# HG changeset patch # User William Stein # Date 1251004432 25200 # Node ID 2baaec83027ec87a519719d7f528df87938ee1e9 # Parent fb791cdddfca91b9a373e598c97dfe865e6a74b5 trac 6811 -- prime_pi.plot is wrong diff -r fb791cdddfca -r 2baaec83027e doc/en/reference/functions.rst --- a/doc/en/reference/functions.rst Wed Aug 19 22:32:37 2009 -0700 +++ b/doc/en/reference/functions.rst Sat Aug 22 22:13:52 2009 -0700 @@ -12,3 +12,4 @@ sage/functions/special sage/functions/wigner sage/functions/generalized + sage/functions/prime_pi \ No newline at end of file diff -r fb791cdddfca -r 2baaec83027e doc/en/reference/plotting.rst --- a/doc/en/reference/plotting.rst Wed Aug 19 22:32:37 2009 -0700 +++ b/doc/en/reference/plotting.rst Sat Aug 22 22:13:52 2009 -0700 @@ -15,6 +15,7 @@ sage/plot/density_plot sage/plot/disk sage/plot/line + sage/plot/step sage/plot/matrix_plot sage/plot/plot_field sage/plot/point diff -r fb791cdddfca -r 2baaec83027e sage/functions/prime_pi.pyx --- a/sage/functions/prime_pi.pyx Wed Aug 19 22:32:37 2009 -0700 +++ b/sage/functions/prime_pi.pyx Sat Aug 22 22:13:52 2009 -0700 @@ -5,7 +5,8 @@ * R. Andrew Ohana * William Stein -TESTS: +TESTS:: + sage: z = sage.functions.prime_pi.PrimePi() sage: loads(dumps(z)) Function that counts the number of primes up to x @@ -70,7 +71,8 @@ r""" Return the number of primes $\leq x$. - EXAMPLES: + EXAMPLES:: + sage: prime_pi(7) 4 sage: prime_pi(100) @@ -86,18 +88,20 @@ sage: prime_pi(500509) 41581 - The prime_pi function allows for use of additional memory. + The prime_pi function allows for use of additional memory:: + sage: prime_pi(500509, 8) 41581 The prime_pi function also has a special plotting method, so it plots - quickly and perfectly as a step function. + quickly and perfectly as a step function:: + sage: P = plot(prime_pi, 50,100) """ - def __repr__(self): """ - EXAMPLES: + EXAMPLES:: + sage: prime_pi.__repr__() 'Function that counts the number of primes up to x' """ @@ -105,7 +109,8 @@ def __cmp__(self, other): """ - EXAMPLES: + EXAMPLES:: + sage: P = sage.functions.prime_pi.PrimePi() sage: P == prime_pi True @@ -158,8 +163,8 @@ 21151907950 41203088796 - We know this implementation is broken at least on some 32 bit - systems for 2^46, so we are capping the maximum allowed value. + We know this implementation is broken at least on some 32-bit + systems for `2^{46}`, so we are capping the maximum allowed value.:: sage: prime_pi(2^40+1) Traceback (most recent call last): @@ -289,24 +294,30 @@ prime = self.primes[position] return position - def plot(self, xmin=0, xmax=100, *args, **kwds): + def plot(self, xmin=0, xmax=100, vertical_lines=True, **kwds): """ - EXAMPLES: + Draw a plot of the prime counting function from xmin to xmax. + All additional arguments are passed on to the line command. + + WARNING: we draw the plot of prime_pi as a stairstep function + with explicitly drawn vertical lines where the function + jumps. Technically there should not be any vertical lines, but + they make the graph look much better, so we include them. + Use the option ``vertical_lines=False`` to turn these off. + + EXAMPLES:: + sage: plot(prime_pi, 1, 100) + sage: prime_pi.plot(-2,50,thickness=2, vertical_lines=False) """ - primes = prime_range(xmin, xmax+2) - base = self(xmin) - if xmin <= 2: - v = [(xmin,0),(min(xmax,2),0)] - ymin = 0 - else: - v = [] - ymin = base - for i in range(len(primes)-1): - v.extend([(primes[i],base+i+1), (primes[i+1],base+i+1)]) - P = sage.plot.all.line(v, *args, **kwds) - P.axes_range(xmin=xmin, xmax=xmax, ymin=ymin, ymax=base+len(primes)) - return P + y = self(xmin) + v = [(xmin, y)] + for p in prime_range(xmin+1, xmax+1): + y += 1 + v.append((p,y)) + v.append((xmax,y)) + from sage.plot.step import plot_step_function + return plot_step_function(v, vertical_lines=vertical_lines, **kwds) ############# prime_pi = PrimePi() diff -r fb791cdddfca -r 2baaec83027e sage/plot/all.py --- a/sage/plot/all.py Wed Aug 19 22:32:37 2009 -0700 +++ b/sage/plot/all.py Sat Aug 22 22:13:52 2009 -0700 @@ -26,3 +26,5 @@ from plot3d.tachyon import Tachyon from colors import Color, hue, rainbow + +from step import plot_step_function diff -r fb791cdddfca -r 2baaec83027e sage/plot/step.py --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/sage/plot/step.py Sat Aug 22 22:13:52 2009 -0700 @@ -0,0 +1,63 @@ +""" +Step function plots +""" + +#***************************************************************************** +# Copyright (C) 2009 William Stein , +# +# Distributed under the terms of the GNU General Public License (GPL) +# +# This code is distributed in the hope that it will be useful, +# but WITHOUT ANY WARRANTY; without even the implied warranty of +# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +# General Public License for more details. +# +# The full text of the GPL is available at: +# +# http://www.gnu.org/licenses/ +#***************************************************************************** + +def plot_step_function(v, vertical_lines=True, **kwds): + r""" + Return the line graphics object that gives the plot of the step + function `f` defined by the list `v` of pairs `(a,b)`. Here if + `(a,b)` is in `v`, then `f(a) = b`. The user does not have to + worry about sorting the input list `v`. + + INPUT: + + - `v` -- list of pairs (a,b) + + - ``vertical_lines`` -- bool (default: True) if True, draw + vertical risers at each step of this step function. + Technically these vertical lines are not part of the graph + of this function, but they look very nice in the plot so we + include them by default + + EXAMPLES:: + + We plot the prime counting function:: + + sage: plot_step_function([(i,prime_pi(i)) for i in range(20)]) + + sage: plot_step_function([(i,sin(i)) for i in range(5,20)]) + + We pass in many options and get something that looks like "Space Invaders":: + + sage: v = [(i,sin(i)) for i in range(5,20)] + sage: plot_step_function(v, vertical_lines=False, thickness=30, rgbcolor='purple', axes=False) + """ + from plot import line + # make sorted copy of v (don't change in place, since that would be rude). + v = list(sorted(v)) + if len(v) <= 1: + return line([]) # empty line + if vertical_lines: + w = [] + for i in range(len(v)): + w.append(v[i]) + if i+1 < len(v): + w.append((v[i+1][0],v[i][1])) + return line(w, **kwds) + else: + return sum(line([v[i],(v[i+1][0],v[i][1])], **kwds) for i in range(len(v)-1))