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2021-03-20 00:25:40 +0200 marked best answer LaTeX Greek names for symbolic variables

Instead of the following:

x,y,z,s1,s2,s3,s4,s5 = var('x,y,z,s_1,s_2,s_3,s_4,s_5')

I want to display s_1, s_2, s_3, s_4, s_5 as $\sigma_1, \sigma_2, \sigma_3, \sigma_4, \sigma_5$. So for example, when I type show(s1/s2) , it would typeset

$$ \frac{\sigma_1}{\sigma_2}. $$

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2021-03-17 00:19:20 +0200 edited question LaTeX Greek names for symbolic variables

LaTeX Greek names for symbolic variables Instead of the following: x,y,z,s1,s2,s3,s4,s5 = var('x,y,z,s_1,s_2,s_3,s_4,s_

2021-03-17 00:18:54 +0200 edited question LaTeX Greek names for symbolic variables

LaTeX Greek names for symbolic variables Instead of the following: x,y,z,s1,s2,s3,s4,s5 = var('x,y,z,s_1,s_2,s_3,s_4,s_

2021-03-17 00:16:08 +0200 edited question LaTeX Greek names for symbolic variables

LaTeX Greek names for symbolic variables Instead of the following: x,y,z,s1,s2,s3,s4,s5 = var('x,y,z,s_1,s_2,s_3,s_4,s_

2021-03-17 00:15:49 +0200 asked a question LaTeX Greek names for symbolic variables

LaTeX Greek names for symbolic variables Instead of the following: x,y,z,s1,s2,s3,s4,s5 = var('x,y,z,s_1,s_2,s_3,s_4,s_

2021-03-16 09:12:24 +0200 marked best answer Kernel error with 9.2 Windows installer 0.6.2

Here's the error message I get in SageMath 9.2 Notebook server console when I just open an empty Jupyter notebook:

[E 23:52:03.742 NotebookApp] Uncaught exception POST /api/sessions (127.0.0.1)
HTTPServerRequest(protocol='http', host='localhost:8888', method='POST', uri='/api/sessions', version='HTTP/1.1', remote_ip='127.0.0.1')
Traceback (most recent call last):
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/web.py", line 1703, in _execute
    result = await result
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 742, in run
    yielded = self.gen.throw(*exc_info)  # type: ignore
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/notebook/services/sessions/handlers.py", line 72, in post
    type=mtype))
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 735, in run
    value = future.result()
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 742, in run
    yielded = self.gen.throw(*exc_info)  # type: ignore
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/notebook/services/sessions/sessionmanager.py", line 88, in create_session
    kernel_id = yield self.start_kernel_for_session(session_id, path, name, type, kernel_name)
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 735, in run
    value = future.result()
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 742, in run
    yielded = self.gen.throw(*exc_info)  # type: ignore
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/notebook/services/sessions/sessionmanager.py", line 101, in start_kernel_for_session
    self.kernel_manager.start_kernel(path=kernel_path, kernel_name=kernel_name)
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/tornado/gen.py", line 735, in run
    value = future.result()
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/notebook/services/kernels/kernelmanager.py", line 176, in start_kernel
    kernel_id = await maybe_future(self.pinned_superclass.start_kernel(self, **kwargs))
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_client/multikernelmanager.py", line 186, in start_kernel
    km.start_kernel(**kwargs)
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_client/manager.py", line 304, in start_kernel
    kernel_cmd, kw = self.pre_start_kernel(**kw)
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_client/manager.py", line 251, in pre_start_kernel
    self.write_connection_file()
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_client/connect.py", line 474, in write_connection_file
    kernel_name=self.kernel_name
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_client/connect.py", line 138, in write_connection_file
    with secure_write(fname) as f:
  File "/usr/lib/python3.7/contextlib.py", line 112, in __enter__
    return next(self.gen)
  File "/opt/sagemath-9.2/local/lib/python3.7/site-packages/jupyter_core/paths.py", line 447, in secure_write
    .format(file=fname, permissions=oct(file_mode)))
RuntimeError: Permissions assignment failed for secure file: '/home/sage/.local/share/jupyter/runtime/kernel-5ecbbfc0-978c-428b-bf7b-3ae1eadf2539.json'. Got '0o644' instead of '0o0600'.
[W 23:52:03.749 NotebookApp] Unhandled error
[E 23:52:03.750 NotebookApp] {
  "Host": "localhost:8888",
  "User-Agent": "Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:86.0) Gecko/20100101 Firefox/86.0",
  "Accept": "application/json, text/javascript, */*; q=0.01",
  "Accept-Language": "en-US,en;q=0.5",
  "Accept-Encoding": "gzip, deflate",
  "Content-Type": "application/json",
  "X-Xsrftoken": "2|c76e4f22|0cebf84dc6b5cb852f3878b5a6f02816|1615866062",
  "X-Requested-With": "XMLHttpRequest",
  "Content-Length": "84",
  "Origin": "http://localhost:8888",
  "Connection": "keep-alive",
  "Referer": "http://localhost:8888/notebooks/notebooks/Untitled.ipynb",
  "Cookie": "username-localhost-8888=\"2|1:0|10:1615866721|23:username-localhost-8888|44:ZDE5MTYwYWQzMTk3NDlmNTkzOGRlMDYxMzdhMDM2NTc=|2ea52166afb14e6831b4349df7eea58fe65ab4e4de70181b2aaba715ab04df0d\"; _xsrf=2|c76e4f22|0cebf84dc6b5cb852f3878b5a6f02816|1615866062"
}
[E 23:52:03.750 NotebookApp] 500 POST /api/sessions (127.0.0.1) 290.02ms referer=http://localhost:8888/notebooks/notebooks/Untitled.ipynb
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2021-03-16 08:47:41 +0200 answered a question Kernel error with 9.2 Windows installer 0.6.2

