2022-06-29 08:22:23 +0200 received badge ● Famous Question (source) 2020-12-09 04:14:01 +0200 received badge ● Famous Question (source) 2020-12-03 16:50:30 +0200 received badge ● Notable Question (source) 2020-04-01 09:20:27 +0200 received badge ● Nice Question (source) 2020-04-01 09:17:13 +0200 received badge ● Popular Question (source) 2020-01-27 20:47:54 +0200 received badge ● Popular Question (source) 2019-06-08 19:51:35 +0200 received badge ● Notable Question (source) 2019-05-28 14:39:33 +0200 received badge ● Notable Question (source) 2019-05-04 17:42:38 +0200 asked a question MatrixSpace quotientRings I'm trying to work with a quotingring of a matrix space. Now I use the following code. But since $n$ is my modulus I expect my second matrix to be equal to $M_1$ in this quotient ring. But it's like its just ignoring the fact that its a quotient ring and it does every computation in MS. What am I doing wrong or is my understanding of quotient rings flawed? Thanks in advance. MS = MatrixSpace(ZZ,2,2) n=MS([[17,19],[11,31]]) R = MS.quotient_ring(MS*n*MS) #or R = MS.quotient_ring(n) M1 = R([[1,1],[1,1]]) print(M1) M2 = R(n+M1.lift()) print(M2)  this code gives this as a result [1 1] [1 1] [18 20] [12 32]  2019-05-04 17:41:57 +0200 asked a question Matrix quotient rings I'm trying to work with a quotingring of a matrix space. Now I use the following code. But since $n$ is my modulus I expect my second matrix to be equal to $M_1$ in this quotient ring. But it's like its just ignoring the fact that its a quotient ring and it does every computation in MS. What am I doing wrong or is my understanding of quotient rings flawed? Thanks in advance. MS = MatrixSpace(ZZ,2,2) n=MS([[17,19],[11,31]]) R = MS.quotient_ring(MS*n*MS) #or R = MS.quotient_ring(n) M1 = R([[1,1],[1,1]]) print(M1) M2 = R(n+M1.lift()) print(M2)  2018-11-30 02:14:27 +0200 received badge ● Popular Question (source) 2018-10-19 09:23:40 +0200 received badge ● Taxonomist 2018-03-21 15:36:04 +0200 received badge ● Popular Question (source) 2017-05-03 16:17:51 +0200 commented question converting linear map to matrix representation p=5 F.=GF(p^p,modulus=x^p-x-1) V=[c^i for i in [0..p-1]] s=c^6+c^3+c^2+1 Now I want to get the coeffecients of s represented to the base V[i], how do i do that 2017-05-02 23:13:58 +0200 asked a question converting linear map to matrix representation I have a linear map $\alpha$ from $F_{p^n} \longrightarrow F_{p^n}$, where we see $F_{p^n}$ as a vector space over $F_p$ with a $V_i$ as base elements. I want to create the matrix representation for $\alpha$. For that I have to calculate $\alpha(V_i)$ and then write it in the basis $V_i$ to get my values for the matrix. How exactly do I do the last in sage ? For eg. a polynomial ring it's easy because the elements are already written according to its base but in general thats not the case... 2017-04-29 19:39:32 +0200 asked a question field extension not implemented I'm trying to construct some field extenstions of GF(p), this is what I have p=5 F=GF(p) R1. = F['x'] F1. = F.extension(x^p - x - 1) R2. = F1['x'] F2. = F1.extension(x^p - x - alpha1^(p-1)) R3. = F2['x'] F3. = F2.extension(x^p - x - (alpha1*alpha2)^(p-1)) R4. = F3['x'] F4. = F3.extension(x^p - x - (alpha1*alpha2*alpha3)^(p-1))  It creates F3 like it should but it doesn't create F4. I get a NotImplementedError... What did I do wrong? 2017-04-29 15:43:27 +0200 received badge ● Supporter (source) 2017-04-29 15:42:59 +0200 commented answer Chain of fields in sage I have to construct a chain like that, with 5 different elements. When i use the extend function for the 4th time it gives "NotImplementedError"... 2017-04-28 21:46:46 +0200 asked a question Chain of fields in sage I would like to construct the field Fp(alpha,beta) where alpha is a root of x^p-x-1 (over Fp[x]) and beta is a root of the polynomial x^p-x-alpha^(p-1) (over Fp(alpha)[x]). I have tried the following  F0.=GF(p)['x'] f1=x^p-x-1 R1.=F0.quotient(f1)['alpha1'] F1.=Frac(R1) f2=x^p-x-alpha1^(p-1) R2.=F1.quotient(f2)['alpha2'] F2.=Frac(R2)  but I think it creates the field F1 well, but it goes wrong for R2... It also feels like there should be a much more straightforward way to do this in sage. What would be the proper way to do this ? 2014-12-05 16:47:14 +0200 received badge ● Student (source) 2014-12-05 16:14:56 +0200 asked a question AttributeError: must give both plot endpoints I use this piece of code in my project: print h print h(3.2) print parent(h) plot(h(x) , (-4,4), thickness=2, color='green' )  and this is my output: 2.14250281996159*x + 1.74284059736793 8.59884962124501 Univariate Polynomial Ring in x over Real Field with 53 bits of precision Traceback (most recent call last): File "", line 1, in File "_sage_input_231.py", line 10, in exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cHJpbnQgaApwcmludCBoKDMuMikKcHJpbnQgcGFyZW50KGgpCnBsb3QoaCh4KSAsICgtNCw0KSwgdGhpY2tuZXNzPTIsIGNvbG9yPSdncmVlbicgKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in File "/var/sage/tmp2yTHkg/___code___.py", line 6, in exec compile(u"plot(h(x) , (-_sage_const_4 ,_sage_const_4 ), thickness=_sage_const_2 , color='green' )" + '\n', '', 'single') File "", line 1, in File "/opt/sage/sage-6.3/local/lib/python2.7/site-packages/sage/misc/decorators.py", line 705, in wrapper return func(*args, **kwds) File "/opt/sage/sage-6.3/local/lib/python2.7/site-packages/sage/misc/decorators.py", line 550, in wrapper return func(*args, **options) File "/opt/sage/sage-6.3/local/lib/python2.7/site-packages/sage/plot/plot.py", line 1163, in plot G = funcs.plot(*args, **original_opts) File "polynomial_element.pyx", line 286, in sage.rings.polynomial.polynomial_element.Polynomial.plot (build/cythonized/sage/rings/polynomial/polynomial_element.c:5907) AttributeError: must give both plot endpoints  Why does this happen ? I have specified my endpoints right? so why is it saying I didn't ? I tried a lot to solve this but i can't get it solved.. anyone who can tell me whats wrong ? Thanks in advance 2014-11-15 12:08:49 +0200 received badge ● Editor (source) 2014-11-15 12:08:18 +0200 asked a question Solving an equation in multiple variables I have this equation : sqrt((b-a)^2 + (B-A)^2) == A+B and i would like to have it solved to b-a=+- 2 * sqrt(AB) in sage. Right now I have the following code but it doesn't really output what I want. I just get A^2 - 2AB + B^2 + a^2 - 2ab + b^2 == A^2 + 2AB + B^2 and I don't know how to make sage solve it further. my code: var('a,b,c,A,B,C') eq1 = (sqrt((b-a)^2 + (B-A)^2) == A+B) (eq1^2).expand() Thanks in advance