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2020-04-14 22:33:50 +0100 received badge  Supporter (source)
2020-04-14 00:24:52 +0100 commented answer How to find the longest word in a subgroup of the symmetric group using Sage?

@FrédéricC, thank you very much. I tried to use the following commands to find the longest word in $W_{J}$, $J=\{1,2\}$. But it doesn't give the answer $s_1 s_2 s_1$.

W = CoxeterGroup(['A',4])
w = W.long_element()
t = w.coset_representative([1,2])
t.reduced_word()
2020-04-12 22:25:40 +0100 asked a question How to find the longest word in a subgroup of the symmetric group using Sage?

Let $S_n$ be the symmetric group over $\{1,2,\ldots,n\}$. Let $J$ be a subset of $\{1,\ldots, n-1\}$ and let $W_J$ be the subgroup of $S_n$ generated by $s_j, j\in J \subset \{1, \ldots, n-1\}$, where $s_j$'s are simple reflections. How to find the longest word in $W_J$ in Sage? The following is some codes.

W = SymmetricGroup(8)
[s1,s2,s3,s4,s5,s6,s7] = W.simple_reflections()

Thank you very much.

2020-04-10 19:16:14 +0100 received badge  Scholar (source)
2020-04-10 17:01:06 +0100 received badge  Editor (source)
2020-04-10 16:59:43 +0100 asked a question How to convert an element in a Symmetric group to a one-line notation in Sage

Let $S_n$ be the symmetric group over ${1,2,\ldots,n}$. Let $w=s_{i_1} \cdots s_{i_m} \in S_n$, where $s_i$'s are simple reflections. How to convert $w$ to a one-line notation in Sage? The following are my codes.

W = WeylGroup("A7", prefix="s")
[s1,s2,s3,s4,s5,s6,s7] = W.simple_reflections()
w=s2*s4*s6

I want to convert $w$ to a one line nation. Thank you very much.

2018-08-13 12:17:12 +0100 received badge  Student (source)
2018-08-06 00:23:02 +0100 asked a question How to find the normal form of an elliptic curve using Sage?

Let $C$ be the following curve in $\mathbb{C}^2$. \begin{align} & 11664 {c_1}^3 {c_2}^2 + 536544 {c_1}^3 c_2 + 6170256 {c_1}^3 + 67068 {c_1}^2 {c_2}^2 + 1542564 {c_1}^2 c_2 \ & + 3085128 c_1 {c_2}^2 - 32393844 c_1 c_2 + 3085128 c_1 + 17739486 {c_2}^2 + 6941538 c_2 = 0. \end{align} I checked that this curve has genus $1$ using Sage. Therefore it is an elliptic curve. How to change coordinates such that the equation of this curve is of the form $y^2 = f(x)$, where $f$ is some polynomial. Thank you very much.

I tried to use the following codes in Sage.

R.<c1,c2> = QQ[]; Jacobian(11664c1^3c2^2 + 536544c1^3c2 + 6170256c1^3 + 67068c1^2c2^2 + 1542564c1^2c2 + 3085128c1c2^2 - 32393844c1c2 + 3085128c1 + 17739486c2^2 + 6941538c2)

But there is an error: NoEmbeddingError: not a sub-polytope of a reflexive polygon. How to find the normal form of the curve using Sage? Thank you very much.