in range(1,ceil(r))]
tab2 = [q for q in tab if q[0]*q[1] <= r]
return tab2
@interact
def lattice_plot(r = slider(1,20,.05,default = 15.6)):
var('x')
cr = Integer(ceil(r))
p = plot(r/x,1,cr, plot_points = 200)
pts = points([[i,j] for i in range(1,cr) for j in range(1,cr)],
rgbcolor = (0,0,0), pointsize = 1)
lpts = lattice_pts(r)
lpts_gr = points(lpts, rgbcolor = (0,0,1))
html('Number of lattice points = ' + str(len(lpts)))
html('Dirichlet estimate = ' + str(dirich(r)))
show(p+pts+lpts_gr, figsize = [5,5], xmin = -1, xmax = cr, ymin =
-1, ymax = cr)
}}}
On Jan 14, 11:21 pm, kcrisman <kcris...@gmail.com> wrote:
> Dear support,
>
> I would like to (easily) plot an integer lattice and then be able to
> highlight certain points on it for a class. Basically, I want to be
> able to easily do (a static version of, not necessarily manipulate)
> what the Mma
> Demonstrationhttp://demonstrations.wolfram.com/LatticePointsUnderAHyperbola/
> does. The code for this demo looked extremely unhelpful. A related
> one that would be very helpful
> ishttp://demonstrations.wolfram.com/ModularArithmetic/,
> (which is similar to some of the things the hopefully soon-to-be open
> source PascGalois project does).
>
> I suspect that matrix_plot or whatever would in theory be able to do
> at least some of this (like the second one) but I don't think this
> would give me labeled rows and columns, and I have no idea how to use
> any regular plotting commands to do it without pretty much literally
> putting in every line and point by hand, which is quite daunting.
>
> I know this is possible in Sage, but I am wondering if there is a way
> that is slick enough that I would actually want to do it (as opposed
> to what I would do, which would involve too many loops and points and
> errors trying to get them to look nice). Not asking for mockups of
> the demos above, just for hints as to how (or whether) one might
> easily get nice matrix_plot-esque modular things or nicely labeled
> wire-screen plots like in these examples.
>
> Thanks,
> - kcrisman
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