Ask Your Question

# Road's profile - activity

 2022-05-15 10:40:57 +0200 received badge ● Popular Question (source) 2021-11-27 21:22:54 +0200 received badge ● Popular Question (source) 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 $$\frac{\sigma_1}{\sigma_2}.$$ 2021-03-20 00:09:03 +0200 marked best answer 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  2021-03-20 00:08:33 +0200 received badge ● Popular Question (source) 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  2021-03-16 08:56:24 +0200 received badge ● Self-Learner (source) 2021-03-16 08:56:24 +0200 received badge ● Teacher (source) 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 2021-03-16 04:56:20 +0200 received badge ● Scholar (source) 2020-11-24 17:34:00 +0200 received badge ● Good Question (source) 2020-11-24 00:02:47 +0200 received badge ● Nice Question (source) 2020-11-23 23:28:39 +0200 received badge ● Famous Question (source) 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  2020-11-11 17:33:16 +0200 received badge ● Popular Question (source) 2019-05-26 15:36:28 +0200 received badge ● Notable Question (source) 2019-05-26 15:36:28 +0200 received badge ● Popular Question (source) 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. 2019-01-08 08:37:20 +0200 received badge ● Famous Question (source) 2018-07-16 21:28:54 +0200 received badge ● Supporter (source) 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. 2018-02-20 21:32:22 +0200 received badge ● Notable Question (source) 2018-02-20 21:32:22 +0200 received badge ● Popular Question (source) 2017-07-27 16:59:11 +0200 received badge ● Student (source) 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.