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2020-01-08 14:05:47 -0600 asked a question SageMath-9.0.app fails to start on macOS 10.14.6

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

Can anyone help ?

Thank you

2019-04-12 14:26:19 -0600 commented answer multiprocessing.Pool does not work

Thank you !

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2019-04-12 12:50:35 -0600 asked a question multiprocessing.Pool does not work

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

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2018-08-22 10:30:44 -0600 commented answer su2 matrix exponentiation

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.

2018-08-22 10:29:20 -0600 answered a question su2 matrix exponentiation

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).

2018-08-22 06:57:53 -0600 asked a question su2 matrix exponentiation

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

2018-01-26 13:06:35 -0600 commented question integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer

rho is a constant

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

returns

2*x/m
2018-01-25 15:16:50 -0600 asked a question integral(rho*sqrt(1/(-m*sin(u)^2 + 1)),(u,0,x)) gives a wrong answer

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.

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2017-06-08 14:49:42 -0600 answered a question integrate x^3/(exp(x)-1) between 0 and infinity

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.

2017-06-08 12:56:33 -0600 asked a question integrate x^3/(exp(x)-1) between 0 and infinity

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

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2016-11-27 10:41:11 -0600 asked a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4) is not satisfactory

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

2016-11-27 10:33:16 -0600 commented question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)

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

2016-11-27 10:32:16 -0600 answered a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)

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

2016-11-27 07:30:06 -0600 asked a question simplifying ( x^beta )^( (mu - Lambda) / ( mu -2)) * x ^ ( alpha - beta + 4)

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

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2015-05-08 09:45:48 -0600 edited question unable to solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z])

here is the script:

x, y, z = var('x, y, z');
y0 = var('y0');
solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]);
[x^2 + y^2 == 4, (y - y0)^2 + z^2 == 4]

but if:

y0 = 0

solve([x^2+y^2==4, (y-y0)^2+z^2==4], [x, y, z]);

gives the expected answer:

[[x == r1, y == -sqrt(-r1^2 + 4), z == r13, [x == r2, y ==
sqrt(-r2^2 + 4), z == r2, [x == r3, y == -sqrt(-r3^2 + 4), z ==
-r3], [x == r4, y == sqrt(-r4^2 + 4), z == -r4]]

With parameter y0, I would expect:

[x = +- sqrt(4-u^2),
y = u,
z = +- sqrt(4-(u-y0)^2)]

Thank you for helping me.