The error stems from Jupyter insisting on certain permissions for a file: RuntimeError: Permissions assignment failed f

2021-03-16 05:00:53 +0200 asked a question Kernel error with 9.2 Windows installer 0.6.2

Kernel error with 9.2 Windows installer 0.6.2 Here's the error message I get in SageMath 9.2 Notebook server console whe

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2020-11-23 23:19:48 +0200 asked a question latex of elements of multivariate polynomial quotient ring

Here is a block of code:

R = PolynomialRing(QQ, 'a, b, c')
a, b, c = R.gens()
I = R.ideal(a**2 + a + 1)
S = R.quotient(I, names=R.variable_names()).fraction_field()
a, b, c = S.gens()
show(a**2/b**3)  # this looks wrong
latex(a)  # = \text{\texttt{a}}, should just be `a`
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2019-04-30 02:07:59 +0200 commented question Symbolic sum/product of Laurent/power series

c[i] and d[i] are indexed symbolic variables. I'm trying to do symbolic calculation on power/Laurent series and extract the coefficients at the end. The snippet I wrote was my single example in detail. The tricky part about this for me is the symbolic variables n, c[i], and d[i]. I need to coefficients at the end to be expressed in forms of sums or products running over i.

2019-04-26 19:44:06 +0200 asked a question Symbolic sum/product of Laurent/power series

How can I do something like this?

#f = some Laurent/power series in x e.g. 
#a,b,w are symbolic such that e.g. 2*w**2 = 3
f = 1/x + w + a*x + b*x**2 + ((a+b)/w)**2*x**3 + O(x**7)
#g[i] = some power series in x derived from f, c[i], d[i], e.g.
g[i] = (x*f + c[i])/(d[i]*f + x**2)
#product of n first g[i]
#n is symbolic
G = product(g[i], i=1..n)
#extract coefficients of x in G
G.coeff(x,-1), G.coeff(x,0), G.coeff(x,1)

Thank you.

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2018-07-16 20:32:22 +0200 asked a question ImportError: cannot import name polytools

I'm using SageMath 8.2 Notebook to solve a symbolic equation.

But I'm getting "ImportError: cannot import name polytools".

Thank you.

EDIT: Shutting down the notebook and re-opening fixed it.

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2017-07-24 20:49:10 +0200 asked a question NameError: name 'var' is not defined

I'm using Jupyter Notebook on CoCalc. I can't create symbolic variables.

var('a,b,c')

results in NameError: name 'var' is not defined. I tried

from sage.calculus.var import *

but it still doesn't work and gives the same error.

2017-07-14 18:08:01 +0200 asked a question Map between projective curves defined in an extension field

For example, suppose I have the following 2 projective curves:

k = GF(13)
x,y,z = ProjectiveSpace(k, 2, 'x,y,z').gens()
E = Curve(2*x^2 + 8*y*z + 8*z^2)
W = Curve(x^2 + y*z + z^2)

I like to define a map from E to W that involves $\sqrt 2$ and $\sqrt 8$, which do not exist in k = GF(13), but do in an extension of k:

x = PolynomialRing(k,'x').gen()
K = GF(13**2, 'w', modulus=x^2-2)
w = K.gen()

So $w = \sqrt 2$ and $2w = \sqrt 8$. The map I like to define sends $(x:y:z)$ to $(wx:2wy:2wz)$.

In this particular example, it's obvious that $(wx:2wy:2wz) = (x:2y:2z)$; but it's just a simple example do demonstrate the problem.

Something like this doesn't work:

x,y,z = ProjectiveSpace(k, 2, 'x,y,z').gens() #or ProjectiveSpace(K, 2, 'x,y,z').gens()
E.Hom(W)([w*x, 2*w*y, 2*w*z])

Thank you.

2017-06-21 18:11:17 +0200 asked a question Compose Affine/Projective Curve morphism with Elliptic Curve isogeny

When I tried to do this, I got TypeError: ... must be a map to multiply it by Isogeny ...

And when I tried to dehomogenize projective curve morphism in x,y,z by z-coordinate, the remaining variables become x0 and x1. Can I keep them as x and y instead?

EDIT: Example code:

k = GF(23)
x,y,z = k['x,y,z'].gens()
d = k(2)
C = Curve([x^3+y^3+z^3-3*d*x*y*z]) #domain curve
a = d+2
b = 4*(d^2+d+1)/3
E = EllipticCurve(y^2-x^3-(a*x+b)^2) #codomain curve
m = b
n = 4*(d^3 -1)/3
X = m*(x+y+z)
Y = n*(z-y)
Z = -z-y-d*x   
f = C.Hom(E)([X,Y,Z]) #map from C to E
Q = E(2,9,1) #a point on E
g = E.isogeny(Q) #isogeny
g*f #TypeError here