daniel.e2718's profile - activity

Is there a way to export a 3d plot as a pdf file?

I know you can't do p.save('filename.extension') because 3dplot doesn't create a graphics item. But is there a way to do this?

namelist = ['f'+str(i) for i in range(10)]; namelist
for i in range(len(namelist)):
    namelist[i] = lambda x: 1/x^i

1 - create a list of function names (f0, f1, f2, ...)

2 - for each item in namelist

3 - take that that item and make it a function that raises x to a negative power equal to the position of that item (f0(x) = 1/x^0, f1(x) = 1/x^1, ...)

Is this possible?

EDIT:

Made some progress by changing the type of namelist[i] to Expression by var(i)...

Here I link to a worksheet with which I'm having the darnedest trouble...

PlotTest

The code in the worksheet makes it easy to plot many similar plots, and this is a pretty organized way to do it. I got it to work once, but I changed something and made too many changes afterward to get it working again to undo back to my original code.

The problem is in the third cell, obviously. I want to assign to 'a' "plot all of the functions in the list funclist." I realize that they aren't functions, really (they aren't assigned names such as f0,f1,f2, etc), but I'll try to solve that another day. But anyway, how can I set this loop up to add all of these plots and dump them into an object? I need to be able to input 'a' and get a plot containing all of these.

As is evident from the worksheet, I can't use the operator += (though I swear I did the first time).

I would rather not to do it like this:

a = plotlist[0]
for i in range(1,len(plotlist)):
    a += plotlist[i]

Because that requires that I spread out the definition of 'a' and has an unnecessary amount of code. However, that seems to be the easiest way to do it.

But I would like to be able to do it in two lines of code --- for i in plotlist, add all these plots to this object. Or three lines, if I have to initialize 'a' beforehand (give it a type or whatever.)

Is there a way to use the values of solve() without having that pesky 'var == ' in front of it?

in   h = x^2-9; h
out     x |--> x^2 - 9
in   sols = solve(h == 0, x); sols
out     [x == -3, x == 3]
in   sols[0]
out     x == -3
in   h(sols[0])
out     (x == -3)^2 - 9

What the heck is that last line?!

Is there a way to extract the value of sols[0] for use without needing to copy/paste the value?

The Sage 3D plots don't support output in a 2D vector format (like PDF), at least not for now. You can do it by calling matplotlib directly: PDF version of the image below

from mpl_toolkits.mplot3d import axes3d
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
import matplotlib.pyplot as plt
import numpy as np
from matplotlib import rc
rc('text', usetex=True)

rays = [(-3, -2, 4), (0, 1, 0), (1, 0, 0), (2, 1, -4)]
extrapoints = [(-1, -1, 2), (1, 1, -2)]
cones = [[0,1,2],[0,1,3],[0,2,3],[1,2,3]]

poly3d = []
for cone in cones:
    verts = [ rays[i] for i in cone ]
    poly3d.append(verts)

polygons = Poly3DCollection(poly3d, facecolor='green', 
                            linewidths=2,
                            alpha=0.1)
polygons.set_alpha(0.3)

fig = plt.figure()
fig.set_figwidth(13.0/2.54)
fig.set_figheight(9.0/2.54)

ax = axes3d.Axes3D(fig)
ax.scatter3D(*zip(*rays), s=50, c='red')
ax.scatter3D(*zip(*extrapoints), s=50, c='blue')
ax.scatter3D([0],[0],[0], s=20, c='black')

ax.add_collection3d(polygons)  
ax.set_xlabel(r'$X$')
ax.set_ylabel(r'$Y$')
ax.set_zlabel(r'$Z$')
ax.set_xlim3d(-3, 2)
ax.set_ylim3d(-2, 1)
ax.set_zlim3d(-4, 4)

r = rays[0]
ax.text(r[0]-0.2,r[1],r[2], r'${}^{'+str(r)+'}$', 
        horizontalalignment='right',
        verticalalignment='top',
        color='red')

r = rays[3]
ax.text(r[0]-0.2,r[1],r[2], r'${}^{'+str(r)+'}$', 
        horizontalalignment='right',
        verticalalignment='top',
        color='red')

r = rays[1]
ax.text(r[0],r[1],r[2]+0.3, r'${}^{'+str(r)+'}$', 
        horizontalalignment='center',
        verticalalignment='bottom',
        color='red')

r = rays[2]
ax.text(r[0],r[1],r[2]-0.3, r'${}^{'+str(r)+'}$', 
        horizontalalignment='center',
        verticalalignment='top',
        color='red')

r = extrapoints[0]
ax.text(r[0],r[1],r[2]-0.3, r'${}^{'+str(r)+'}$', 
        horizontalalignment='center',
        verticalalignment='top',
        color='blue')

r = extrapoints[1]
ax.text(r[0]+0.2,r[1],r[2], r'${}^{'+str(r)+'}$', 
        horizontalalignment='left',
        verticalalignment='bottom',
        color='blue')


ax.text(-0.2,0,0, r'${}^0$', 
        horizontalalignment='right',
        verticalalignment='top',
        color='black')

# plt.show()

for axis in [ax.w_xaxis, ax.w_yaxis, ax.w_zaxis]:
    axis.get_major_locator()._integer = True
    for t in axis.get_ticklabels(): 
        t.set_fontsize(6)

plt.savefig('fig_NablaBsing.pdf', bbox_inches='tight')

Is there a direct way to apply a function to each entry of a matrix and return the resulting matrix?

A = matrix([[1,2],[3,4]])
B = matrix([[j^2 for j in i] for i in A])

Not terribly hard, but it's not ideal.

*Exactly* what I was looking for! Thanks! EDIT: Good question though. Why doesn't it work if you specify the variable of the function?

I think you want v = function('v') for the first line; the first argument is the name of the function.

Here's the full code:

v = function('v')
u(x) = (v(x) + v(-x))/2
delta = 10^(-90)
u(delta).substitute_function(v, gamma)

I'm puzzled as to why it doesn't work if v is defined as v = function('v', x). Anyone know?

I want to substitute one function for another. Consider this:

v = function('x')
u(x) = (v(x)+v(-x))/2
delta = 10^(-90)
u(delta).subs(v=gamma(x))

The very last line is what I'm trying to accomplish. I know it's the wrong command, but I'm wanting to make the substitution $v(x)\to\Gamma(x)$.

Is there a way along these lines to do such a functional substitution?

I think you're going to be interested in list comprehensions and generator expressions.

Using listcomps, your code compresses to:

sage: funclist = [1/x^i for i in range(10)]
sage: plotlist = [f.plot((x, 1, 10)) for f in funclist]
sage: plot(plotlist)

(Note that I changed the x lower limit to make it look better.)

[BTW, as for your ability to use "a += something", that was almost certainly because you already had an "a" floating around from before.]

If you want to one-line it:

plot([(1/x^i).plot((x, 1, 10)) for i in range(10)])