jepstra's profile - activity

@tmonteil Thank you very much for the answer. It works perfectly. However, I would like to show the input cell and also the input code, for educational purposes. I'll edit the question to include this nuance. Thanks again!

I would like to embed a Sage Cell in a webpage whose content comes from a GitHub .py file, so that changes in this file are immediately shown in the webpage. I have tried to use javascript / jquery like this (with the standard scripts in the head) and with some variations:

<div class="sage"><script type="text/x-sage" id="sage1"></script></div>
<script>$('#sage1').load("https://rawgit.com/path_to_the_file.py");</script>

and it sometimes work, but not always. I guess it has to do with the order of all the scripts involved in the process. Which would be the most appropiate and clean way to inject such code in a Sage Cell?

EDIT: I would like to show the input cell together with the input code, for educational purposes. So the content of the input cell has to be replaced with the content of the .py file.

I'm trying to plot several algebraic surfaces, most of which have singularities and other especial properties. Using implicit_plot3d and viewer='threejs' works fine for instance

var('x,y,z')
p=x^3+y^3+z^3+1-0.25*(x+y+z+1)^3
r=5
color='aquamarine'
s = implicit_plot3d(p==0, (x,-r,r), (y,-r,r), (z,-r,r), plot_points=50, region=lambda x,y,z: x**2+y**2+z**2<=r*r, color=color)
s.show(frame=False, viewer='threejs')

But when increasing plot_points=100, SageCell does note return any output (demo) (in a Sage Notebook, everything works fantastic). I guess the query may be too hard for SageCell...

Is there a way to optimize the code / query for SageCell to plot algebraic surfaces with acceptable quality?

@j.c. excellent, really!

Is there a nice way to combine MatrixPlot with something else to have a label in each cell such as in this picture?

@eric_g thank you very much!!

Thank you very much for your comment and attention!! I'm afraid I'm not very used to the code inside Sage... but I hope I may contribute to SageMath in the future.

I guess there might be some mistake in my code, but I cannot use plot_vector_field3d and show the result with three.js viewer. The code is

var('x y z')
f = (x, y, z)
show(plot_vector_field3d(f, (x,-3,3), (y,-3,3), (z,-3,3), aspect_ratio=1), viewer='threejs')

and it only shows an empty box. How to explain this behaviour?

I am trying to write some code to plot a function of an integral whose integrand depends on two variables, much like the following:

a = var('a')
b = var('b')
plot3d(numerical_integral((x+a+b), 0, 1, params=[a,b])[0],(a,0,1),(b,0,1))

This code raises an error NotImplementedError: free variable: b. Which would be the correct way to implement this code?

@nbruin Works like a charm!! This was the way I needed to reduce the scope of the cython environment. I didn't know how to do it.

@emmanuel-charpentier I have added a minimal working example (of course the actual code is much larger) that does not compile neither in a Sage notebook nor a SageMathCell. Could you try it? Thank you very much!

I'm trying to make an interactive applet to visualize the Mandelbrot Set, much in the way of the implementation of interactive fractals (wiki.sagemath.org/interact/fractal#Exploring_Mandelbrot - cannot copy full link because of not enough karma ;-))

But I'd like to embed the applet in a webpage using SageMathCell, and for this all the code must be encapsulated in just one cell, something in the following scheme

%cython
def function(...)
    ...

@interact
...

Unfortunately, %cython and @interact behave badly together, because the latter is unknown to the former (just try to join the code in the two cells of the example above or try the following minimal working example

%cython
def square(float x0):
    return x0*x0

@interact
def _(x0=-2.5):
    print(square(x0))

which, surprisingly enough, raises different errors in a online Sage Cell and in a Sage Notebook Cell)

Which would be the smartest way to mix everything up? Any suggestion is highly appreciated.

@tmonteil Thank you very much! This is exactly what I needed

This question is about writing some code that factors a desired polynomial within $\mathbb{Q}$, $\mathbb{R}$ and $\mathbb{C}$ for educational purposes.

So far, I have the following code:

@interact
def _(p = input_box(default=x^5 + x^4 - 8*x^3 + 11*x^2 - 15*x + 2, label = 'P(x) = ')):
    q.<x> = PolynomialRing(QQ, 'x')
    r.<x> = PolynomialRing(RR, 'x')
    c.<x> = PolynomialRing(CC, 'x')
    a.<x> = PolynomialRing(AA, 'x')
    qp = PolynomialRing(QQ, 'x')(p)
    print(factor(qp))
    rp = r(p)
    print(factor(rp))
    cp = c(p)
    print(factor(cp))
    ap = a(p)
    print(factor(ap))

whose output is

(x - 2) * (x^4 + 3*x^3 - 2*x^2 + 7*x - 1)
(x - 2.00000000000000) * (x - 0.147637797932293) * (x + 3.96552349222940) * (x^2 - 0.817885694297105*x + 1.70805524786870)
(x - 2.00000000000000) * (x - 0.408942847148552 - 1.24129810909174*I) * (x - 0.408942847148552 + 1.24129810909174*I) * (x - 0.147637797932293) * (x + 3.96552349222940)
(x - 2.000000000000000?) * (x - 0.1476377979322930?) * (x + 3.965523492229398?) * (x^2 - 0.8178856942971048?*x + 1.708055247868697?)

The factorization is perfect, but I would like the output to be symbolic whenever possible (ie. written with radicals instead of decimals). I know about the use of the ring 'AA' and that the numbers ending with '?' may be translated into symbolic, but I do not know the smartest way to do this.

Which would be the smartest way to achieve this goal? In the same way, ideas to improve the previous code are also welcome