2023-10-12 01:25:22 +0200 received badge ● Famous Question (source) 2023-04-06 08:36:29 +0200 received badge ● Notable Question (source) 2023-04-06 08:36:29 +0200 received badge ● Popular Question (source) 2022-03-17 03:49:25 +0200 received badge ● Popular Question (source) 2020-05-31 00:04:19 +0200 received badge ● Famous Question (source) 2019-12-04 17:30:09 +0200 received badge ● Notable Question (source) 2019-08-21 08:08:20 +0200 asked a question Change base Field of Vector Space Given a number field $L$, I can construct a vector space $V$ over the rational field as follows : V,fr,to = L.vector_space() Now, if I want to define the same vector space over a subfield of $L$, say $K$ rather than the rational field, is there any command. 2019-08-06 10:49:59 +0200 commented answer polynomials with bounded coefficients Thanks a lot, didn't know of this function. 2019-08-06 10:05:16 +0200 asked a question polynomials with bounded coefficients I have a list L, and would like to construct all polynomials of degree d, with coefficients from the list. An example is the following : SET=[]; K.=FiniteField(17); F. = PolynomialRing(K,'x'); for f in F.monics( of_degree=8): S=f.coefficients(sparse=False); if S==([K(1),K(16)]): SET=SET+[f]; print SET;  The above command is too time consuming. Is there a simpler way, when we can get the output in less time. 2019-07-22 15:47:25 +0200 received badge ● Popular Question (source) 2019-07-22 10:22:45 +0200 asked a question Base field of Residue field Let $K$ be a number field, $O_K$ be its ring of integers, $p$ prime ideal in $\mathbb{Z}$ and $\mathfrak{p}$ be a prime ideal above $p$. I am trying to construct the $\mathbb{Z}/p\mathbb{Z}$ vector space $O_K/\mathfrak{p}$, and a $\mathbb{Z}/p\mathbb{Z}$ subspace spanned by certain images of elements of $O_K$. For constructing the prime, I am able to use Q=K.primes_above(p)[0], but I do not know how to view the residue field F=K.residue_field(Q) as the vector space over $\mathbb{Z}/p\mathbb{Z}$. The command V,fr,to=F.vector_space() indicates $\textbf{ValueError: too many values to unpack}$. Here K= $\mathbb{Q}(\zeta_{11})$ and $p=3$. Can someone suggest me alternative commands for the same. 2018-08-13 19:08:46 +0200 received badge ● Scholar (source) 2018-07-18 08:59:32 +0200 asked a question Construct a system of linear equations I would like to construct a system of linear equations as follows and find a basis of the solutions : Fix $p$, $q$ $$a_{i, j} - 3a_{i-1,j} - 4a_{i,j-1} +10a_{i-1,j-1} = 0$$ for all $$0 \le i \le \frac{p-1}{2} - 1 ; 0 \le j \le q-2$$ with further conditions : $a_{-1,j} = -a_{\frac{p-1}{2}-1, j}, a_{i,-1} = a_{i,q-2}$ for all $i,j$ satisfying the above conditions Further more, is there a way that the same can be implemented for $a_{i,j,k}$ and so on. 2018-03-10 07:25:16 +0200 received badge ● Editor (source) 2018-03-10 07:24:19 +0200 asked a question Relative Vector spaces Consider a field L containing a subfield F. I would like to look at L as a F vector space without using the command relativise. Is there any way to obtain this. For example : Let L.=CyclotomicField(53*52), and F.=CyclotomicField(53). I would like to construct a $F$ linear isomorphism $\phi : L \mapsto F^{24}$. 2017-11-08 11:31:41 +0200 received badge ● Student (source) 2017-11-08 10:52:56 +0200 asked a question User defined Embedding I have 2 isomorphic number fields L.and M., and I would like to define an embedding from L to M sending a to b. Is this possible without using the command L.embeddings(M)?