tmonteil's profile - activity

If you define o as the orbits:

sage: o = group.orbits()

you can get the list of number of vertices in each orbit as follows:

sage: [len(i) for i in o]

If you prefer a vector:

sage: vector([len(i) for i in o])

Does it work when launch the notebook by clicking to the "jupyter noebook" icon, not typing sage -n from the shell ?

What feature of maxima is missing in Sage ? The only code from maxima that i see is the plotting, so i just explained how to move that part in Sage.

You should give more deatils (e.g. your linear proogram, what do you want to restrict, etc). Without more informations, given a linear program p of dimension 2 or 3, you can get its polyhedron as follows:

sage: p.polyhedron()

that you can plot as follows:

sage: p.polyhedron().plot()

You can do BFS and DFS as follows:

sage: G = graphs.PetersenGraph()
sage: G.plot()
sage: list(G.breadth_first_search(start=3))
[3, 2, 4, 8, 1, 7, 0, 9, 5, 6]
sage: list(G.depth_first_search(start=3))
[3, 8, 6, 9, 7, 5, 0, 4, 1, 2]

What you get is the ordered list of vertices visited in both searches, starting from vertex 3.

Regarding coloring, i am not sure about your exact question. If you want to provide colors to the vertices to show the order of visit, you can try somthing like:

sage: G.plot(vertex_colors={rainbow(40)[i]:[v] for i,v in enumerate(G.breadth_first_search(start=3))})

With more striking example:

sage: G = graphs.Grid2dGraph(10,10)
sage: G.plot()
sage: G.plot(vertex_colors={rainbow(500)[i]:[v] for i,v in enumerate(G.breadth_first_search(start=(0,0)))})
sage: sage: G.plot(vertex_colors={rainbow(500)[i]:[v] for i,v in enumerate(G.depth_first_search(start=(0,0)))})

Is it homework ? Before trying to solve such a problem with Sage, how would you have solved it by hand ?

You can add plots in Sage, so in your case:

sage: plot_slope_field(4*y/x+x*sqrt(y),(x,0,4),(y,0,10),headaxislength=3,headlength=3, color='red') + plot(1/4*x^4*(log(x)+2)^2,0,4, ymax=10, color='blue')

k is supposed to be fixed ?

Once you have 1000 karma points, you will be able to do that :)

You have to install the Python packages in the Sage virtual environement. For this, you have to open a terminal (assuming you are using GNU/Linux) and type:

sage --pip install tensorflow

And then, from Sage:

sage: import tensorflow

The solutions are correct but they are not fully simplified.

sage: f= x^2 - (1 + I)*x + 6 + 3*I
sage: solve(f==0,x)
[x == -1/2*sqrt(-10*I - 24) + 1/2*I + 1/2, x == 1/2*sqrt(-10*I - 24) + 1/2*I + 1/2]

For each solution, you can simplify its right-hand-side as follows:

sage: [s.rhs().full_simplify() for s in solve(f==0,x)]
[3*I, -2*I + 1]

How can I solve x^2 - (1 + I)*x + 6 + 3*I == 0 to get answers z = 3*I and z = 1 - 2*I ? When I enter

solve(x^2 - (1 + I)*x + 6 + 3*I == 0, x)

I get

[x == -1/2*sqrt(-10*I - 24) + 1/2*I + 1/2, x == 1/2*sqrt(-10*I - 24) + 1/2*I + 1/2]

Not exactly Markdown, but close to it, you can discover the syntax by editing a post and clicking on the icons on top of the edit section (e.g. B, I, planet, ", 101010, picture,...).

For example bild is obtained with **, italic with *, and so on.

Regarding formatting Sage, you can have a monospaced code either with the button 101010, or by adding 4 spaces at the beginning of very code line.

I edited your other question, you can check the markup by editing it.

Could you please give us some informations so that someone can try to reproduce your problem:

• which version of Sage did you use ?
• which OS ?
• did you install Sage from the binaries, and which ones ?
• did you compile Sage yourself ?

%time is not a function, it is a "ipython magic", you can use it within the command line or a notebook.

