epimetheus's profile - activity

Happy New Year

Hi,

SageMath-9.0.app fails to start on macOS 10.14.6 :

• the file:///Applications/SageMath-9.0.app/Contents/Resources/loading-page.html appears on Firefox
• the log file says :
  /Applications/SageMath-9.0.app/Contents/Resources/sage/src/bin/sage: line 617: exec: python3: not found

However, everything works fine in a term window

• /Applications/SageMath-9.0.app/Contents/Resources/sage/sage --notebook=jupyter

• copy and paste one of these URLs: http://localhost:8888/?token=688ebf86...

Can anyone help ?

Thank you

Thank you !

Hi,

when trying to run SM_black_hole_rendering.ipynb with sagemanifols

https://nbviewer.jupyter.org/github/s...

the cell 28 does not execute well

Process PoolWorker-1: Traceback (most recent call last): File "/Applications/SageMath-8.7.app/Contents/Resources/sage/local/lib/python2.7/multiprocessing/process.py", line 267, in _bootstrap self.run() ...

Can anyone help ?

Thank you

Epi

Thank you for your answer.

I have added these sage commands

((G_exp.expand().simplify_full() - cos(t)*matrix.diagonal([1,1]))/sin(t)).expand().simplify_trig()
((G_exp[1,0].real_part().simplify_trig() + i* G_exp[1,0].imag_part().simplify_trig()).factor())/sin(t)
(-i*sigma_x*u[0]-i*sigma_y*u[1]-i*sigma_z*u[2]).factor()

for checking the expected result (exp(tX)=cos(t)Id+sin(t)X, X in su(2) and det(X)=1).

It is surprising that the sage exp cannot perform it.

Thank you for your answer.

I have added these sage commands

((G_exp.expand().simplify_full() - cos(t)*matrix.diagonal([1,1]))/sin(t)).expand().simplify_trig()
((G_exp[1,0].real_part().simplify_trig() + i* G_exp[1,0].imag_part().simplify_trig()).factor())/sin(t)
(-i*sigma_x*u[0]-i*sigma_y*u[1]-i*sigma_z*u[2]).factor()

for checking the expected result (exp(tX)=cos(t)Id+sin(t)X).

Hi,

does anyone know if sage math is able to successfully calculate exp(G) where G belongs to su(2) ? The sagemath commands are given below :

var('phi theta', domain='real')

u = vector([cos(phi)*sin(theta),sin(phi)*sin(theta),cos(theta)])
u.norm().simplify_trig()

sigma_x = matrix([[0,1],[1,0]])
sigma_y = matrix([[0,-i],[i,0]])
sigma_z = matrix([[1,0],[0,-1]])
sigma_x, sigma_y, sigma_z

var('t',domain='real')

G = -i*t*(sigma_x*u[0]+sigma_y*u[1]+sigma_z*u[2])
G.trace(), (G.det()/t**2).simplify_full(), G.is_hermitian()

 exp(G)

exp(G) returns the following error code :

TypeError: ECL says: Error executing code in Maxima: Unable to find the spectral representation

Thank you for helping.

Epi

rho is a constant

integral(sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x))

returns

2*x/m

HI everybody,

var('x u m')
assume(x>0)
assume(m>0)
assume(m<1)
integral(rho*sqrt(1/(-m*sin(u)^2 +1)),(u,0,x))

returns

2*rho*x/m

Expected answer is

elliptic_f(x,m)

Does anyone know how to fix this ?

Thank you.

Before proceeding, I have installed the giac package 1.2.3.25

integral(x^3/(exp(x)-1),x,0,infinity, algorithm='giac')

returns

ValueError: Unknown algorithm: giac

even after restarting SageMath

What would you advice ?

Thank you.

If I type

integrate(x^3/(exp(x)-1),x,0,infinity) I get -1/15pi^4 + limit(-1/4x^4 + x^3log(-e^x + 1) + 3x^2dilog(e^x) - 6xpolylog(3, e^x) + 6polylog(4, e^x), x, +Infinity, minus)

The command numerical_integral(x^3/(exp(x)-1),0,infinity) gives 6.4939394075

I have two questions :

1. How do I evaluate the limit ?
2. The correct answer is pi^4/15(=6.49393940226683) : why SageMath does not give it with symbolic integration ?

Thanks

The SageMath commands

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

donot give the correct answer which I would expect that is g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

Does anyone know why ?

Here is what I would expect

x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))

Here is what SageMath answers :

 x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))

It does not mix the exponants of x in the numerator with those of x in the denominator.

Thank you

Philippe

This is what I would expect :

x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))

instead of

x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))

Thank you

Philippe

This is what I would expect :

x^(-(Lambda*beta - alpha*mu + 2*alpha - 2*beta - 4*mu + 8)/(mu - 2))

instead of

x^(alpha - beta + 4)/(x^beta)^((Lambda - mu)/(mu - 2))

Thank you

Philippe

the sage command

var('x alpha beta Lambda mu')
f(x) = ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)
f(x).simplify()

does not give the correct answer g(x)

alpha_x = ((x*f.diff(x)/f).simplify_full()).factor()
g(x) = x^alpha_x

does anyone know why ?

thank you

Philippe