I do not know about cocalc, but on sagenb and jupyter you can simply do:

show(A)

Or, if you want to see dots on the nonzero indices:

plot(A)

Or, if you want to see the matrix in a pdf file:

view(A)

Here are some remarks:

First, remove any time-related lines and variables from your function. You can later time it with:

sage: %time Newton_Raphson(f, 0.2)

or even:

sage: %timeit Newton_Raphson(f, 0.2)

so that you get a race between many executions.

Then, you might want to run something like:

sage: %time Newton_Raphson(f,1)

and see that your code is lagging.

To understand what happens, let me suggest to add some debug information just after the while statement:

print start

As you can see, the value of the start real number is expressed as a huge symbolic expression involving exponentials. So you can imagine that handling such expression and testing inequalities with them is very slow (and more and more slow since the size of the expression increases a lot at each iteration).

Since you the Newton Raphson will never reach the zero of the function exactly, wht you are looking for is an approximation, so you don not care to have a long expression for such a point whose only virtue is to be close to the zero. So, yo may want a numerical approximation. For this, you can transform each of foo, dfoo and ddfoo as functions tranforming floating-point numbers into floating-point numbers, which you can do by using the fast_float function.

So just after defining dfoo and ddfoo, it suffice to add the lines:

foo = fast_float(foo)  
dfoo = fast_float(dfoo)                        
ddfoo = fast_float(ddfoo)

Of course, you should not re-define foo before defining dfoo as Sage is not able to compute the derivative of a such numerical function, you prefer exact symbolic computations for such a computation of derivatives.

With such improvement, you can now get:

sage: %time Newton_Raphson(f,0)
CPU times: user 4 ms, sys: 0 ns, total: 4 ms
Wall time: 3.25 ms
(0.8571428346650166, 7, 0.0)

Hmm, apparently the error is zero. The reason is that in your code there is:

start = NR
error = (NR - start)

so of course the error is zero ! perhaps should you permute those two lines.

Could you please tell u show did you define a ?

I am not sure to understand your request, but if it is OK to work with n fixed, does the following help you ?

sage: n = 3
....: var('a','b')
....: assume(a>0,b>0)
....: X = [SR.var('X_{}'.format(i)) for i in range(n)]
....: L = prod(a*b*X[i]^(a-1)*(1-X[i]^a)^(b-1) for i in range(n))

sage: L
X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*b^3

sage: L.diff(a)
-X_0^(a - 1)*X_0^a*(-X_0^a + 1)^(b - 2)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*(b - 1)*b^3*log(X_0) - X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*X_1^a*(-X_1^a + 1)^(b - 2)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*(b - 1)*b^3*log(X_1) - X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*X_2^a*(-X_2^a + 1)^(b - 2)*a^3*(b - 1)*b^3*log(X_2) + X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*b^3*log(X_0) + X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*b^3*log(X_1) + X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^3*b^3*log(X_2) + 3*X_0^(a - 1)*(-X_0^a + 1)^(b - 1)*X_1^(a - 1)*(-X_1^a + 1)^(b - 1)*X_2^(a - 1)*(-X_2^a + 1)^(b - 1)*a^2*b^3

Could you plase make your question more explicit ? Dou you want to count the number of solutions to this equation ? On which domain ?

You should define your deformed cube as a polyhedron, see the inline doc at:

sage: Polyhedron?

See also:

• https://doc.sagemath.org/html/en/them...
• https://doc.sagemath.org/html/en/them...

Could you please provide your current code (in particular the differential equation) ?

Culd you please provide your implementation of the quaternions ?

You can use text3d and add it to the previous plot:

sage: text3d("plop",(1,2,0))

There is a dedicated function for parametric plots:

sage: parametric_plot(x1sol, (ts, 0, 1))

You can use product provided by the itertools Python module:

sage: list(product([0,1,2], repeat=2))
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]

Sure, but what is your question ?

You can draw a sphere as follows:

sage: sphere((0,0,0), size=1, color='red')

You can add plots together:

sage: sphere((0,0,0), size=1, color='red') + sphere((2,0,0), size=1.5, color='green')

You can ensure that all the axes are on the same scale, with aspect_ratio=1:

sage: sphere((0,0,0), size=1, color='red') + sphere((2,0,0), size=1.5, color='green', aspect_ratio=1)